T Balint

F Lamperti
email: f.lamperti@sssup.it

A Mandel

M Napoletano

A Roventini

A Sapio

Complexity and the Economics of Climate Change: a Survey and a Look Forward

Keywords: climate change, climate policy, climate economics, complex systems, agent-based models, socio-economic networks C63, Q40, Q50, Q54

We provide a survey of the micro and macro economics of climate change from a complexity science perspective and we discuss the challenges ahead for this line of research. We identify four areas of the literature where complex system models have already produced valuable insights: (i) coalition formation and climate negotiations, (ii) macroeconomic impacts of climate-related events, (iii) energy markets and (iv) diffusion of climate-friendly technologies. On each of these issues, accounting for heterogeneity, interactions and disequilibrium dynamics provides a complementary and novel perspective to the one of standard equilibrium models. Furthermore, it highlights the potential economic benefits of mitigation and adaptation policies and the risk of under-estimating systemic climate change-related risks.

Introduction

This paper provides a survey of the economics of climate change from a complexity science perspective and underlines the challenges ahead for this line of research.

Mitigation and adaptation to climate change represent governance challenges of an unprecedented scale because of their long-term horizon, their global nature and the massive uncertainties they involve.

Against this background, equilibrium models generally used in Integrated Assessment Models (IAM) represent the economy as a system with a unique equilibrium, climate policy as an additional constraint in the optimization problem of the social planner and consider the uncertainty of climate-related damages to be predictable enough to be factored out in the expected utility of a representative agent. There is growing concern in the literature that this picture might convey a false impression of control (see [START_REF] Pindyck | Climate Change Policy: What Do the Models Tell Us?[END_REF][START_REF] Stern | The structure of economic modeling of the potential impacts of climate change: Grafting gross underestimation of risk onto already narrow science models[END_REF][START_REF] Stern | Current climate models are grossly misleading[END_REF][START_REF] Weitzman | Tail-hedge discounting and the social cost of carbon[END_REF][START_REF] Revesz | Global warming: Improve economic models of climate change[END_REF]Farmer et al., 2015, among many contributions) and that IAMs might underestimate both the cost of climate change and the benefits resulting from the transition to a low carbon-emission economy [START_REF] Stern | Current climate models are grossly misleading[END_REF].

Network and agent-based models have been increasingly advocated as alternatives fit to handle out-of-equilibrium dynamics, tipping points and large transitions in socio-economic systems (see e.g [START_REF] Tesfatsion | Handbook of computational economics: agent-based computational economics[END_REF][START_REF] Balbi | Agent-based modelling of socio-ecosystems: A methodology for the analysis of adaptation to climate change[END_REF][START_REF] Kelly | Selecting among five common modelling approaches for integrated environmental assessment and management[END_REF][START_REF] Smajgl | Empirical characterisation of agent behaviours in socio-ecological systems[END_REF][START_REF] Farmer | A third wave in the economics of climate change[END_REF][START_REF] Stern | Current climate models are grossly misleading[END_REF][START_REF] Mercure | Modelling complex systems of heterogeneous agents to better design sustainability transitions policy[END_REF]. These classes of models consider the real world as a complex evolving system, wherein the interaction of many heterogeneous agents possibly reacting across different spatial and temporal scales give rise to the emergence of aggregate properties that cannot be deduced by the simple aggregation of individual ones [START_REF] Flake | The Computational Beauty of Nature[END_REF][START_REF] Tesfatsion | Handbook of computational economics: agent-based computational economics[END_REF]. The development of agent-based integrated assessment model can overcome the shortfall of equilibrium models and ease stakeholder participation and scenario exploration [START_REF] Moss | Agent-based integrated assessment modelling: the example of climate change[END_REF]Moss, 2002a). Indeed, the higher degree of realism of ABMs [START_REF] Farmer | The economy needs agent-based modeling[END_REF][START_REF] Farmer | A third wave in the economics of climate change[END_REF] allows to involve policy makers in the process of the development of the model employed for policy evaluation [START_REF] Moss | Policy analysis from first principles[END_REF].

In this paper we present a critical review of the existing literature about complex system approaches to the economics of climate change, focusing in particular on agent-based models. Even if this research line is still in its infancy, it has already produced valuable insights into the functioning of economies facing climate and environment issues. We identify the main results, policy implications, limitations, and open issues that future research efforts should address. Moreover, we consider how the discussed contributions might serve as building blocks for a new generation of models.

We distinguish four main fields relevant to the economics of climate change in which complex system models have been fruitfully applied. 1 The first consists in the analysis of climate negotiations and coalition formation (cf. Section 2). There, we show that out-of-equilibrium dynamics, learning and influence among and within heterogeneous actors are pivotal to get a full understanding of the barriers and the potential paths to cooperation that are key concerns for international climate-policy negotiations like the recent Paris agreement.

Second, we concentrate on agent-based models studying the macroeconomics of climate change (see Section 3). These models study in particular how the interactions between heterogeneous agents affect the aggregate performance of an economy facing increasing climate risks. They have shed new light on the different role that micro-level climate and weather shocks have on macroeconomic dynamics, on the risk stemming from climate policy and the profound interconnectivity affecting the overall system.

The next milestone in this field is the development of the first generation of agent-based integrated assessment models.

Third, we consider the functioning of the energy sector, which is by far the largest emitter of greenhouse gases globally (see Section 4). In this field, deregulation (especially in electricity market) has pushed modelers to shift their attention from monopoly and oligopoly settings to complex structures characterized by heterogenous players interacting in energy markets with different institutional settings.

ABMs have been employed to study pricing rules, market power in complex institutional settings, the evolution of financial networks and networks of influence in the energy industry. Finally, agent-based models have also been employed to analyze the comparative effects of climate policies on electricity prices, the energy technology mix and energy efficiency.

Fourth, agent-based models have been largely employed to study the process of technical change and innovation diffusion, which lie at the core of the structural change needed for the transition to a low-carbon economy (cf. Section 5). Herein, an adequate characterization of the Knightian uncertainty [START_REF] Knight | Risk, Uncertainty, and Profits[END_REF] affecting search for innovations, a correct accounting of path dependencies in technological development and a strong emphasis on the role that interaction structures and institutions play on the selection landscape are essential to correctly analyze conditions that might favor (or impede) shifts from one technological paradigm to an alternative one (see [START_REF] Dosi | Chapter 3 -technical change and industrial dynamics as evolutionary processes[END_REF], for a comprehensive discussion on innovation and technical change from an evolutionary perspective).

Finally, we provide a general critical assessment of the adoption of agent-based and network models to study the micro and macro economics of climate change (see Section 6). In particular, we will stress the current weaknesses and the potential research directions to further improve such models in order to address the complex interconnections between economic dynamics and climate change.

Coalitions formation and climate negotiations

Effectiveness and stability of international climate agreements are pivotal to the fulfilment of the long run objectives of decoupling output and emissions growth and, ultimately, containing rise in global mean surface temperature. Figure 1a shows that global emissions are quite fragmented overall but, on the other side, few large players account for more than half of the total value. This fact highlights the importance of international cooperation, where agreements between major players is required to get substantial effects in the short run. In line with the seminal contribution of [START_REF] Barrett | Self-enforcing international environmental agreements[END_REF], the main outcome of the game-theoretic literature on the formation of international environmental agreements has been that it is extremely difficult to sustain global cooperation among a large number of strategic actors solely on the grounds of environmental benefits. This negative result is somehow at odds with the mild successes obtained on climate change mitigation through the Kyoto protocol and, more recently, the Paris agreement. A commonly accepted explanation for the presence of this gap in the theory is that a static one-shot game model with a large number of homogeneous players can possibly serve as a benchmark but does not account for the full complexity and the specific context of international agreements such as those pursued in climate negotiations. Therefore, the literature has developed in two complementary directions that tried to account respectively for (i) the multi-dimensional and heterogeneous aspects of actors' strategies and (ii) the dynamic, "local" and/or hierarchical nature of the interactions between agents.

Within the equilibrium-centered game-theoretic literature, these developments have led to positive results about the stability of grand coalitions when effects due to networks (see e.g [START_REF] Benchekroun | Tax differentials and the segmentation of networks of cooperation in oligopoly[END_REF]Claude, 2007), heterogeneity (e.g McGinty, 2006) or more simply transfers (see e.g [START_REF] Hoel | Incentives to participate in an international environmental agreement[END_REF] are accounted for. A wide literature that linked pay-offs in the "emissions game" to the outcome of integrated assessment models (IAMs) also developed. In particular, [START_REF] Lessmann | The stability and effectiveness of climate coalitions[END_REF] compare stability results for climate agreements from five different IAMs and find that, across all models, heterogeneity of regions improves incentives to participate.

The equilibrium-centered literature focused only on the stability issue relying on very strong assumptions about the rationality and the stationarity of preferences of state actors. As a consequence, it remained silent about the barriers and the potential paths to cooperation that are key concerns for policy applications. In order to get a full understanding on them, one needs models accounting for out-of-equilibrium dynamics, learning and influence among and within state actors.

Learning and cooperation

A first step in that direction has consisted in investigating behavioral and institutional aspects of learning and cooperation in game-theoretic settings. [START_REF] Breton | A dynamic model for international environmental agreements[END_REF] considers a set of countries that can be either signatory or non-signatory of an emission reduction agreement. Non-signatory countries maximize their individual welfare, while signatory countries maximize their joint welfare and punish non-signatories (e.g through trade sanctions). The proportion of signatory countries is then assumed to follow a replicator dynamics. Numerical solutions show the emergence of multiple equilibria corresponding to no-cooperation and either partial or full cooperation. Phase transition mechanisms underline the existence of thresholds in terms of the stock of emission and/or number of signatories above which the system eventually reaches full cooperation. [START_REF] Smead | A bargaining game analysis of international climate negotiations[END_REF] represent negotiations as an N-player bargaining game where countries/players bargain about their percentage emission reduction.

The agents are adaptive and update their pledges on the basis of expectations formed using a variant of fictitious play. Cooperation and disagreement are both equilibria of the underlying game as well as attractors of the ensuing dynamics. The authors argue that a potential obstacle to successful negotiations not related to the stability of feasible solutions is "whether learners can find these solutions and avoid disagreement equilibria". They also point out that the larger the number of players, the less likely cooperation emerges. Interestingly, however, they show that prior/sequential agreements between subsets of countries increase the chance of reaching a global solution.

Both contributions put emphasis on the progressive formation of climate clubs as pathways for efficient mitigation policy (see e.g. [START_REF] Nordhaus | Climate clubs: Overcoming free-riding in international climate policy[END_REF][START_REF] Heitzig | Self-enforcing strategies to deter free-riding in the climate change mitigation game and other repeated public good games[END_REF]. Yet, the focus on states as the only relevant actors as well as the uni-dimensionality of the perspective limit the new insights that can emerge from such models. They are also silent about the formation and the evolution of preferences and contrast with the emphasis put by [START_REF] Putnam | Diplomacy and domestic politics: the logic of two-level games[END_REF] on the linkages between national and international politics. Moreover, in the context of climate policy, they are at odds with [START_REF] Jaeger | Three views of two degrees[END_REF], who argues that the consensus on the objective of limiting global warming to 2 degrees resulted from a combination of physical, environmental, economic, diplomatic or ethical arguments, which let the 2 degrees target emerge as a focal point on the basis of which actors can anticipate and make decisions. As emphasized by [START_REF] Janssen | Governing social-ecological systems[END_REF] and [START_REF] Lempert | Methods for long-term environmental policy challenges[END_REF], agent-based models are particularly well-fitted for such multilevel, multi-agents decision-making problems.

The role of interactions

From a macro-level perspective, [START_REF] Courtois | Games of influence in climate change negotiations: Modelling interactions[END_REF] subsume the standard game-theoretic approach to international environmental agreements by considering that agents and countries employ the outcome of a game-theoretic analysis as an expert's recommendation, but actually determine their policy in a sequence of bargaining interactions with their peers. During such interactions, agents can either imitate, persuade or dissuade each others to cooperate to climate change mitigation. Depending on the propensity of countries to imitate and on their bargaining power, different stable configurations emerge in the model corresponding to different levels of international collaboration. Such results extend the one of the standard game-theoretic literature, by shedding light on the behavioral determinants of failure and success in negotiations.

A second series of contributions has focused on the bottom-up formation of climate policies through the interactions of micro-level agents. In the battle of perspectives of Janssen and de Vries (1998), three types of agents (Individualists, Hierarchists and Egalitarian) coexist. They differ in their "world-view", which captures their beliefs about climate sensitivity, the cost of mitigation and its climate-related impacts. They also have different preferences about macro-economic and climate policy objectives.

The economy is actually governed according to a weighted average of the preferences of the population.

As the system evolves through time, world-views might turn out to be more or less accurate, and their share in the population evolves according to their fitness. The authors emphasize that these adaptive dynamics can yield trajectories that differ massively from those induced by "utopia" (in which there is a unique well-defined social preference and correct expectations) and therefore one needs to account for bias and errors in the definition of long-term emission scenarios. [START_REF] Isley | The effect of near-term policy choices on long-term greenhouse gas transformation pathways[END_REF] consider firms that lobby a government for more or less stringent climate policies (e.g carbon price or carbon tax). Beneath the strategically determined climate policy, the economic pathway is defined following the agent-based dynamics introduced in Dosi et al. (2010). In this framework, the authors investigate the efficiency of different institutional architectures for climate policy.

They emphasize that a necessary condition for an effective policy is the emergence of a stable constituency in favor of a stringent climate policy which, in turn, requires a steady stream of technological innovation to maintain firm heterogeneity. This series of linkages highlights the importance of accounting for the interdependencies between, inter alia, the economic, industrial and political spheres and how this is made possible by agent-based modeling.

Relatedly, [START_REF] Earnest | Coordination in large numbers: An agent-based model of international negotiations[END_REF] and [START_REF] Greeven | Society's response to climate change-A scenario discovery study using agent-based modelling[END_REF] aim to provide a comprehensive perspective on the political issues linked to international negotiations by implementing an agent-based version of [START_REF] Putnam | Diplomacy and domestic politics: the logic of two-level games[END_REF] two-level games, with negotiators and their constituencies as agents. [START_REF] Earnest | Coordination in large numbers: An agent-based model of international negotiations[END_REF] considers negotiators who ought to coordinate on an international (environmental) agreement that is acceptable by their constituencies. Both negotiators and their constituencies have evolving preferences. Negotiators are sensitive to the preferences of other negotiators and of their own constituencies. Constituencies also influence each other transnationally. Such a model seems to better account for the complexity of climate negotiations and allows to study path histories that are important to multiple equilibria games. The main findings of the model are that factors favoring coordination are (i) a large number of negotiating parties, (ii) dense transnational influence, (iii) fast-evolving preferences, (iv) sensitivity to constituencies preferences, and (v) relative independence from other negotiators' preferences. Similarly, [START_REF] Greeven | Society's response to climate change-A scenario discovery study using agent-based modelling[END_REF] uses the two-level game framework of Putnam, but further adds to the model uncertainties about the probability of climate-related impacts and the awareness of the public about such risks. The model is then used to identify consistent and plausible narratives on the pathways leading to the emergence of climate change mitigation. In that, it highlights the potential usage of agent-based modeling for scenario discovery (see also [START_REF] Rozenberg | Building ssps for climate policy analysis: a scenario elicitation methodology to map the space of possible future challenges to mitigation and adaptation[END_REF][START_REF] Gerst | Agentbased modeling of climate policy: An introduction to the {ENGAGE} multi-level model framework[END_REF].

Open issues

Being grounded on heterogenous, interacting actors, agent-based models offers a methodology both to gain insights about the workings of the international negotiation process and to build scenarios about potential long-term trajectories. [START_REF] Downing | Understanding climate policy using participatory agent-based social simulation[END_REF] also emphasize the potential of agent-based model for stakeholder engagement in the design of climate policies and puts forward as a prototype of such an approach an agent-based model of water management in the Thames region of England (see also [START_REF] Tesfatsion | Waccshed: A platform for the study of watersheds as dynamic coupled natural and human systems waccshed: A platform for the study of watersheds as dynamic coupled natural and human systems[END_REF]. However, to be extended at a broader scale, this approach requires to integrate climate negotiation models with ABMs representing the evolution of the economy over the long term. In that, the macro agent-based models presented in the next Section could constitute a useful starting point to link climate negotiations and macroeconomic dynamics.

Climate-change macroeconomics

Studying the co-evolution between climate change and macroeconomic dynamics poses non trivial challenges. First the lack of long macroeconomic time series makes difficult to empirically explore the inter-dependences between the two systems.2 Second, climate and macroeconomic dynamics occur at different time scales. Third, the poor understanding of human responses to warmer climates and extreme weather events renders difficult the characterization of climate damages.

Given the foregoing issues, one of the main advantage of macro ABM is to allow for a micro-level representation of the interactions between climate change and economic dynamics (as emphasized in particular by Moss, 2002aand, more recently, Farmer et al., 2015). Indeed, the agent-based approach can better account for the out-of-equilibrium dynamics shifting the economy from a business-as-usual to a green growth path. Moreover, network and agent-based models can provide a more accurate representation of climate-related damages considering distributional issues and the role of system connectivity.

Relatedly, complexity-based models can be employed to study how climate change risks impact on financial market dynamics. Finally, the fast pace at which ABMs have blossoming in the last years has lead to the development of a new generation of agent-based integrated-assessment models [START_REF] Lamperti | Faraway, so close: an agent-based model for climate, energy and macroeconomic policy[END_REF].

Macro-climate ABMs

With respect to the analysis of the energy transition, a pioneering contribution is this of [START_REF] Robalino | Carrots and sticks for new technology: Abating greenhouse gas emissions in a heterogeneous and uncertain world[END_REF] (see also [START_REF] Brouwers | Agent models of catastrophic events[END_REF], which use a simple ABM to test the effectiveness of "carrots" (incentives to technology adoption) vis-à-vis that of "sticks" (carbon taxes and emissions trading, which increase the price of high-emitting technologies for all users) in pushing the economy towards a low-carbon development path. They show that coupling carbon taxes and technology incentives is the best approach to cut greenhouse gas emissions. Their result is mainly driven by the heterogeneity of consumers' preferences and expectations.3 Notwithstanding these interesting insights, the model is too simple to account for multiple equilibria and endogenous growth. This limitation might be particularly relevant in the design of climate policy. As suggested by [START_REF] Jaeger | Reframing the problem of climate change: from zero sum game to win-win solutions[END_REF], policy makers should reframe the problem of climate change from a zero-sum game to win-win solutions, i.e. designing mitigation measures that are beneficial for the economy. In a framework where several equilibria are possible, the mitigation problem is not linked to scarcity but rather to a coordination issue [START_REF] Jaeger | Scarcity and coordination in the global commons[END_REF].

One of the first attempts to dynamically model a complex economy together with a climate module can be traced back to the LAGOM model family [START_REF] Haas | Agents, bayes, and climatic risks-a modular modelling approach[END_REF]. Heterogeneous households and producers face the risk of climate-related damages and are offered insurance contracts. An "expectation manager" helps insurers and households to up-date their expectations on the basis of new observations. Finally, the model is characterized by the presence of a market module where interactions Drawing on the Keynes+Schumpeter model (K+S, cf. Dosi et al., 2010), they study a complex economy composed of two vertically related industrial sectors and an energy production module, where competing technologies can be used to generate energy that is subsequently distributed through the system. The model is calibrated on US macroeconomic data and simulated until the end of the century to study different carbon tax recycling schemes. They find that only a policy focused on subsidies to carbon-free technology oriented R&D allows a swift transition away from "dirty" energy technologies, and, in turns, to higher economic growth. Similar results are found in the ABM developed by [START_REF] Rengs | Testing innovation, employment and distributional impacts of climate policy packages in a macro-evolutionary systems setting[END_REF].

The major issues addressed in the contributions described so far is the identification of possible growth trajectories for both the economy and aggregate emissions, and in the adoption of fiscal policy (mainly carbon-taxes and subsidies) to direct the system towards some of these directions. The value added consists in the analysis of growth as a stable phenomenon emerging from an ecology of heterogeneous agents, whose different reactions to policies and uncertain environments can move the economy along trajectories that cannot be deduced otherwise. However, a key element is missing the picture. Indeed, the relationship between macroeconomic properties and the climate is explored in a single direction. The feedbacks that agents (firms, energy-production plants, households, etc.) receive from a increasing and possibly more volatile temperatures have been generally ignored. Building on the baseline setting provided by Dosi et al. (2010), [START_REF] Isley | An evolutionary model of industry transformation and the political sustainability of emission control policies[END_REF] construct a prototype for a hybrid agent-based integrated assessment model that could support the design of a government's regulatory climate policies. The authors underline the usefulness of the approach in analyzing transformative solutions, that is, in examining how measures intended to reduce GHG emissions can trigger marketinduced transformations, which, in turn, affect the government's ability to maintain its policy in an environment where agents affect the climate and receive back climate-related damages. However, in the latter framework, the climate system is left out of the picture and damages are linked to emissions, not to the average surface temperature. Moreover, environmental damages are modeled like in standard IAM (see e.g. [START_REF] Nordhaus | An optimal transition path for controlling greenhouse gases[END_REF][START_REF] Nordhaus | A question of balance: economic modeling of global warming[END_REF][START_REF] Tol | On the optimal control of carbon dioxide emissions: an application of fund[END_REF] as aggregate cuts to potential GDP levels.

Climate shocks, damages and system connectivity

In most Integrated Assessment Models, climate damages are accounted for by an ad hoc damage function that impacts output (at the sectoral or the macro level) as a function of temperature increases brought about by GHG emissions (see the discussion in [START_REF] Pindyck | Climate Change Policy: What Do the Models Tell Us?[END_REF]. This approach ignores the propagation of shocks and the feedbacks that might relate damages to different sectors. Moreover, as most IAMs do not allow for agent heterogeneity, they entirely overlook distributional issues linked to climate damages.

Against this background, one of the characterizing features of complex systems lies in their representation of real phenomena as emerging from the interactions of heterogeneous agents. This approach alllows to model the emergence of aggregate damages from micro shocks in production, procurement or finance percolating along network structures where households, firms, banks and the government interact. For example, [START_REF] Hallegatte | An adaptive regional input-output model and its application to the assessment of the economic cost of katrina[END_REF] provides a model of shock propagation within Louisiana after the impact of hurricane Katrina. In the model, firms adapt their behavior in an input-output network. The model has also been employed to to assess the risks of coastal floods in a climate change framework and extended to examine the role of inventories in production dynamics and supply shortages [START_REF] Hallegatte | Assessing climate change impacts, sea level rise and storm surge risk in port cities: a case study on copenhagen[END_REF][START_REF] Hallegatte | Modeling the role of inventories and heterogeneity in the assessment of the economic costs of natural disasters[END_REF]. Simulation results show that propagation mechanisms are essential for the assessment of the consequences of disasters, and that taking into account residual production capacities is necessary not to overestimate the positive economic effects of reconstruction.

A straightforward consequence is the central role played by the topology of the production network, (taking also into account transportation). Acclimate is particularly well suited to study the propagation of shocks and it has been extended to better explore the differences between top-down cascades promoted by forwards linkages and demand-induced backward dynamics [START_REF] Wenz | Acclimate-a model for economic damage propagation. part ii: a dynamic formulation of the backward effects of disaster-induced production failures in the global supply network[END_REF]. However, as it runs at very short-time scales (from days to some week), price adjustment mechanisms are nearly absent at the current stage and technical change is overlooked.

Integrated assessment agent-based models

Despite the methodological advantages that agent-based models offer to the representation of production networks, the study of system's resilience and its reaction to different kind of shocks, there have

Finance and climate risks

The financing of the transition towards a low-carbon economy has still not been accurately explored in the economic literature. Indeed, as discussed above, the vast majority of modeling efforts focuses on government's fiscal policy. Recently, the role that financial and banking systems might play in inducing "green" investments and "green" entrepreneurship has received increasing attention [START_REF] Mazzucato | The (green?) entrepreneurial state[END_REF][START_REF] Campiglio | Beyond carbon pricing: The role of banking and monetary policy in financing the transition to a low-carbon economy[END_REF]. Different types of green fiscal (carbon tax, tax relief and breaks on investment in renewable energy) and targeted monetary policies (green bonds and quantitative easing) are simulated in the Eirin model [START_REF] Monasterolo | A hybrid system dynamics -agent based model to assess the role of green fiscal and monetary policies[END_REF], which combines system dynamics and agent-based features. The authors find that green policy measures allow to improve economic performance without creating pressures on the financial system vis-à-vis a business-as-usual scenario. In such a context, the relation between fast de-carbonization policies and financial stability is emerging as a prominent concern on the climate policy agenda. On one side the financial system can foster the transition to a green development path. On the other side, it is increasingly exposed to climate risks.

Within this setting, the structure of the relationships among financial institutions might be crucial for the stability of the whole system. Focusing on this issue from a network perspective, [START_REF] Battiston | A climate stress-test of the eu financial system[END_REF] analyze the exposure of different classes of actors in the system using a well known macronetwork stress testing model (Battiston et al., 2012;[START_REF] Bardoscia | Debtrank: A microscopic foundation for shock propagation[END_REF]. They find that the direct exposure to fossil fuel and energy-intensive sectors, while limited overall, is relevant for investment funds, which in turns are highly connected with the banking system. Further, the housing sector can potentially trigger shocks which can be amplified by the financial system. Given the empirically welldocumented degree of interdependences between actors in the financial, production and energy sides of the economy [START_REF] Buldyrev | Catastrophic cascade of failures in interdependent networks[END_REF][START_REF] Beale | Individual versus systemic risk and the regulator's dilemma[END_REF]Battiston et al., 2012;[START_REF] Homer-Dixon | Synchronous failure: the emerging causal architecture of global crisis[END_REF], the role of such relationships with respect to climate policy and their response to a changing climate, is likely to be a challenge for future macro-oriented agent-based and network models.

Open issues

Our understanding of the aggregate effects produced by climate change on the economic system is still limited. Complexity theory pushes forward the idea that single components are linked, interacting and heterogeneous. As a by-product, aggregate effects emerge from the evolution of micro behaviours.

From a macroeconomic perspective, there are three main issues that the future developments of agent-based and network models should account for. The first concerns inequality and the distributional effects of climate change. While standard models (e.g. DSGE rooted on the representative agent paradigm) require ad-hoc assumptions to deal with heterogeneity and typically confine it to a single side of the economy [START_REF] Bosetti | Taxing Carbon under Market Incompleteness[END_REF][START_REF] Dennig | Inequality, climate impacts on the future poor, and carbon prices[END_REF], agent-based models provide a "natural" framework to answer questions like what are the income classes that will be more adversely affected by climate change? Does inequality affect system resilience to climate change?. However, to provide adequate answer, models rooted in complexity theory need to better account for social welfare and policy evaluation.

The second issue concerns the relationships between financial and interbank markets and the transition to a low carbon economy. While transitions are usually modeled from the real side, i.e. as self-financing structural process driven by technical change (see also section 5), better understanding the role of finance and its interrelations with innovation is the challenge ahead.

The third issue we is intimately linked to both the second and the first. While most general equilibrium models find a smooth, optimal growth path for our economy, agent-based ones endogenously generate crises, fluctuations and growth instability. Relevant questions for future research concern the investigation of what kind of climate and weather events mostly affect system's stability and how financial markets might deal with associated climate and climate-policy risks.

Energy markets

As the the energy sector is the main producer of CO 2 emissions (cf. Figure 1), it has a pivotal role in the transition to a low-carbon economy.

Prior to deregulation, the dispatch program was solved through optimization methods by regulated 13 Documents de travail du Centre d'Economie de la Sorbonne -2016.58 or State-owned vertically integrated utilities, whose goal was to minimize the system-wide cost of electricity generation and transmission. The adequacy of optimization models in depicting how electricity markets work has declined after the deregulation of energy markets, a process that has unfolded in many countries in the last 20 years (see e.g. Borenstein et al., 2000 or Jamasb and[START_REF] Jamasb | Electricity market reform in the european union: review of progress toward liberalization & integration[END_REF]. With the intended consequence of lower electricity prices for end users, competition has been introduced in a market characterized by technological entry barriers. Oligopoly models assuming optimizing producers have been crafted to analyse the new scenario (see [START_REF] Ventosa | Electricity market modeling trends[END_REF]), yet they often neglect the complexity of setting bids and offers for power on a physical network subject to load balancing constraints and spatial externalities. Cognitive biases of market participants cannot be neglected, either (see [START_REF] Rothkopf | Daily repetition: A neglected factor in the analysis of electricity auctions[END_REF][START_REF] Denton | Spot market mechanism design and competitivity issues in electric power[END_REF][START_REF] Rassenti | Discriminatory price auctions in electricity markets: low volatility at the expense of high price levels[END_REF].

Electricity markets are thus perfect candidates for the application of computational methods, see e.g. [START_REF] Tesfatsion | Agent-based computational economics: modeling economies as complex adaptive systems[END_REF], [START_REF] Sun | Dynamic testing of wholesale power market designs: An open-source agent-based framework[END_REF], or overviews in [START_REF] Weidlich | A critical survey of agent-based wholesale electricity market models[END_REF] and [START_REF] Guerci | Agent-based modeling and simulation of competitive wholesale electricity markets[END_REF]. ABMs have entered the policy-making process as decision-support tools (e.g., [START_REF] Nicolaisen | Market power and efficiency in a computational electricity market with discriminatory double-auction pricing[END_REF][START_REF] Guerci | Modeling and implementation of an artificial electricity market using agent-based technology[END_REF][START_REF] Li | Development of open source software for power market research: the AMES test bed[END_REF]. Through ABMs, scholars have explored issues such as pricing rules and market power exercise [START_REF] Bower | Experimental analysis of the efficiency of uniform-price versus discriminatory auctions in the england and wales electricity market[END_REF][START_REF] Bunn | Evaluating individual market power in electricity markets via agent-based simulation[END_REF][START_REF] Bunn | Unilateral and collusive market power in the electricity pool of england and wales[END_REF][START_REF] Guerci | Learning agents in an artificial power exchange: Tacit collusion, market power and efficiency of two double-auction mechanisms[END_REF][START_REF] Kowalska-Pyzalska | Turning green: Agent-based modeling of the adoption of dynamic electricity tariffs[END_REF] and, closer to our interests, the comparative effects of climate policies on the diffusion of renewables and on energy efficiency, that in turn affect electricity prices. Few works have compared the explanatory power of optimizing models and ABMs with respect to electricity market dynamics, concluding in favor of ABMs (see [START_REF] Saguan | Market power in power markets: Game theory vs. agent-based approach[END_REF]Guerci and[START_REF] Guerci | Comparison and empirical validation of optimizing and agent-based models of the italian electricity market[END_REF]).8

Support to renewables and its effects

The influence of climate policy on electricity markets can work through several channels. Climate policy can stimulate the diffusion of energy efficiency and renewable energy technologies, which in turn impact upon the properties of electricity price series by changing the shape and dynamics of electricity demand and supply. The pattern of effects closely depends on the policy mix that has been implemented.

The integration in the existing transmission and distribution networks of a large number of microgenerators, characterized by unpredictable generation profiles, represents an important challenge for transmission system operators (Bruckner et al., 2005, Anaya and[START_REF] Anaya | Integrating distributed generation: Regulation and trends in three leading countries[END_REF] in the special issue edited by [START_REF] Boffa | Introduction to the special issue "The regional integration of energy markets[END_REF], given that the existing grids were conceived under the so-called centralized generation paradigm [START_REF] Kunneke | Institutional reform and technological practice: the case of electricity[END_REF]. In a recent attempt to study a 100% renewable scenario in the Australian market, [START_REF] Elliston | Simulations of scenarios with 100australian national electricity market[END_REF] try to match the actual hourly electricity demand of five selected states and one territory of Australia. The 100% renewable supply scenario is shown to be technically feasible, but the challenge is to cover winter evenings in the days when the sun-powered supply is low, i.e. overcast days, and wind speed is too low. Biomass fueled gas turbines coupled with the efforts to increase the winter peak demand are necessary to solve this issue. The need to rely on gas fueled micro-generation is consistent with the results in [START_REF] Faber | Exploring domestic micro-cogeneration in the netherlands: An agent-based demand model for technology diffusion[END_REF], whose ABM indicates that gas prices, as primary fuel of this technology, are a critical component in the success of the decentralized paradigm.

Is the cost of large renewable penetration rates worth it? In the short run, lower electricity prices ensue because fossil fuel sources, characterized by relatively high marginal costs, are displaced (the socalled merit order effect). de Miera et al. ( 2008) simulated the power market solution based on Spanish data, to find that the merit order effect was stronger than the cost of renewable energy support arising from feed-in-tariffs. In Banal-Estanol and Ruperez Micola (2011), the merit order effect is not enough to lead to competitive pricing. This is the outcome of a simulation model in which two symmetric high-cost plants compete with a low-cost wind power plant. Intermittency in wind power generation gives rise to uncertainty on the market-clearing solution, which is hedged by generating companies by means of positive price-cost margins. In the above cited works, power plant capacities were given. [START_REF] Browne | How does market power affect the impact of large scale wind investment in 'energy only' electricity markets?[END_REF] explore the merit order effect in a model wherein capacity investments are instead endogenized. In such a long-term scenario, simulations show that the merit order effect is counteracted by market power exercise, which is also causing an inefficient electricity dispatch.

One reason behind the persistence of market power in the long-run concerns the network configurations arising in an increasingly decarbonized electricity industry. Along these lines, [START_REF] Guerci | High wind Penetration in an Agent-Based Model of the Electricity Market. The Case of Italy[END_REF] investigate the impact of increasing wind power capacity on the Italian wholesale electricity prices and on power grid configurations. The simulation outputs show that electricity prices decrease in response to increasing wind power generation, but remain above marginal costs due to the increasing frequency of grid congestion, calling for investments in transmission infrastructures. The simulations in L'Abbate et al. ( 2014) aimed to assess the prospective effects of interconnections between Northern Africa and Italy, which could exploit the immensely rich potential of the Sahara desert for solar thermal power production, as envisaged by the Mediterranean Solar Plan (see also [START_REF] Sapio | The diffusion of renewable energy technologies in the mediterranean basin[END_REF] and the book by [START_REF] Cambini | Regional energy initiatives in the mediterranean basin[END_REF] on this issue). The authors found that Italy would become a net importer of renewables from Africa, leading to electricity price reduction. The endogenous adaptation of grid infrastructures, though, is missing from both models.

Taking steps forward from the above literature, [START_REF] Mureddu | Green power grids: How energy from renewable sources affects networks and markets[END_REF] develop an hybrid agent based and network model, which uses grid topology as an input and simulates the behaviour of heterogeneous plants. The model allows to forecast the energy price and to disentangle the contribution of each primary energy source to the downward and upward electricity balancing markets. As a significant result, the authors show that market shares in the balancing market do not depend only on energy costs but stem from the a blend of dynamic response, energy costs, geographical position (which constitute the network element of the model) and interactions among the different energy sources.

Energy efficiency

A simulation study of the impact of climate policies on households energy use is performed via a domestic stock agent-based model by [START_REF] Lee | An analysis of {UK} policies for domestic energy reduction using an agent based tool[END_REF], focusing on the UK. They investigate multiple scenarios (e.g. taxes, subsidies, and decarbonisation) for the evaluation of domestic energy efficiency policies. Simulation results show that the current goals (80% reduction of energy consumption by 2050)

will not be completely achieved. In the most favourable scenario, a 60% reduction may be achieved from 2008 to 2050. The study briefly analyses another policy, namely the introduction of a carbon tax, that has a significant impact in the energy demand reduction in a long-term horizon, but with many political obstacles such as the risk of fuel poverty (i.e. households spend more than 10% of their income for heating and hot water) and the increase of electricity prices. The ABM in Jackson (2010) rather highlights the benefits of coordinating energy efficiency and smart grid policies, by showing through simulations that peak hour electricity demand can be reduced by one third when energy efficiency and smart grids policies are considered together.

Carbon trading and green certificates

Most literature on climate policy frames the discussion on how to achieve the emission reduction targets through market-based tools, such as carbon trading. For recent overview of the current carbon trading schemes, the reader is referred to [START_REF] Perdan | Carbon trading: Current schemes and future developments[END_REF] and [START_REF] Sorrell | Carbon trading in the policy mix[END_REF].9

In [START_REF] Wang | Cap and trade modeling in electricity markets using an agent-based approach[END_REF], energy generating companies are modeled as adaptive agents that are bidding in an electricity market with cap-and-trade emission systems in place. Q-learning is used to model the process of strategy updating by agents trading on different time horizons (year, week, dynamic). The results show that generating companies can receive higher profits through higher frequency of trading, raising questions on the adequate market micro-structure for emission trading with respect to the ultimate policy objective. Such an intuition is further strengthened by [START_REF] Zhang | An adaptive agent-based modeling approach for analyzing the influence of transaction costs on emissions trading markets[END_REF], where an ABM is used to model the Chinese market for emissions, highlighting that transaction costs can decrease total emission trading amount and market efficiency remarkably.

Recently, the ABM developed by [START_REF] Zhang | Emissions trading and technology adoption: An adaptive agent-based analysis of thermal power plants in China[END_REF] shows that an emissions trading system influences obsolete power generating technologies with lower abatement levels, but does not promote the adoption of the most advanced technology. Furthermore, national emissions trading encourages power plants to adopt technologies with relatively higher removal rates compared with separate regional emissions trading systems, but a national program also decreases the adoption of the most advanced technologies. [START_REF] Bunn | Supporting the externality of intermittency in policies for renewable energy[END_REF], instead, have focused on the comparative role of targeting capacity versus energy markets. Their simulations show that the replacement of coal with wind imposes extra costs related to reserve capacity, and have compared alternative policies to face this challenge, namely capacity payments funded by customers and a reliability requirement on wind generators with capital cost or energy feed-in subsidies. They find that support through capital grants is more costeffective than through green certificates.

Open issues

Few attempts have been made to analyze the interlinkages between different markets or, more generally, to embed the energy sector in the broader economic and financial landscape. Recent insights on the network structure behind the European emission trading system (EU-ETS, see [START_REF] Karpf | A network-based analysis of the EU ETS[END_REF] suggest that the shape of the network structure itself is an important issue, possibly shedding light on the increasing financialisation of the energy sector and its long-term effects under different climate scenarios.

Relatedly, as far as the authors know, the interconnectedness of producers with their parent companies and the underlying systemic risks within energy markets has not received an in-depth exploration, as it has been done for financial markets (for example see the DebtRank measure in Battiston et al., 2012).

The financial interdependence of electricity markets players represents a promising field for further study. Similarly for the dynamics of mergers and acquisitions between energy companies reacting to merit order effects. Finally, while the effects of climate policies on energy markets have long been under scrutiny, not enough is known about the direct effects of climate change on energy use and on the availability of renewable energy sources.

Eco-innovation and climate-friendly technology diffusion

There is a growing academic interest in eco-innovation, 10 defined, rather broadly, as "the creation or implementation of new, or significantly improved, products, processes, marketing methods, organizational structures, and institutional arrangements which lead to environmental improvements compared to relevant alternatives" [START_REF] Kemp | Eco-innovation: definition, measurement, and open research issues[END_REF]. By fostering eco-innovation, society and policy makers can tackle a number of pressing problems, such as the depletion of natural resources, 11 security of energy supply in countries depending on fossil fuel imports, and climate change due to greenhouse gas emissions. However, innovation is not a sufficient condition for adaptation to and mitigation of climate change: it is ineffective without diffusion and adoption. By technology diffusion one means, following [START_REF] Rogers | Diffusion of innovations[END_REF], "the process by which an innovation is communicated through certain channels over time among the members of a social system".

Climate-friendly technologies are characterized by several specificities, which need to be taken into account in any robust approach to modelling diffusion of green innovation [START_REF] Allan | Diffusion of green technology: a survey[END_REF]. First, one needs to consider that no single technology can stop global warming, unless one believes in climate engineering [START_REF] Keith | A case for climate engineering[END_REF]. Second, both climate change and technical change are highly cumulative processes. The full benefits of technology diffusion for the climate are only attained with a delay of several years, which also complicates policy assessments. Third, diffusion of climate-friendly technologies typically occurs in industries organized as large technical systems (e.g. the electricity industry, see [START_REF] Künneke | Aligning modes of organization with technology: Critical transactions in the reform of infrastructures[END_REF][START_REF] Markard | Sustainability transitions: An emerging field of research and its prospects[END_REF], and this renders the diffusion of new technologies a highly unstable, inertial, and path dependent process. 12 Recent evidence on the diffusion of environmentally-friendly technologies can be found in [START_REF] Narbel | What is really behind the adoption of new renewable electricity generating technologies?[END_REF].

In standard, neoclassical economics, knowledge is nearly synonymous to codifiable information and assumed to almost immediately spread within the economy as well as across economies. This probably explains why, after acknowledging that diffusion has received little attention in the literature on green technology, [START_REF] Pizer | Endogenizing technological change: Matching empirical evidence to modeling needs[END_REF] conclude that simplistic representations that ignore diffusion may be sufficient, since most innovations exert their main impact within a decade. The issue of diffusion has not been neglected in empirical works (also by Popp himself, see [START_REF] Popp | Technology and the diffusion of renewable energy[END_REF] and neoclassical models are able to reproduce the empirically observed S-shape of technological diffusion paths, but fundamental issues such as the role of uncertainty, or the role of agents' heterogeneity and the structures of interaction networks are not adequately taken into account. 13

11 See the literature spawned by The Limits to Growth [START_REF] Meadows | The limits to growth[END_REF], as summarized e.g. by [START_REF] Turner | A comparison of the limits to growth with 30 years of reality[END_REF] and [START_REF] Dosi | Energy, development and the environment: an appraisal three decades after the limits to growth debate[END_REF].

12 The history of new technology diffusion in the electricity industry is enlightening in this respect. The diffusion of nuclear power, highly compatible with existing technologies, due to similar plant size and incorporating existing turbines, was relatively fast, as it would have been the diffusion of combined-cycle gas turbines, if not hampered by oil crises in the 1970s. On the contrary, wind power is based on new technical principles and equipment, and has little compatibility with the existing infrastructure, as the output of wind farms in hardly predictable. Hence, it finds a formidable barrier to its diffusion. 13 The workhorses of technology diffusion in the neoclassical camp are the "probit models" [START_REF] Geroski | Models of technology diffusion[END_REF], and the "epidemic models" [START_REF] Kiesling | Agent-based simulation of innovation diffusion: a review[END_REF][START_REF] Bass | A simultaneous equation regression study of advertising and sales of cigarettes[END_REF].

In what follows, we briefly survey ABMs of diffusion in climate economics, by classifying them according to the issues they have addressed.

Behavioral heterogeneity and income inequality

In ABMs, optimizing behavior is assumed away, or it is only one of the possible behavioral patterns.

In a number of works (e.g. [START_REF] Sopha | Exploring policy options for a transition to sustainable heating system diffusion using an agent-based simulation[END_REF][START_REF] Van Duinen | Going beyond perfect rationality: drought risk, economic choices and the influence of social networks[END_REF], and [START_REF] Janssen | Fashions, habits and changing preferences: Simulation of psychological factors affecting market dynamics[END_REF] before them) agents alternatively engage in repetition, if their income satisfaction (the ratio between actual income and potential income) is high and income uncertainty is low; in social comparison if changes in the surrounding environment cause the satisfaction level to drop and uncertainty to grow; in imitative behaviors if satisfied and uncertain; in deliberation (i.e. optimization) if their income levels are below the satisfaction threshold, but uncertainty is perceived to be mild. Adoption paths, though, are affected by the very heterogeneity in individual behaviors and preferences, as shown in the ABMs of [START_REF] Windrum | Consumer heterogeneity and the development of environmentallyfriendly technologies[END_REF], Janssen and[START_REF] Janssen | Simulating diffusion of green products[END_REF][START_REF] Schwoon | Simulating the adoption of fuel cell vehicles[END_REF].

Higher heterogeneity, indeed, can magnify the influence of some sub-sets of agents, accelerating regime transitions or, alternatively, locking the system in the existing state. In particular, [START_REF] Windrum | Consumer heterogeneity and the development of environmentallyfriendly technologies[END_REF] study how heterogeneous consumers preferences affect the incentives of firms to explore technological paradigms characterized by different levels of eco-friendliness. In their model, firms innovate by searching in a fully modular NK technological landscape (see [START_REF] Frenken | Interdependencies, nearly-decomposability and adaptation[END_REF], and the landscape fitness is inversely related to environmental pollution. Consumers have hedonic preferences and are heterogeneous in the importance they give to environmental quality or to other attributes of the good.

They can also change their preferences, and in particular imitate those of consumers in classes having better fitness. The paper shows that higher dispersion of preferences for environmental quality lowers global pollution. This is because more dispersion implies a higher fraction of consumers who are heavily concerned with climate issues. These "eco-warriors" provide firms with the incentives to explore the technological landscape towards goods with a better environmental content, further triggering imitation of consumers from other preferences classes.

The nexus between green technology diffusion and behavioral heterogeneity can be better grasped by considering the multi-dimensional features of green eco-friendly products. [START_REF] Sopha | Exploring policy options for a transition to sustainable heating system diffusion using an agent-based simulation[END_REF] focus on the role of policies to foster the diffusion of new heating technologies, inspired by the case of subsidies to heat pumps and wood-pellet heating in Norway, which were beneficial only to the diffusion of the former. The model features households, who are placed on a social network and randomly follow repetition, imitation, deliberation, or social comparison behaviors. The simulations show that policies improving one attribute of the good at a time are not enough to foster diffusion. Complementarity among attributes constrains the efficacy of the diffusion policies.

Agent heterogeneity can in fact hamper diffusion if it implies that the distance between pioneer consumers and the remaining population is too high. Income inequality, in particular, can create a gap that is difficult to bridge, unless appropriate policies are designed, perhaps even in the macroeconomic domain. This is the take home message from [START_REF] Vona | Income inequality and the development of environmental technologies[END_REF], who assess the effects of environmental taxation and income inequality on the diffusion of energy efficiency technologies. In the model, a fall in the relative price of the green good stimulates adoption, which in turn feeds back into further price decrease via learning. An environmental tax can foster the above dynamics, as it affects the relative price of green goods. The effects of the tax are moderated by the average income level, by income inequality, and by the rate of technological learning. The paper shows that, in a high income country with sufficiently fast learning, income inequality slows down the diffusion of the green technology, because of the mentioned gap between pioneers and the other potential adopters. Reforms that aim to achieve a more equal income distribution can also improve the effectiveness of carbon taxes in stimulating the diffusion of green technologies.

Learning and information spread

One of the key parameters in [START_REF] Vona | Income inequality and the development of environmental technologies[END_REF] was the learning rate. A debated issue in climate policy concerns the adequacy of the phase-out period for subsidies as compared to the learning rate that an unsubsidized industry would attain (e.g. the grid parity debate on renewable energy). Subsidies to technologies that are able to "stand on their own legs" would be wasteful. [START_REF] Cantono | A percolation model of eco-innovation diffusion: The relationship between diffusion, learning economies and subsidies[END_REF] tackle this issue by modeling an economy populated by consumers who are heterogeneous in their willingness to pay for green goods and in their social network positions.

Consumers receive information on a new green technology from their neighbors. As the number of adopters grows, the price of the new green good declines, fostering further adoption. The model is simulated under various scenarios, with and without a short-term subsidy, and tinkering with the subsidy phase-out period. Simulations show that subsidies are effective if the phase-out parameter is higher than a threshold. Moreover, both very slow and very fast learning may neutralize the subsidy effects -either because it takes too much to attain the critical diffusion level, or because technology would be adopted even without subsidies.

For consumer learning to be triggered, information on the new technologies is essential. Information spread policies, though, seem to deliver their effects only under certain conditions. One of the implications from [START_REF] Sopha | Exploring policy options for a transition to sustainable heating system diffusion using an agent-based simulation[END_REF] is that policies based on moral suasion (e.g. through education) are ineffective. Eco-labeling is examined by [START_REF] Bleda | Graded eco-labels: a demand-oriented approach to reduce pollution[END_REF], who compare how two implementations of this policy (binary eco-labels, graded eco-labels) impact on green technology diffusion.

Consumers scan the market in search of the highest quality product. Yet, quality is a bi-dimensional concept in the model: it concerns user quality as well as environmental quality. Consumers discard products with quality below a given threshold and choose randomly among the remaining products.

Environmental quality can only be inferred through eco-labels. Firms invest cumulated profits in R&D in response to technology diffusion patterns, under the assumption that user and environmental quality are negatively correlated. Three scenarios are compared: without eco-labeling, with binary eco-labels, and with graded eco-labels. Simulation results show that an upward trend in environmental quality is only achieved with graded eco-labels.

Open issues

The reviewed ABMs fully take account of agent heterogeneity and direct non-price interactions, but ABMs could fruitfully meet the systems approach challenge by [START_REF] Soete | An integrated approach to european innovation and technology diffusion policy[END_REF], according to whom the speed of diffusion of a new technology depends not only on the market for the innovation itself, but also on markets for related technologies, on the internal structure of the adopting firms (including the flexibility of its organization), and on its current knowledge base and capability to learn.

To our knowledge, ABMs of green technology diffusion have not addressed this challenge yet. As an instance of this, no attention has been paid so far to the firm-level strategies employed to reduce emissions, and in particular to the choice between "end-of-pipe" clean-up technologies and "process redesign" (see e.g. the discussion in [START_REF] Allan | Diffusion of green technology: a survey[END_REF]. 14 Secondly, ABMs still do not capture some 14 End-of-pipe technologies are the traditional target of environmental regulation and reduce emissions and/or mitigate their adverse impacts by treating an effluent stream and either neutralising the emissions or redirecting them to less harmful disposals. In contrast, pollution prevention can be enacted by means of a re-design of production processes.

However, whereas end-of-pipe pollution control entails explicit and large capital outlays, related to the installation of new equipment, the costs of process re-design are more subtle and hard to calculate, which then poses several hurdles to the other important specificities of climate-friendly technologies, such as the global nature of the climate externalities. Concerning policy assessments, it is worth noting that it is unclear from the existing ABMs whether diffusion benefits more from market-based policies or from command-and-control ones.

ABMs have so far mainly focused on how single policies affect the introduction and diffusion of climatefriendly technologies. An extensive policy exploration approach would, instead, assess the effect of policy portfolios and of varying the weights of the various policies in the portfolio.

Conclusions

The consequences of climate change for human welfare are likely to be enormous, and the intellectual challenges presented by the economics of climate change are daunting. Complex systems science offers flexible tools to analyse the relationship between the physical and the socio-economic system. By accounting for heterogeneous agents and their interactions, agent based and network models allow one to isolate mechanisms and effects that would otherwise be missing in the picture. This explains why these models have recently been put forward as prominent alternatives to standard models rooted in the general equilibrium paradigm [START_REF] Farmer | A third wave in the economics of climate change[END_REF][START_REF] Stern | Current climate models are grossly misleading[END_REF][START_REF] Mercure | Modelling complex systems of heterogeneous agents to better design sustainability transitions policy[END_REF].

In this paper, we reviewed the existing literature on complex system approaches to climate-related issues. We identified four major areas of contribution and, for each of them, we discussed the open challenges. The surveyed fields encompass climate negotiations and the formation of coalitions, macroeconomic and financial aspects linked to climate change, which comprehend (but are not limited to) integrated assessment, energy sector dynamics, and the innovation in climate-friendly technologies and their diffusion.

Various challenges remain to be undertaken and climate economics might benefit from a more extensive use of agent-based and network approaches. In particular, the relationship between inequality and climate damages and the effects of agents' interconnectivity on climate policies and on the systemic stability of production and financial networks are amongst the major issues that complexity theory models of climate change are starting to investigate, and that would be extremely difficult to analyse relying on any other framework.

At the same time, as the adoption of agent-based and network models to study the economics of climate change is quite recent, there are still high margins of improvements and issues to be addressed.

In particular, the next generation of ABMs should try to bridge the different research areas discussed in this survey. Fully-fledged integrated-assessment agent-based model should provide a more detailed description of energy markets, "green" technological innovation and diffusion along the lines of the micro diffusion of more eco-friendly production processes.

and meso models presented in Sections 4 and 5. Similarly, climate coalition formation and should be studied in macro ABMs. Finally, both micro and macro ABM should provide a better account of the interrelations between financial markets, the real economy and climate change. How can financial markets promote or hinder the discovery and diffusion of eco-friendly technologies? What is the impact of stranded assets on energy production and more generally on macroeconomic dynamics? Can new financial institutions (e.g. development banks, see [START_REF] Mazzucato | The (green?) entrepreneurial state[END_REF] and unconventional policy measures (e.g. "green" quantitative easing) foster the transition to a low-carbon economy? These are some of the questions that network and agent-based models should answer in the next years.

Figure 1 :

 1 Figure 1: Global emissions by country and sector.

  involving households and insurers determine weather insurance prices through. LAGOM operates at multiple time scales: market interchanges occurs much faster than climate change, and industrial production takes place at intermediate frequencies. The flexible accounting for different time scales is an advantage of ABMs vis-á-vis traditional IAMs, which usually consider yearly equilibrium adjustments both in the economic and climate system.4 Mandel et al. (2009) and, more recently,[START_REF] Wolf | A multi-agent model of several economic regions[END_REF] have further extended the LAGOM model to simulate a growing economy with the possibility of specifying different interacting economic areas and to study the properties of economic growth as emerging from spatially explicit production networks. In each region, energy is produced within specific sectors with carbon emissions as a by-product. The model could then be used to test different mitigation policies.Economic dynamics mainly affects climate change via the degree of environmental friendliness of production technologies, i.e. the amount of GHG emissions stemming from production. In general, production might involve goods, capital and energy. There are few sufficiently sophisticated agentbased models to deal with all these three aspects.[START_REF] Beckenbach | Multi-agent modeling of economic innovation dynamics and its implications for analyzing emission impacts[END_REF], for example, limit themselves to the study of a generic production process, which is decomposed across different but not well-specified sectors. In a Schumpeterian setting, growth is triggered by firms' innovation and imitation strategies, and emission dynamics depends on two exogenous parameters governing the diffusion of lowcarbon innovations and their quality.[START_REF] Gerst | Agentbased modeling of climate policy: An introduction to the {ENGAGE} multi-level model framework[END_REF] propose an agent-based model that completely endogenizes the process of technical change leading to the diffusion of less emission-intense machines.

  which determines how firms are linked each other and how (intermediate) goods flow though these links. Similarly,[START_REF] Henriet | Firm-network characteristics and economic robustness to natural disasters[END_REF] disaggregate industry input-output tables to represent the production structure of regional economies at firm level. They show that aggregate damages stemming from exogenous disasters are deeply affected by the network structure and the final outcomes depend especially on network concentration and clustering. 6Systems' connectivity increases dramatically the complexity of studying the impact of climate events, and the impossibility to reduce the problem through simple aggregation or to impede failures at all scales calls for a re-design of how modeling climate and weather damages (see also,[START_REF] Helbing | Globally networked risks and how to respond[END_REF]. Moving from a relatively restricted geographical focus to a global perspective,[START_REF] Bierkandt | Acclimate-a model for economic damage propagation. part 1: basic formulation of damage transfer within a global supply network and damage conserving dynamics[END_REF] introduce Acclimate, a model designed to evaluate the consequences of extreme climate events through the global supply chain. The model nests agent-based features (consumption and production sites are treated as agents) in an input-output network employed to track flows of goods in the system

  been little efforts in employing these tools to investigate the effects of climate change on the aggregate economy.7 To the best of our knowledge,[START_REF] Lamperti | Faraway, so close: an agent-based model for climate, energy and macroeconomic policy[END_REF] introduces the first attempt to bridge a fully-fledged agent-based integrated assessment model with a representation of climate-economic feedbacks, which take the form of stochastic shocks hitting agents with probability and size depending on the dynamics of the global mean surface temperature. The model, called DSK, builds onDosi et al. (2010[START_REF] Dosi | Income distribution, credit and fiscal policies in an agent-based keynesian model[END_REF] and is composed by two industries populated by heterogenous firms, a financial sector, an energy module and, a climate box grounded on[START_REF] Sterman | Management flight simulators to support climate negotiations[END_REF]. The model replicates a wide range of macro and micro stylized facts as well empirical regularities concerning climate change and economic dynamics (e.g. cointegration among energy consumption, GDP and GHG emissions). Given its satisfying explanatory power, the model can be employed as a laboratory to study the short (transitions) and long-run (development trajectory) effects of a wide ensemble of climate, energy, innovation, fiscal and monetary policies. The model can also be extended to account for heterogenous banks, financial markets and population growth. The latter element, often overlooked in climate-macroeconomic modeling, can play a determinant role in shaping future scenarios and it has been previously included within an agent-based model in[START_REF] Castesana | Development of an agent-based model and its application to the estimation of global carbon emissions[END_REF].

  Adoption decisions by optimizing agents and heuristic followers are different, as the latter's behavior is more inertial, implying longer adoption lags. If they, moreover, engage in social comparison or imitation, such inertia is magnified by their neighbor's inertia. This makes a strong case for public policy to encourage green technology adoption. The above are some implications of the ABM crafted by van[START_REF] Van Duinen | Going beyond perfect rationality: drought risk, economic choices and the influence of social networks[END_REF], exploring the adoption of new irrigation technologies by agricultural producers in the face of increasing drought risk. In that model, the perceived satisfaction and uncertainty depend on climate change effects, hence producer behaviors(repetition, social comparison, imitation, deliberation) are endogenous. Climate uncertainty is found to be an additional influence slowing down adoption, regardless of behavioral assumptions.

  5

5 Input-output are powerful tools to assess how a shock on one or several sectors propagates into the economy through intermediate consumption and demand

[START_REF] Haimes | Leontief-based model of risk in complex interconnected infrastructures[END_REF]

;

[START_REF] Okuyama | Modeling spatial economic impacts of an earthquake: input-output approaches[END_REF]

;

[START_REF] Cochrane | Economic loss: myth and measurement[END_REF]

.

Documents de travail du Centre d'Economie de laSorbonne -2016.58

We do not consider land-use agent-based models. This increasing stream of literature, where ABMs are largely applied, has its own specific features and would deserve a more extensive and autonomous treatment. See[START_REF] Matthews | Agent-based land-use models: a review of applications[END_REF] for a survey on the topic and[START_REF] Filatova | Spatial agent-based models for socio-ecological systems: Challenges and prospects[END_REF] for a recent discussion.

For example, in[START_REF] Dell | Temperature shocks and economic growth: Evidence from the last half century[END_REF], the authors are constrained to employ a relatively short sample of 50 years and find that temperature shocks seem not to affect developed countries.

The superiority of combining taxes and subsidies with respect to solutions based on a single policy prescription has also been obtained in a general equilibrium model by[START_REF] Acemoglu | The environment and directed change[END_REF].

Or, in a variety of cases, adjustment periods of

years (see e.g.[START_REF] Nordhaus | An optimal transition path for controlling greenhouse gases[END_REF][START_REF] Bosetti | Witch a world induced technical change hybrid model[END_REF]. 9 Documents de travail du Centre d'Economie de laSorbonne -2016.58

In particular, concentration (degree of redundancy of suppliers and clients) acts as a risk sharing feature and clustering (degree of geographically dense interactions) allows small groups of interconnected firms to positively react to shocks happening outside the community they belong to.

On the contrary,[START_REF] Okuyama | Disaster impact and input-output analysis[END_REF] discuss and devote a special issue of Economic Systems Research to combine the treatment of climate-related disasters within standard input-output or computable general equilibrium models.

Applications of the ABM methodology to other energy markets are less frequent, e.g.[START_REF] Voudouris | The {ACEGES} laboratory for energy policy: Exploring the production of crude oil[END_REF] on crude oil markets.

An investigation of personal carbon trading as a future evolution of emission trading policies is discussed by Fawcett (2010).

Also known as green innovation, environmental innovation, environmentally-friendly innovation, or sustainable innovation.

Acknowledgments

The authors would like to acknowledge financial support from different European Projects. Francesco Lamperti, Antoine Mandel, Mauro Napoletano, Andrea Roventini and Alessandro Sapio acknowledge financial support from European Union 7 th FP grant agreement No. 603416 -IMPRESSIONS. Tomas Balint and Antoine Mandel acknowledge financial support from European Union 7 th FP grant agreement No. 610704 -SIMPOL. Antoine Mandel, Mauro Napoletano and Andrea Roventini acknowledge financial support from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 640772 -DOLFINS and No. 649186 -ISIGrowth. All the usual disclaimers apply.


Bergström, Xio-Ya Jie Xian-Guan

Nomenclatural note on the homonymy between the octocoral genus Dendrobrachia Brook 1889 and the entoproct phylum Dendrobrachia

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