Claire Borsenberger

Helmuth Cremer

Denis Joram

Jean-Marie Lozachmeur

Estelle Malavolti

E-commerce and parcel delivery: environmental policy with green consumers

Keywords: Consumers' environmental awareness, Pigouvian rule, emission taxes, ecommerce, parcel delivery operators, vertical integration. JEL Codes: H21, L42, L81, L87

published or not. The documents may come

Consumers'environmental awareness (CEA) has been increasing considerably over the last decades. It appears to a¤ect their demand behavior in essentially all sectors. However, e-commerce and its environmental impact have drawn a particularly signi…cant attention in the public debate and the appeals for policy intervention have become increasingly pressing as e-commerce has been expanding. This expansion has been particularly drastic during the last two years because of the Covid epidemic and the attention devoted to the environmental footprint of the sector has risen accordingly. This phenomenon has for instance been documented by recent surveys [START_REF] Anderson | Tax incidence in di¤erentiated product oligopoly[END_REF] which showed that individuals declare being more conscious about the impact of their purchasing behavior on environment and most of them, especially the under 35 years old population, would like to modify their behavior accordingly. Being more conscious means that individuals clearly identify and are more sensitive to new characteristics for the goods such as brand responsibility, ethical labor, if repair is feasible, transparency, etc. This will translate into deciding to refuse consuming goods or to reduce the consumption of theses goods that would not be compliant with their tastes in regards environment. This could also translate into refusing to buy imported goods and being willing to pay more for goods satisfying these new characteristics. [START_REF] Amir | Optimal licensing of uncertain patents in the shadow of litigation[END_REF] One can of course expect CEA to act as a discipline devise which brings retailers and delivery operators to adopt cleaner production technologies. For instance, the use of electric vehicles or cargobikes for urban delivery may be appealing for environmentally conscious customers, enhance their demands, and provide the delivery operator with a competitive edge. While one may doubt that this mechanism might be su¢ cient to achieve an adequate level of emission reduction, one can certainly expect CEA to a¤ect the appropriate environmental policy design.

In this paper, we study how CEA a¤ects the design of environmental policy in the e-commerce sector. We study the appropriate design of taxes at the di¤erent levels of the value chain under CEA. We also examine if there is a need for regulation requiring delivery operators to reveal the environmental footprint of their activity. While the retail activity of course also generates emissions, we will concentrate on the environmental impact of delivery.

To deal with those issues, we consider a model which is based on Borsenberger et al. (2022). There are two retailers/producers who sell a di¤erentiated product and two parcel delivery operators. The delivery of these goods generates CO2 emissions.

The total level of these emissions creates a global (atmosphere) externality which is a potential source of global warming and climate change. We assume that the delivery cost decreases with the level of emissions, at least up to some level. In other words, it is more expensive for the delivery operator to use "green" technologies. Because of CEA consumer's utility decreases with the environmental cost associated with the product they buy. Speci…cally, the level of emissions generated by its delivery involves a monetary cost in utility. When this level of emissions is not revealed by the delivery operator, consumers assume that it uses a dirty technology. In a …rst step we assume that the environmental cost that reduces consumers'utility is the same for all consumers, but we also consider the case where consumers di¤er in their environmental awareness.

We consider di¤erent scenarios re ‡ecting the type of competition and the vertical structure of the industry. In a reference scenario, we will consider "pseudo" perfect competition à la Mussa and Rosen (1978) in which retailers and delivery operators are independent and behave competitively so that all prices and delivery rates including the price of environmental quality re ‡ect marginal cost. Then, we will consider a setting where all …rms remain independent but where there is imperfect competition which involves strategic interaction in a two-stage game where operators choose environmental quality in a …rst stage and then compete in delivery rates. We will study the (subgame perfect) Nash equilibrium. In another scenario, we assume that there is vertical integration between one of the retailers and one of the delivery operators.

We study the di¤erent equilibria, implying di¤erent levels of emissions and outputs, policy under the di¤erent market structures. Finally, we examine if operators …nd it pro…table to reveal their levels of emissions to consumers.

Model

Consider an e-commerce sector with two products i = 1; 2 which are substitutes and di¤erentiated by their environmental impact. For simplicity, we assume that this impact is determined by the emissions of the delivery operator. [START_REF] Amir | Does the cost paradox preclude technological progress under imperfect competition?[END_REF] There are two operators, delivering each a single product, so that the index i = 1; 2 can also be used for of delivery operators. There are two retailers, indexed A and B, which sell both products.

Preferences are represented by

u(x 1 ; x 2 ) p 1 x 1 p 2 x 2 x 1 e 1 x 2 e 2 ; (1)
where x 1 and x 2 denote consumption of the two goods, p 1 and p 2 the prices charged by the retailers, while e 1 and e 2 are the (per unit) emissions associated with their delivery.

Environmental concern, CEA, is expressed in monetary terms, with representing the perceived cost of one unit of emissions. Maximizing (1) yields the demand functions

x 1 (q 1 ; q 2 ) and x 2 (q 1 ; q 2 ), which are determined by

u 0 1 (x 1 ; x 2 ) = p 1 + e 1 = q 1 ; (2)
u 0 2 (x 1 ; x 2 ) = p 2 + e 2 = q 2 ; (3)
where u 0 j = @u @x j ; j = 1; 2; and q j denotes the "full price" including environmental damage.

Costs of retailers j = A; B, for goods i = 1; 2 are given by y ji k, where k is their marginal cost and y ji the quantity of good i they sell. In words, we assume that marginal costs are constant, equal across retailers and the same for the two products.

The costs of delivery operator i = 1; 2 are given by c i (z i ; e i ), where z i is the number of parcels delivered and e i is emissions per parcel delivered. Each operator delivers a single good. Assume for simplicity that:

c i (z i ; e i ) = C i (z i ) i (e i )z i ; (4)
where 00

i (e i ) < 0 and 0 i (e i ) > 0 for e i < e i and 0 i (e i ) = 0 for e i e i :

Intuitively, assumption (5) implies that delivering in a less polluting way is more costly.

Further we assume that for any level of e we have 0 1 (e) < 0 2 (e) so that delivery operator 1 is cleaner: we have e 1 < e 2 and when when 0 1 (e 1 ) = 0 2 (e 2 ) we have e 1 < e 2 . It will become clear below that this assumption implies that in equilibrium delivery operator 1 will use the cleaner technology and thus have a lower level of e.

Market clearing requires that for each good i, the total amount sold by both retailers y Ai + y Bi is equal to demand x i and to the amount delivered z i . Formally we have

y A1 + y B1 = x 1 = z 1 ; y A2 + y B2 = x 2 = z 2 :
Total emissions, E, have a social cost (E) and they are given by

E = x 1 e 1 + x 2 e 2 :
This de…nition …ts CO 2 emissions, which are global and additive.

First best

We start by characterizing the …rst-best (FB) allocation. To de…ne social welfare, we follow the by now standard approach initially advocated by Hammond (1987) and Harsanyi (1995) and do not include the CEA term in welfare. [START_REF] Borsenberger | E-commerce, parcel delivery and environmental policy[END_REF] This is commonly referred to as "laundering out" the altruistic term.

With this objective function, the FB allocation solves the following problem

max x i ;e i SW F = u(x 1 ; x 2 ) kx 1 kx 2 C 1 (y 1 ) + y 1 1 (e 1 ) C 2 (y 2 ) + y 2 2 (e 2 ) (E) (6)
The FOCs are:

0 i (e i ) = 0 (E ) (7)
u 0 1 (x 1 ; x 2 ) = k + C 0 1 (x 1 ) 1 (e 1 ) + e 1 0 (E ) (8)
u 0 2 (x 1 ; x 2 ) = k + C 0 2 (x 2 ) 2 (e 2 ) + e 2 0 (E ) (9)
We assume throughout the paper that < 0 (E ). In words, the (marginal and average) environmental cost perceived by the consumer is smaller than the full social marginal damage.

We now turn to the laissez-faire and study the equilibrium allocation.

Equilibrium when consumers observe emissions

Assume for the time being that emissions associated with the delivery of the two products are observable to consumers. This may be the case for instance because there is a regulatory requirement for retailers and/or delivery operators to report the level of emissions or because the …rms decide to reveal their levels of emissions.

As a reference consider outcome which is (pseudo)-competitive following Mussa and Rosen (1978). This implies the usual price marginal cost pricing concerning quantity, but also concerning (environmental) quality e.

Prices and delivery rates p(e) and r(e) are then functions of environmental quality, so that p i = p(e i ) and r i = r(e i ). For future reference we consider the possibility that delivery operators are subject to an emission tax . Setting this tax to zero then yields the laissez-faire. Furthermore we can use the equilibrium expressions to study the FB implementation and in particular the required level of the emissions tax.

Retailers solve max e j ;y j j = p(e 1 )y j1 ky j1 r(e 1 )y j1 + p(e 2 )y j2 ky j2 r(e 2 )y j2 ; which yields

p i = k + r i ; (10)
p 0 (e i ) = r 0 (e i ): (11)
Demand is obtained maximizing utility

max x i ;e i u(x 1 ; x 2 ) x 1 p (e 1 ) x 2 p (e 2 )
x 1 e 1

x 2 e 2 which yields

u 0 i (x 1 ; x 2 ) = p i + e i ( 12
)
p 0 (e i ) = (13)
for i = 1; 2.

Supply functions of delivery operators are obtained by

max z i ;e i = r(e i )z i C i (z i ) + i (e i )z i e i z i which yields r(e i ) = C 0 i i + e i (14) r 0 (e i ) = 0 i (e i ) + : (15)
Substitution ( 10) and ( 14) into (12) and using the market clearing conditions yields

u 0 i (x 1 ; x 2 ) = k + C 0 i i + e i + e i ; (16) 6
while combining (11), ( 13) and (15) show that in equilibrium we have 0 i (e i ) = + :

When = 0 we obtain the laissez-faire characterized by

0 i (e i ) = ; (17)
u 0 i (x 1 ; x 2 ) = k + C 0 i i + e i = p i : (18)
Consequently we have e 1 < e 2 and e i < e i as long as > 0. Absent of CEA that is when = 0 both delivery operators set e i = e i to minimize their delivery cost while neglecting any environmental consideration. Not surprisingly CEA will lead to lower levels of emissions but as long as < 0 (E ), emission will be larger than optimal.

Condition (18) shows that prices re ‡ect marginal cost but environmental costs are only included to the extent that they are perceived by consumers. Consequently in spite of the CEA, equilibrium consumption levels will be larger than when the full environmental cost is accounted for.

Let us now turn to the FB implementation. In order to respect equality between ( 8) and ( 16), the emissions tax must satisfy

= 0 (E ) : (19)
When = 0 we obtain the traditional Pigouvian rule stating that the tax must re ‡ect the marginal social damage. With CEA the rule is amended and now requires that the tax re ‡ects the part of the marginal social damage which is not perceived by consumers.

Substitution of (11) and ( 13) in (15) show that ( 7) is also satis…ed with such a tax.

In other words, the linear tax on emissions via its impact on the delivery operator's marginal cost and the consumer price is su¢ cient to implement the FB. Consumption levels will also be at their FB levels. This shows that the result obtained by Borsenberger et al. (2022) remains valid when CEA is considered.

Observability of emissions

In the previous section we have assumed that the levels of emissions e i are observable.

When they are not observable we return to an equilibrium with e i = e i ; since e i is not observed by consumers their willingness to pay is zero. Consequently, there is no incentive for delivery operators to reduce emissions. This leads of course to a lower level of welfare. Consequently, a regulation requiring delivery operators and/or retailers to reveal the level of emissions is welfare improving.

This observation in turn raises the question if …rms will spontaneously have an incentive to reveal e i . In the considered scenario where all …rms are price takers the answer is obviously a¢ rmative and this follows from basic microeconomic theory. Delivery operators want to communicate their e, because this shifts the inverse demand curve upwards so that (with increasing marginal costs) equilibrium pro…ts will increase. This suggests that no regulation is necessary. However absent of a regulatory, and possibly certifying authority it is not clear if the operators can credibly announce their e i , especially since there is a clear incentive to announce a lower level than the actual one.

6 Imperfect competition in the delivery sector: independent …rms

The game

We assume that delivery operators move …rst and play a two stage game: …rst they choose e and then r. The retailers continue to set prices at marginal costs. We …rst determine the subgame perfect equilibrium of the delivery operator's game assuming that they anticipate the retailers'behavior. Then we examine how the …rst best (which does not change) can be implemented by imposing a tax on delivery of i per unit and a tax on emissions, at rate i . For the time being we assume that consumers know the emission levels associated with their consumption. We revisit this issue in Section 9 below.

Demand functions x i (q 1 ; q 2 ) continue to be determined by equations ( 2) and (3).

Furthermore, marginal cost pricing by retailers implies that

p i = k + r i (20)
remains valid.

Equilibrium

To avoid repetitions, we introduce the tax instruments from the outset. This gives us the expressions we need for the FB implementation, while we can easily obtain the laissez-faire (LF) by setting both taxes at zero. We solve the model by backward induction.

Stage 2: determination of delivery rates r i

Delivery operator i chooses r i by solving:

max r i i = (r i + i (e i ) i i e i ) x i (q 1 ; q 2 ) C i (x i (q 1 ; q 2 ))
where from ( 2) and ( 3) and (20) we have q i = k + r i + . The FOCs are:

x i (q 1 ; q 2 ) + @x i (q 1 ; q 2 ) @q i [r i + i (e i ) i i e i C 0 i (x i (q 1; q 2 ))] = 0 (21)
for i = 1; 2. This de…nes r e i (e 1 ; e 2 ) and demands where demand levels are given by ( 22).

x e i = x i (k +
Using the envelop theorem, the …rst-order conditions are 0 i (e i ) i x e i + @x i (q 1 ; q 2 ) @q i + @x i (q 1 ; q 2 ) @q j @r e j @e i [r e i + i (e i )

i i e i C 0 i (x e i )] = 0; ( 23
) for i = 1; 2.
These expressions evaluated at i = 0 and i = 0 determine the LF. Since now we have imperfect competition on top of the externality generated by emissions, we cannot expect the equilibrium to be e¢ cient. However, comparing the FB and the LF is now much more complex than in the pseudo-competitive scenario considered in Section 4.

Some results concerning emission levels are established in Appendix A. We show that under standard conditions, emissions continue to be set at their maximum levels e i = e i , exactly like in the competitive scenario considered in Section 4. In other words absent of CEA, emissions are too large and at their maximum levels. Intuitively, when = 0, emissions have no impact on demand and …rms simply set them to minimize their cost. [START_REF] Cremer | Intergenerational transfer of human capital and optimal education policy[END_REF] Furthermore a positive value of (the presence of CEA) tends to mitigate this ine¢ ciency and we may get smaller emission levels and an interior solution provided that is large enough. In that case, e has also an e¤ect on demand which induces delivery operators to limit their emissions.

Implementation of the …rst best

Using (2), ( 3) and (20), the operators'marginal pro…t [r i + i (e i )

i i e i C 0 i ] which appears in expressions ( 21) and ( 23) can be rewritten as

r i + i (e i ) i i e i C 0 i (x i ) = u 0 i k e i + i (e i ) i i e i C 0 i (x i ) (24)
Using ( 8) and ( 9) the RHS of (24) can be further rearranged as

u 0 i k e i + i (e i ) i i e i C 0 i (x i ) = e i 0 (E ) i i e i (25)
implement the FB must satisfy the following system of equations

x i + @x i @q i e i 0 (E ) i i e i = 0 (26)
0 (E ) i x i + @x i @q i + @x i @q j @r j @e i e i 0 (E )

i i e i = 0 (27)
We show in Appendix B that these equations can be rearranged to yield the following expressions for the implementing taxes i = 0 (E ) @x i @q j @r j @e i @x i @q i ; (28)

i + i e i = x i @x i @q i + e i 0 (E ) : (29)
where @x i =@q i < 0 and @x i =@q j > 0. Consequently, i will in general di¤er from 0 (E ) so that the straight Pigouvian rule that applied under perfect competition has to be amended. Furthermore, the sign of the adjustment depends on @r j =@e i that is the impact of an increase in the competitor's emissions on an operator's equilibrium delivery rate. More precisely we have @r j =@e i Q 0 () i Q 0 (E ) :

Studying the sign of @r j =@e i is complicated at this level of generality. We show in Appendix A that @r j =@e i has the same sign as 0 i (as long as @ 2 x i =@q i @q j 0). [START_REF] Hammond | Altruism, in: The New Palgrave:A Dictionary of Economics[END_REF] Intuitively, when = 0, so that there is no CEA, e i has no impact on demand but only on costs and we have @r j =@e i < 0. When > 0, e i re ‡ects quality to that there is also a product di¤erentiation e¤ect which goes in the opposite direction. Expression (A13) indeed shows that the absolute value of @r j =@e i decreases as increases but that @r j =@e i remains negative. To see this recall that in the …rst best we have 0 i (e i ) = 0 (E ) and by our assumption < 0 (E ) we thus have 0 i < 0. To sum up, under imperfect competition, the emissions tax is always lower than 0 (E ) (its counterpart under perfect competition) but the wedge decreases as increases.

Turning to equation ( 26), it shows that the total tax per unit of output is given by i + i e i =

x i @x i @q i + e i 0 (E ) :

While the …rst term in the RHS is negative, the second is positive given our assumption that 0 (E ) > 0. Consequently, the sign of the total tax per output is ambiguous.

7 Vertical integration between operator 2 and retailer B

We now assume that retailer B and delivery operator 2 are integrated. We use the index 2B for this …rm. The game is as follow: in stage 1, delivery operator 1 and …rm 2B choose their levels of e: In stage 2, delivery operator 1 chooses its delivery price r 1 and the …rm 2B chooses p 2B . As in the previous section we consider a tax on delivery volume of i per unit and tax on emissions at rate i .

First, observe that there will be foreclosure: …rm 2B has no incentive to deliver product 2 for retailer A. That way it can maintain a monopoly of this product. The price of good 1 continues to be given by its marginal cost

p 1 = r 1 + k;
With these assumptions, we have q 1 = r 1 + k + e 1 and q 2 = p 2B + e 2 so that demands can be rewritten as x i (r 1 + k + e 1 ; p 2B + e 2 ) for i = 1; 2B.

We solve the game by backward induction, starting with Stage 2. The problem of delivery operator 1 is

max r 1 1 = (r 1 + 1 (e 1 )
1 1 e 1 ) x 1 C (x 1 ) :

The FOC is

x 1 + r 1 + 1 (e 1 ) 1 1 e 1 C 0 (x 1 ) @x 1 @q 1 = 0 (30)
The problem of …rm 2B is

max p 2B 2B = (p 2B + 2 (e 2 ) k 2 2 e 2 ) x 2 C(x 2 ):
The FOC is

x 2 + p 2B + 2 (e 2 ) k 2 2 e 2 C 0 (x 2 ) @x 2 @q 2B = 0 (31)
Equations ( 30) and (31) de…ne r 1 (e 1; e 2 ) and p 2B (e 1 ; e 2 ) so that demands are given by x 1 (r 1 (e 1 ; e 2 ) + k + e 1 ; p 2B (e 1 ; e 2 ) + e 2 ) and x 2 (r 1 (e 1 ; e 2 ) + k + e 1 ; p 2B (e 1 ; e 2 ) + e 2 ).

Turning to Stage 1, the problem of delivery operator 1 is:

max e 1 1 = (r 1 + 1 (e 1 ) 1 1 e 1 ) x 1 C (x 1 )
Using the envelop theorem (that is, making use of expression 30) the FOC can be written as

0 1 (e 1 ) 1 x 1 + r 1 + 1 (e 1 )
1

1 e 1 C 0 (x 1 ) @x 1 @q 1 + @x 1 @q 2 @r 2 @e 1 = 0: (32)
The problem of …rm 2 is

max e 2 2B = (p 2B + 2 (e 2 ) k 2 2 e 2 ) x 2 C (x 2 )
Using the envelop theorem (using expression 31), the FOC is given by:

0 2 (e 2 ) 2 x 2 + (p 2B + 2 (e 2 ) k 2 2 e 2 ) @x 2 @q 2 + @x 2 @q 1 @r 1 @e 2 = 0: (33)
These expressions evaluated at i = 0 and i = 0 determine the LF, which with the combination of the externality and imperfect competition will again not be e¢ cient.

Interestingly, the properties of this equilibrium regarding emissions are similar to those obtained for independent …rms. In particular we establish in Appendix C that when = 0 we continue to have maximum emissions with e i = e i . Furthermore, and not surprisingly, the presence of CEA with > 0 will mitigate this ine¢ ciency.

Implementation of the …rst best

We now examine how the FB can be achieved by the two considered tax instruments.

In Appendix D we show that this requires i = 0 (E )

@x i @q j @r j @e i @x i @q i for i = 1; 2B. ( 34
) i + i e i = x i @x i @q i + e i 0 (E ) (35)
Interestingly, the expressions are the same as their counterparts in the case of independent …rms, that is (28) and ( 29) and the discussion provided there continues to apply.

However, while the rules are the same, the levels will di¤er because equilibrium levels di¤er.

8 Heterogeneity in the level of environmental concern

A main …nding of the model so far is that, the tax required to compensate for the environmental impact of the delivery is reduced (from its Pigouvian level) by the monetary equivalent of the consumers'environmental concern. This simple rule applies when all consumers have the same CEA. We now examine how it has to be amended when consumers di¤er in their valuation for the environment. To do so, we consider heterogenous consumers who di¤er only in their 's. For simplicity assume that a proportion of the total population of consumers values the environment at > 0 while the remaining part, 1 has no concern for the environment ( = 0).

The preferences of the consumers of type E, who care about the environment are

u(x 1 ; x 2 ) p 1 x 1 p 2 x 2 x 1 e 1 x 2 e 2 ;
while the preferences of the consumers of type O who are not concerned about environmental issues are

u(x 1 ; x 2 ) p 1 x 1 p 2 x 2 :
We continue to consider demand levels as function of full prices which include environmental concern, if any. We can thus de…ne

q E i = p i + ; q O i = p i ;
and denote demand levels by

x E i (q E 1 ; q E 2 ); x O i (q O 1 ; q O 2 ):
They are obtained as shown in expressions ( 2)-(3), with the q i 's properly rede…ned. We can then de…ne aggregate demands as

X 1 (p 1 ; p 2 ) = (1 )x O 1 + x E 1 ; X 2 (p 1 ; p 2 ) = (1 )x O 2 + x E 2 :
For the delivery stage, the market clearing conditions are now:

y A1 + y B1 = X 1 = (1 )x O 1 + x E 1 = z 1 ; y A2 + y B2 = X 2 = (1 )x O 2 + x E 2 = z 2 :
Total emissions are determined in the same way as before and so is social welfare, which continues to be given by (6). Recall that the CEA terms are not included in social welfare. Consequently, the …rst-best solution does not change.

De…ning the (pseudo) competitive equilibrium in this setting is complicated and raises some conceptual issues. Consequently it looses its attractiveness as simple benchmark scenario. For the sake of illustration we thus concentrate on the imperfect competition setting with independent …rms, which is not more complex when consumers are heterogenous. In particular, one easily checks that the equilibrium conditions derived in Section 6 remain valid, except that x 1 and x 2 have to be replaced by X 1 and X 2 .

In other words, with homogenous consumers there was no need to distinguish between individual and aggregate demand, but now this distinction becomes relevant and it is the level of aggregate demand that matters for the retailers and the delivery operators.

For the rest, the properties of the equilibrium discussed there continue to apply. In particular when = 0 were return to maximum emissions in the laissez-faire. [START_REF] Harsanyi | A theory of social values and a rule utilitarian theory of morality[END_REF] Furthermore, CEA will continue to mitigate the level of emissions except that now both and will be relevant.

Implementing the FB is now more problematic, because it requires personalized taxes, which depend on an individual's . These are feasible only when individual 's are observable. Assume for the time being that they are. Then a simple way to achieve the FB is to impose …rst of all per unit taxes at rates e 1 and e 2 on the consumers who do not have any environmental concern. This brings us back to the model considered in Section 6 and the results obtained there continue to apply. To be more precise the taxes on "dirty"consumers come on top of the instruments considered in Section 6 and emissions and output taxes continue to be given by ( 28) and (29).

Revelation of emissions levels

Let us now revisit this issue within the context of imperfect competition. Recall that we have shown in Section 5 that under perfect competition delivery operators …nd it bene…cial to reveal their emissions, assuming of course that they can credibly do this.

As regulatory intervention is thus in principle not necessary, except that it may help conveying reliable information on emission levels.

For simplicity we concentrate on the scenario with independent …rms. The most natural way to deal with this issue is then to introduce an extra stage into our game.

Speci…cally, assume, that in Stage 0, delivery operators simultaneously decide whether they reveal their level of e i or not. If both of them decide to reveal their emissions they play the game considered in Section 6. If either one or both operators decide not to reveal their emissions, the Stage 1 of the game is amended. For non revealing operators there is no incentive to reduce their levels of emissions; consequently, they choose maximum emission e i = e i to minimize their cost. The revealing operator i, if any, will play its best reply to the other operator's strategy, namely e j . Once e i 's are chosen the game proceeds with Stage 2, exactly as in Section 6.

Since no action is taken and no information revealed between the added Stage 0 and Stage 1, for an operator not revealing its emissions is equivalent to choosing maximum emissions in Stage 1. But this option already existed in the original game and we have shown that as long as is large enough it will not be relevant in equilibrium. Consequently, the equilibrium in Stage 0 involves revelation of emissions by both operators. [START_REF] Mussa | Monopoly and Product Quality[END_REF] To sum up, the result obtained in Section 5 for the competitive scenario continues to apply under imperfect competition when emission levels are chosen in a strategic way.

Concluding comments

We have shown that as can be expected, CEA mitigates the ine¢ ciency of the equilibrium by bringing the level of emissions closer to its optimal level. This is true under perfect competition but it also remains true under imperfect competition both in the independent …rms and the vertical integration scenarios.

This e¢ ciency enhancing e¤ect of CEA also a¤ects the design of the appropriate emissions tax, which leads to an amended Pigouvian rule. Under perfect competition the tax is reduced by exactly the monetary level of CEA, . Under imperfect competition the taxation rule is more complicated and the reduction exceeds but the extra adjustment decreases as the CEA increases.

When consumers di¤er in their CEA the design of environmental taxes is more complicated. To achieve a …rst best, personalized taxes are required but they are feasible only when a consumer's degree of CEA is observable. When this is not the case, a uniform tax can only achieve a second-best solution. The characterization of this uniform policy is tedious and left for future research. However, one can expect that the required adjustment from the Pigouvian rule is some weighted average of the individual's levels of CEA.

All these results rely on the assumption that consumers are aware of the levels of emission associated with the product they consume. We show that in our setting delivery operators will …nd it bene…cial to reveal their level of emissions but in practice it may be di¢ cult to do this in a credible way. Consequently, a regulatory intervention associated with some kind of certi…cation is certainly desirable.

where the third term in brakets of (A12) can be rewritten as follows:

@x 1 @q 2 + @ 2 x 1 @q 1 @q 2 M B 1 + @x 1 @q 1 M B 1 r 2 = @x 1 @q 2 + @ 2 x 1 @q 1 @q 2 M B 1 @x 1 @q 1 @x 1 @q 2 C 00 1 = @x 1 @q 2 1 @x 1 @q 1 C 00 + @ 2 x 1 @q 1 @q 2 M B 1 = @x 1 @q 2 @M B 1 @r 1 + @ 2 x 1 @q 1 @q 2 M B 1 :

Factorizing out @x 1 @q 2 @M B 1 @r 1 + @ 2 x 1 @q 1 @q 2 M B 1 in A12 yields @ 1 @e 2 @ 2 @r 2 @ 1 @r 2 @ 2 @e 2 = @x 1 @q 2 M B 1 r 1 + @ 2 x 1 @q 1 @q 2 M B 1 @x 2 @q 2 + @ 2 x 2 @q 2 2 M B 2 + @x 2 @q 2 M B 2 r 2 @x 2 @q 2 M B 2 r 2 @ 2 x 2 @q 2 2 M B 2 @x 2 @q 2 0 2 = @x 1 @q 2 M B 1 r 1 + @ 2 x 1 @q 1 @q 2 M B 1 @x 2 @q 2 @x 2 @q 2 0 2 = @x 2 @q 2 @x 1 @q 2 M B 1 r 1 + @ 2 x 1 @q 1 @q 2 M B 1 0 2 ;

(A13) so that the sign of dr 1 =de 2 is given by the sign of 0 2 . Using the same reasoning, one can show that the sign of dr 2 =de 1 is given by the sign of 0 1 .

B Proof of equations (28)-(29)

Equations ( 26) and ( 27) can be rewritten as e i 0 (E )

i i e i = x i @x i @q i ; (A14) e i 0 (E )

i i e i = ( 0 (E ) i ) x i @x i (:) @q i + @x i (:) @r j @r j @q i : (A15) 0 1 (e 1 ) 1 x 1 + r 1 + 1 (e 1 )

1 1 e 1 C 0 (x 1 ) @x 1 @q 1 + @x 1 @q 2 @r 2 @e 1 = 0

where using (A38) :

r 1 + 1 (e 1 )
1 1 e 1 C 0 (x 1 )

= x 1 = @x 1 @q 1 1 (e 1 ) + 1 + 1 e 1 + C 0 (x 1 )

+ 1 (e 1 )

1 1 e 1 C 0 (x 1 )

= x 1 = @x 1 @q 1 ; so that the FOC wrt. to e 1 yields 0 1 (e 1 ) 1 x 1 x 1 = @x 1 @q 1 @x 1 @q 1 + @x 1 @q 2 @r 2 @e 1 = 0; which using (7) yields 0 (E) 1 = @x 1 @q 1 + @x 1 @q 2 @q 2 @e 1 @x 1 @q 1 : The FOC wrt. e 2 writes 0 2 (e 2 ) 2 x 2 + p 2B + 2 (e 2 ) k 2 2 e 2 C 0 (x 2 ) @x 2 @q 2 + @x 2 @q 1 @r 1 @e 2 = 0;

where using (A39) = x 2 = @x 2 @q 2B ; so that the FOC wrt e 2 can be rewritten as:

p 2B + 2 (e 2 ) k
0 2 (e 2 ) 2 x 2
x 2 @x 2 @q 2B @x 2 @q 2 + @x 2 @q 1 @r 1 @e 2 = 0; which using (7) yields 0 (E) 2 = @x 2 @q 2 + @x 2 @q 1 @r 1 @e 2 @x 2 @q 2 :

2 2 e 2 + 2 (e 2 ) k 2 2 e 2

 22222 C 0 (x 2 ) = x 2 = @x 2 @q 2B 2 (e 2 ) + k + 2 + 2 e 2 + C 0 (x 2 ) C 0 (x 2 )

OpinionWay questionnaire run on 1000 French persons over 18 years old, online sept.

; Retail X 2021 report « Sustainability » 2 However, nowadays there appears to exist a gap between their attitude towards environment and their consumer behavior. One interpretation is the fact that information is di¢ cult to get for consumers on many aspects of the product when it concerns environment. Some policy makers suggest that a label system such as de…ned for energy could be used.

In reality, the retail activity will of course also generate emissions. Following Borsenberger et al.(2022) one could easily generalize our model to account for these extra emissions. This would complicate the analysis but not a¤ect our main results.

See Cremer and Pestieau (2006) for a more detailed discussion.[START_REF] Hammond | Altruism, in: The New Palgrave:A Dictionary of Economics[END_REF] pleads in favor of excluding all external preferences, even benevolent ones, from our social utility function. The reason is that including this term would amount to count the externality twice.

This is true as long as the so called "cost paradox" does not apply; see for instance[START_REF] Amir | Optimal licensing of uncertain patents in the shadow of litigation[END_REF][START_REF] Amir | Does the cost paradox preclude technological progress under imperfect competition?[END_REF] or Aderson et al.(2001). In a setting with strategic complements and observable costs, the strategic e¤ect of a decrease in own cost on the rival's price could lead, in principle, to a pro…t loss that is higher than the pro…t gain from the direct e¤ect of such a decrease. In this case, a …rm would not have a unilateral incentive to decrease its own cost. However, this is unlikely to happen in practice as it requires quite extreme assumptions on the demand elasticities; Aderson et al. (2001), Proposition 3.

This property holds for spearable preferences and for many conventionally considered speci…c utility functions like Cobb-Douglas or CES.

As long as @ 2 Xi=@qi@qj 0.

When is close to zero, the equilibrium in Stage 1 involves maximum emissions. In that case, the outcome is the same irrespective of the decision made in Stage 0. Consequently, revelation by both operators continues to be an equilibrium in that case.

We thank Yassine Lefouli for his comments and suggestions. Helmuth Cremer, Jean-Marie Lozachmeur and Estelle Malavolti gratefully acknowledge the funding received by TSE from ANR under grant ANR-17-EURE-0010 (Investissements d'Avenir program). They have bene-…ted from the …nancial support of Groupe La Poste in the context of the research foundation TSE-Partnership. The views expressed in this paper are those of the authors and do not necessarily re ‡ect those of TSE-P or La Poste.

Appendix

A Comparative statics

Consider the FOCs (21) for i = 1; 2 and let us de…ne i as follow:

1 = x 1 (q 1 ; q 2 ) + @x 1 (q 1 ; q 2 ) @q 1 [r 1 + 1 (e 1 ) C 0 1 (x 1 (q 1 ; q 2 ))]; 2 = x 2 (q 1 ; q 2 ) + @x 2 (q 1 ; q 2 ) @q 2 [r 2 + 2 (e 2 ) C 0 2 (x 2 (q 1 ; q 2 ))];

where q i = k + r i + e i . De…ne

the marginal bene…t of a postal operator i. We have

Di¤erentiating 1 and 2 with respect to r j , e j and using (A1) and (A2) for i; j = 1; 2 yields

Using Cramer rule, one has

where SOC > 0 is the second order condition. so that the sign of dr 1 =de 2 is given by the the opposite sign of the numerator in (A8). Using (A8), (A6) ; (A4) and (A10) yields:

Combining these two equations yields

@q i + @x i (:) @q j @r j @e i ; so that 0 (E ) i = @x i @q i + @x i @q j @r j @e i @x i @q i : Simplifying this expression yields (28).

C Comparative statics

Consider the FOCs (30) and (31) and let us de…ne i , i = 1; 2as follow:

where q 1 = r 1 + k + e 1 and q 2 = p 2B + e 2 . De…ne

and

which represent respectively the marginal pro…t of a postal operator 1 and the integrated …rm 2B. We have

for i = 1; 2. Di¤erentiation of (A16) and (A17) with respect to r 1 , p 2B ; e 1 and e 2 yields

Using Cramer's rule, one has

where SOC > 0. Using (A29), (A31) ; (A25) and (A31) yields:

so that the sign of dr 1 =de 2 is given by the sign of 0 2 .

D Proof of equations (34) and (35)

Demands are implicitly de…ned by

The FOC's wrt. r 1 and p 2B are

1 1 e 1 C 0 (x 1 ) @x 1 @q 1 = 0; (A34)

Recall that

so that (A34) and (A35) yield

Substituting (A36) and (A37) into (8) and (9) and using (7) yields

x 1 = @x 1 @q 1 1 (e 1 ) + 1 + 1 e 1 + C 0 (x 1 ) + k + e 1 = k + C 0 1 (x 1 )

1 (e 1 ) + e 1 0 (E );

x 2 = @x 2 @q 2B 2 (e 2 ) + k + 2 + 2 e 2 + C 0 (x 2 ) + e 2 = k + C 0 2 (x 2 ) 2 (e 2 ) + e 2 0 (E );

which after some simpli…cation yields

x 1 = @x 1 @q 1 + 1 + 1 e 1 + e 1 = e 1 0 (E );

x 2 = @x 2 @q 2B + 2 + 2 e 2 + e 2 = e 2 0 (E ):

x 2 x 2 = q 2 + e 2 0 (E) 2 :

(A39)


Carole Adam

Cédric Lauradoux

A debate game about the use of AI during the COVID crisis

Keywords: Serious game, Artificial Intelligence, COVID-19, education 1For instance, Singapore

A serious game for debating about the use of Artificial Intelligence during the COVID-19 pandemic

Carole Adam, Cédric Lauradoux

INTRODUCTION

Crisis situations are often associated with restrictions of liberties and invasion of privacy, in the name of public safety. Many governments order mandatory evacuation or travel ban during floods, communication surveillance and control following terrorist attacks, or declare a "state of emergency" to provide their police forces with more powers to respond to the emergency situation. More recently during the COVID-19 pandemic, governments around the world have used the "state of health emergency" to justify lock-downs, curfews, contact tracing, sanitary passport, or mandatory vaccination. Surveillance has always existed, but new technologies enabled by Artificial Intelligence (AI), such as facial recognition or social networks, have changed its scale. We are now facing mass surveillance of billions of individuals. Besides, governments may be tempted to re-use technologies, initially adopted as emergency counter-measures against the pandemic, to serve other purposes1, or to extend the duration of new rules beyond the end of the original crisis. The drifts can have serious consequences, with China setting up a social credit system [START_REF] Liu | Multiple social credit systems in China[END_REF], or some countries imposing the need for a COVID-19 vaccinal pass despite the inequalities it creates [START_REF] Tanner | Vaccine Passports Done Equitably[END_REF][START_REF] Gostin | Digital Health Passes in the Age of COVID-19: Are "Vaccine Passports" Lawful and Ethical?[END_REF][START_REF] Kofler | Ten reasons why immunity passports are a bad idea[END_REF]. This pass has been required to enter most countries, to access leisure places, to travel, to work (e.g. healthcare workers in France, or any workplace in Italy), or even in some countries to use some more essential services 2.

AI technologies can offer many benefits, but we believe that it is essential for citizens to also understand their impact on surveillance, their potential biases and errors, in order to be able to make informed choices about what they accept and what they refuse. To this end, we have designed a serious game, where participants take on the roles of citizens with various profiles in a (not so) futuristic town, and debate about the new technologies that could be adopted in their town. This game is part of a wider series of debate games about different societal applications (health, transport) of AI technologies. This debate game is targeted at students in secondary school and high school, and is followed by a debriefing allowing participants to share experience and to learn about the real life implications of what they discussed in a simplified manner. This paper is structured as follows: we start by discussing the need for educating the general public about AI, and how serious games can help. One section is dedicated to the debate game, scenario, roles taken by the participants, and different AI solutions being discussed. Another section is dedicated to the debriefing session after the game, which is key to learning. Finally, one section discusses some first return of experience with groups of different ages. Finally, we conclude and discuss future prospects.

REQUIREMENT FOR EDUCATION

Education to AI

Educating the population is crucial at any time and even more during COVID-19, where the lack of information, or disinformation spreading on social networks, can have serious consequences. Indeed, conspiracy theories and other fake news spread fast, and can increase vaccine hesitancy or rejection [START_REF] Nieves-Cuervo | Infodemic: fake news and COVID-19 mortality trends in six Latin American countries[END_REF][START_REF] Lu | COVID-19 vaccine hesitancy: The effects of combining direct and indirect online opinion cues on psychological reactance to health campaigns[END_REF], with detrimental consequences on health. Besides, even though Artificial Intelligence can help fight COVID-19, there are also dangers to be avoided: [START_REF] Naudé | Artificial intelligence vs COVID-19: limitations, constraints and pitfalls[END_REF]) warns about the requirement for "a careful balance between data privacy and public health". Everybody needs to be aware of the potential benefits and dangers of Artificial Intelligence, whether in the context of the pandemic or in general. This requirement for educating people about AI is particularly highlighted in the latest UNESCO report (UNESCO 2021). This education should not concern only the underlying technologies, but also the value and usage of personal data, and the ethical implications of AI technologies.

"because living in digitalizing societies requires new educational practices, ethical reflection, critical thinking, responsible design practices and new skills, given the implications for the labour market, employability and civic participation" [p.18]. "Public awareness and understanding of AI technologies and the value of data should be promoted through open and accessible education, civic engagement, digital skills and AI ethics training [...] so that all members of society can take informed decisions about their use of AI systems and be protected from undue influence" [p.24]. "Member States should promote general awareness programmes about AI developments, including on data and the opportunities and challenges brought about by AI technologies, the impact of AI systems on human rights and their implications, [...] accessible to non-technical as well as technical groups. Member States should develop [...] AI ethics curricula for all levels, and promote cross-collaboration between AI technical skills education and humanistic, ethical and social aspects of AI education." [p.33]

Serious games

With the goal of involving the population as a whole in learning about AI and its use during the COVID-19 crisis, we believe that serious games [START_REF] Crookall | Serious games, debriefing, and simulation/gaming as a discipline[END_REF]) can be a powerful tool. Serious games have been successfully used in various fields: educating the population about appropriate behaviours in case of natural disasters, e.g. floods [START_REF] Rebolledo-Mendez | Societal impact of a serious game on raising public awareness: the case of FloodSim[END_REF][START_REF] Taillandier | Games ready to use: A serious game for teaching natural risk management[END_REF]; raising awareness about climate change and possible actions [START_REF] Wu | Climate change games as tools for education and engagement[END_REF]; training medical and surgical skills [START_REF] Graafland | Systematic review of serious games for medical education and surgical skills training[END_REF] or communicative skills of future doctors [START_REF] Jackson | Teaching communication skills using role-play: an experience-based guide for educators[END_REF]; or more recently explaining the pandemic and sanitary measures to improve their acceptability [START_REF] Cottineau | Understanding the current COVID-19 epidemic: one question, one model[END_REF].

Serious games do not need to be computerised, and we use this term to refer to any learning game, that uses playful elements to reach a pedagogical goal. There exists various forms of serious games, from computer simulations [START_REF] Taillandier | Games ready to use: A serious game for teaching natural risk management[END_REF], to board games or card games [START_REF] Wu | Climate change games as tools for education and engagement[END_REF], interactive narratives, role-playing games [START_REF] Jackson | Teaching communication skills using role-play: an experience-based guide for educators[END_REF], or debates [START_REF] Simonneaux | Role-play or debate to promote students' argumentation and justification on an issue in animal transgenesis[END_REF]. Given our stated goal of involving the general population, we designed a tabletop game that can be played by anybody regardless of their education, without a computer. Besides, our goal is to develop argumentation skills in future citizens, to enable them to make informed choices. We therefore propose a serious game in the form of a role-playing debate; the design of our game is explained in the following section.

OUR SERIOUS GAME: AI AGAINST EPIDEMIC IN WAFER CITY

Game design process

Our game is part of a larger series of debate games about AI in various fields, developed by Arbre des Connaissances (ADC)3, a scientific mediation association dedicated to opening science towards citizens. These games all take place in the same virtual (more or less futuristic) town, called Wafer city, an average size city with one million citizens. Half of the population is living in the town centre, the other half resides in suburban or rural areas. In each game of the series, a different issue is raised to the municipal council, played by the game participants. The first two episodes of the series were dedicated to AI in transport (Oct. 2018) and AI in health (Feb. 2019). The episode described here was developed by the two authors with the help of two members from the ADC, over about 1 year starting in February 2021, through to first experiments in October 2021, and until the official release in March 2022.

Game context

In our game, Wafer city is threatened by an epidemic. Each citizen of the city has a digital medical record (containing analysis results, current treatments...) managed by the city and available to its policy makers, who must take the best possible measures in order to limit the epidemics spread while addressing the following societal issues:

• Lockdown rules are considered too strict and prejudicial to mental health. It is critical to find measures that are not too restrictive for the population but still effective against the epidemic.

• The violation of rules by a few citizens could jeopardise the epidemic control strategy, thus threatening the entire population. It is therefore essential to effectively enforce sanitary restrictions, without overworking police officers by adding up to their usual missions. Besides, constraining rules might not always be well accepted and effort will be needed to prevent the deterioration of relationships between police and citizens.

• Asymptomatic people could unknowingly spread the epidemic, making it insufficient to test and quarantine only symptomatic people. However, it will be difficult to impose restrictions on healthy people who do not feel concerned. Sanitary restrictions should be adapted to the citizens' health status.

The context description purposely never mentions the name of the virus responsible for the epidemic in Wafer city, and avoids any allusion to COVID-19. Indeed, the game aims at discussing surveillance enabled by AI in a broader context, and should stay topical even after the end of the current pandemic. Besides, we also wanted to take some distance from a very sensitive context, as the COVID-19 epidemic is not over yet.

Sowana

The Sowana company is specialised in Artificial Intelligence and has previously worked with the town on other topics, such as public transportation or health. Sowana has answered the call for proposals of Wafer city regarding the epidemic with three solutions: Eye'Wana, Wana'Like and Wana'Pass, detailed below.

Eye'Wana

Eye'Wana is based on video-surveillance to ensure that sanitary rules are respected equally by all citizens at all times. It promises to unload police forces while avoiding human biases: everybody has the same risks of being controlled and fined when not respecting the rules. This solution is based on three building blocks: (i) a network of CCTVs and a fleet of drones collect videos and images from public places, (ii) computer vision algorithms extract faces from these pictures, and (iii) facial recognition algorithms identify the individuals from their face. Eye'Wana can detect various violations of sanitary rules (failure to wear a mask or to respect physical distancing; violation of curfew or lockdown; etc), identify the author, and notify them of the subsequent fine they have to pay.

This solution therefore answers the need for equality in front of the law, but at the cost of great intrusion into people's privacy, since it is tracking their every move.

Wana'Like

Wana'Like is a free smartphone application to help citizens avoid crowded areas where the risk of contamination is higher. Sowana maintains a list of recommended places, checks if they respect the sanitary protocol, and can ban them if contaminations on their grounds are reported. The application analyses the user's interests from their online activity (social media posts, requests on the Sowana search engine...) to create a user profile. It also uses real-time localisation data to deduce current attendance. By combining this data, Wana'Like can make personalised but safe leisure suggestions, and offers discounts in partner places to further incentivise users to follow the recommendations.

This solution is much less restrictive, but potentially also less efficient. Besides, there are great risks related to commercial use of personal data, loss of privacy, or opinion manipulation. Finally, the question of accessibility to people who do not own a smartphone is also important.

Wana'Pass

Wana'Pass is a health points passport: it analyses the user's health record and data from their sensors (heart rate, temperature...) on a daily basis, to deduce the user's individual health status and risk. It then provides them with a number of points, with users in better health being granted more points, and infected individuals receiving zero. These points will be required to access public places (shops, restaurants, museums, etc), with the riskier places requiring more access points. Each place will need to check and debit the necessary access points; once out of points (or as long as they are infectious), the user cannot enter these places anymore.

This solution aims to answer the problem of equitable rather than equal treatment: it protects people at risk and isolates contagious individuals, while letting healthy people live more normally in order to protect their mental health. However, it poses the question of discriminating and isolating elderly people even more on the pretext of protecting them.

Roles represented in the municipal council

As shown above, the different solutions all have pros and cons, and will be more or less acceptable to different user groups. In our debate game, participants do not play in their own name, but will assume a role as member of a specific group of citizens. The idea of having users play a role other than themselves is not new and is proven to favour perspective-taking [START_REF] Jarvis | Role-playing as a teaching strategy[END_REF][START_REF] Resnick | Diving into complexity: Developing probabilistic decentralized thinking through role-playing activities[END_REF]. We also wanted participants to take distance from their character to keep the debate more peaceful, all the more on a very sensitive topic while the COVID-19 epidemic is still not over. The participants in our game are randomly distributed in 5 small groups of citizens:

• City centre shopkeepers, focus on freedom of action and mobility, make a good living but have little free time;

• Ecologists and alter-globalists, rather young, focused on well-being of all and protection of nature, they favour walking and cycling to commute, and they ask for guarantees before adopting new technologies;

• Elderly people, over 60 years old, retired, focused on keeping their autonomy, can live in or out of town;

• Technology enthusiastic, mainly youngsters, very connected and active online, loving innovation, but with limited income;

• Remote citizens, living outside of town centre, in suburban and rural areas, either to search a better quality of life or lower property prices.

The members of each group will debate together to allocate a total of 5 points to the 3 solutions, keeping in mind the wishes of the role that they represent. Each group will therefore come up with different scores for each solution, which will be put in common and added up in the voting and debriefing phase.

GAME DEBRIEFING

Debriefing is an important part of a serious game and is essential to learning [START_REF] Crookall | Serious games, debriefing, and simulation/gaming as a discipline[END_REF][START_REF] Whalen | All they do is win': Lessons learned from use of a serious game for Circular Economy education[END_REF][START_REF] Dieleman | Games by which to learn and teach about sustainable development: exploring the relevance of games and experiential learning for sustainability[END_REF]. It pursues multiple goals: clarifying concepts manipulated during the game session to improve learning; link the simplified concepts with real-life complexity to ensure that learners can apply their knowledge; and share experiences and reflection between participants. It should be led by an informed moderator with a clear and predefined pedagogical objective in mind. The following paragraphs discuss the debriefing phases of our debate game.

Sharing and debating scores

At the end of the game, each group provides the scores they gave to each solution. The moderator reports the scores of all groups in a table drawn on the blackboard, along with their main arguments for their favourite solutions (see an example on the photo in Figure 3). The solution with the highest total score "wins" this first round of voting. The moderator then triggers a debate between supporters and opponents of the different solutions. For instance, members of one role group that supported a given solution, are asked to try and convince members of another role group that rejected that same solution, and vice versa. If they succeed, the scores on the board can be subsequently updated and the selected solution might even change as a result of this debate (see examples of such scenarios in the return of experience section below).

As recommended by [START_REF] Dieleman | Games by which to learn and teach about sustainable development: exploring the relevance of games and experiential learning for sustainability[END_REF], the debate is supervised by a moderator, who ensures a fair, peaceful and balanced debate between students. Playing a role that does not necessarily match their own opinions also helps students to take some distance with the argument and to speak more freely.

Evaluation scales

To further discuss and compare the different technological solutions offered by AI, the moderator then asks some specific questions in order to guide students to rate solutions on different scales. Some important scales to consider when evaluating AI solutions (inspired by (Castelluccia and Métayer 2020)) include:

• Their efficiency (here against the epidemic): the risk-benefit balance is one key indicator, used by privacy protection agencies to allow use of a technology, and by health institutions before allowing use of a drug;

• Their impact on individuals liberties: how constraining or restrictive are they? How much freedom is sacrificed? Is it worth it? Does it have negative side effects, e.g. on mental health?

• Their impact on privacy: what sort of personal data do they collect, and how sensitive is it? Who gets access to this data? What happens in case of a data leak?

• Their economical and ecological cost: how much will it cost and who will pay for deploying these technologies? What pollution is generated to create, maintain, use and recycle these technologies?

• Their accessibility to all, and the risks of discrimination. Do they ensure strict equality? (i.e. everybody is treated exactly the same) Are they equitable for everybody? (i.e. rules are adapted to everybody)

• Risks of errors and misuses: what risks that these technologies fail? What impact in case of errors? What risk of misuse? Can they be twisted to serve other purposes than their initial goal? With what consequences?

Contextualisation

To link back to reality, the moderators finally illustrate how the different virtual solutions discussed during the game actually relate to very real solutions that are already implemented in some countries.

• Technologies similar to Eye'Wana were used in China [START_REF] Chun | In a time of coronavirus, China's investment in AI is paying off in a big way[END_REF], where a large CCTV cameras network with drones and thermal cameras, complemented with facial recognition, was deployed to implement social control during the COVID-19 pandemic. But drones have also been experimented in France to monitor the beaches of Nice during the lockdown4.

• Wana'Like shares many similarities with social networks, that use recommendation algorithms to make personalised suggestions to the user. These already raise many problems of conflict of interest since they aim to maximise the time spent online by the user, even at the expense of their (mental) health [START_REF] Wells | Facebook knows Instagram is toxic for teen girls, company documents show[END_REF]).

• Wana'pass can be viewed as the result of the progress of medical AI (Petropoulos 2020) combined with China's Social credit system [START_REF] Shen | Social credit system in China[END_REF][START_REF] Liu | Multiple social credit systems in China[END_REF]. It can also be considered as an evolution of the health or vaccinal passport already deployed in many countries, raising discrimination problems due to unequal access to vaccines [START_REF] Tanner | Vaccine Passports Done Equitably[END_REF][START_REF] Gostin | Digital Health Passes in the Age of COVID-19: Are "Vaccine Passports" Lawful and Ethical?[END_REF][START_REF] Kofler | Ten reasons why immunity passports are a bad idea[END_REF].

These examples illustrate very concretely the potential dangers of a drift from useful to forceful use of AI, and help the students take out the intended message that they are all concerned by AI and its use.

RETURN OF EXPERIENCE

This game was first played with 6 groups from 3 high school classes during a national science fair (for a total of 103 students), as a first real-life test. It was later tested with around 80 students from an engineering school.

Game material

The game material5 comprises the following elements:

• Cards describing the roles, one different card to be distributed to each group;

• A sheet explaining the agenda of the municipal council, with the problems at hand;

• One sheet per solution, that provides the marketing argument by Sowana, some technical details about the AI beneath, and a testimony by a citizen that is designed to raise some first interrogations.

• A moderator guide aimed at the teachers who will supervise the game. This guide contains some more technical background, useful definitions, links to additional documentation, questions to feed the debate, and information about some similar but real-life solutions to present during the debriefing.

These elements are provided during the sessions we organise, but they can also be printed by any teacher willing to play the game with their students.

Game setup

During the science fair, each session was played with a group of around 15-17 students, distributed in the 5 role groups, plus one of their professors present either as an observer or as a participant. The engineer school session was played with all 80 students together, distributed in 10 groups (2 per role). Each session lasted for 1.5 hours and was supervised by 2 moderators who facilitated discussions while staying neutral, i.e. without orienting them or making suggestions.

The pedagogical sequence is as follows:

1. The session starts with the moderators providing a brief introduction about AI, some definitions, and presenting the context of the game and the 5 roles represented in the municipal council.

2. The students debate the pros and cons of each solution in turn, within their role group.

3. Each group allocates a total of 5 points to the 3 solutions.

4. Each role group orally provides its scores and arguments that are reported on the board.

5. The winning solution is announced, and the results are discussed and debated, which might change the results.

6. The moderators provide some context about which similar solutions already exist in real life.

7. The high school teacher takes home some documentation and references to deepen the subject with their students in class later.

Example debate

With one group, we had a very interesting debate leading to multiple changes of the selected solution. After the first round (as shown in Table 2) Wana'Pass was shortly winning with 10 points, followed by Eye'Wana with 8 points, and Wana'Like with 7 points. We then guided a debate between students favouring the different solutions, and Since the elderly people group was completely opposed to Wana'Pass (that would most probably grant them very few points to go out), they were asked to try and convince other groups to not choose this solution. They argued that Wana'Pass was inequitable, and convinced shopkeepers to move 1 point from Wana'Pass to Eye'Wana, and Techno-addicts to move 1 point from Wana'Pass to Wana'Like. After that second round, EyeWana was shortly ahead with 9 points, the other solutions scoring 8 points each.

Eye'Wana

Remote people were then asked to provide their arguments against Wana'Like, to which they had given 0 point. They argued that this application could manipulate its users. As a result, elderly people and central shopkeepers removed 1 point to Wana'Like and moved it to Eye'Wana, while ecologists moved 1 point from Wana'Like to Wana'Pass. Wana'Like now scored only 5 points, Wana'Pass 9 points, and Eye'Wana moved ahead with 11 points.

Finally, techno-addicts fiercely opposed to Eye'Wana (for its infringement of liberties, and because their lower income meant more sensitivity to fines) realised they could change the result: they moved 4 points from their favourite but losing solution (Wana'Like) towards their second option Wana'Pass, to prevent Eye'Wana from winning. Interestingly, it is a rare complete loss for Wana'Like (1 point), and the only win for Wana'Pass.

Quantitative results

We consider here only the sessions played during the October 2021 science fair with 6 high school groups (103 students), who are more representative of the target public for our debate game. The results (see Table 4) are:

• Wana'Like was selected three times, mostly because it provides financial advantages and is less constraining than the other solutions.

• In another session, Eye'Wana and Wana'Like received the same number of votes. Wana'Pass was rejected for discriminating the elderly.

• Eye'Wana was selected once because it was considered easier to deploy (no need for a smartphone) and because it enforces equality. In all other sessions, it was judged too intrusive and rejected fiercely.

• Wana'Pass won only once, after the interesting debate summarised above.

Wana'Like Wana'Pass Eye'Wana #Selections 4 1 2

Qualitative feedback

We got a general positive feedback from all the students and their professors. In this section, we discuss some specific comments made by the players after the different sessions. This highlights the importance of the debriefing phase that allows such exchanges with participants, where they take some distance from the events debated in-game.

Link with COVID: despite our efforts to create a "virtual" town and epidemic, most students immediately referred to "COVID" in their discussions. One student mentioned they were against the COVID vaccine, which proved the importance of maintaining some distance from the current context in order to ensure a peaceful and targeted debate. However, this occurred only during debriefing, and did not influence debates since they had to stick to their roles. Besides, we believe this link will attenuate with time as the epidemics fades, while our game will stay topical.

Assumption of infallibility: students generally assumed that the proposed technologies were infallible, and as a result did not consider the harmful impacts of an error. This confirms the need to teach the basics of AI as well as its potential for biases and errors. Knowing how the algorithms work is required to understand how they could also fail.

Safety vs freedom: students focused much more on protecting their freedom than on efficiently fighting the virus. Even though the debates did mention the efficiency of the offered solutions, it came after arguments of loss of privacy or freedom of movement, and actually after any other argument. This might not be surprising in an age group that often does not feel directly concerned by the health risk. It also shows a lack of focus on efficiency in our game instructions. We have since then improved that point by asking participants explicitly to compare the solutions on the different scales listed above, including their efficiency. This involves discussing whether they prefer to accept a very constraining (and efficient) solution for a short time, or a less constraining (but less efficient) solution that will probably need to be maintained for a longer period of time.

Soft and hard surveillance: while protecting their freedom and privacy, most students were either unaware of, or fatalist, regarding the surveillance already exerted on them by social networks algorithms. Most students considered that the most intrusive applications were Wana'Pass due to the use of medical data, or Eye'Wana because it films people permanently. They completely underestimate the risks associated with recommendation algorithms, since they already happily disclose large amounts of personal information on social networks. This shows that AI education should also insist on the value of personal data and what can be done with it.

Age target: having played the game with high school students (aged 15 to 18 years old) and engineering students (aged 22 to 24 years old), we got quite different feedback. Comments from participants tend to suggest that the game is better targeted at high school students, who have less technical background about Artificial Intelligence and feel happy to get an opportunity to discuss the current pandemic and its impact on their lives. On the contrary, engineering students felt more disappointed at the focus on ethical implications of AI when they expected to get more technical knowledge. Surprisingly, some also reported as a negative point that the solutions seemed too unrealistic because "none was good". Incidentally, this is precisely the intended take-home message: no AI technology is a perfect solution, and everybody should be aware of the pitfalls before accepting them.

CONCLUSION

In this paper, we presented a serious game in the form of a municipal debate between players distributed in 5 role groups, in order to choose AI solutions to fight an epidemic. Changing perspective and arguing to defend one's ideas is a good exercise for students, and they seem to have learned about Artificial Intelligence and its dangers in the process. This game therefore reaches its objective of educating the population, and the debriefing phase showed crucial in that process.

In the meantime, debriefing the debates with the participants also provided us with interesting insights about how the population thinks of Artificial Intelligence, its benefits and infallibility. This comforted our idea that we need to educate the next generation about these technologies. While AI can certainly help in fighting a crisis such as the COVID-19 pandemic, it is not infallible, and as it is becoming more and more pervasive in our lives, the potential impact of errors is also becoming more serious. It is therefore necessary that everybody knows the basics behind AI algorithms UNESCO 2021 and can make informed choices about their use.

Figure 1 .

 1 Figure 1. Extract of game card distributed to the players to describe Wana'Like -illustration © Marie Jamon

Figure 2 .

 2 Figure 2. Extract of game cards describing two of the roles. Illustration © Marie Jamon

Figure 3. Game board

	Solution	S1 Eye'Wana	S2 Wana'Like	S3 Wana'Pass
	Alter-glob	0	3 (+) discounts	2 (-) unfair
			(+) normal life
		(-) privacy	(+) control over data (-) mental health
	Shops	4 (+) stay open	0 (-) lose clients	1 (-) lose clients
	Remote	1	3 (-) privacy	1
			(+) discounts	(-) unfair
	Techno	2 (+) fair, jobs	2 (+) freedom	1
			(+) discounts
	Elderly	3 (+) health	2 (-) no smartphone	0 (-) autonomy
		(+) live on		(-) privacy
	TOTAL	10	10	5

Table 1 . Transcription of the game board

 1

Table 2 . Example of blackboard after one round of discussion in one game session: scores (S), positive (blue) and negative (red) arguments.

 2

	Wana'like	Wana'Pass

  Table 3 illustrates the evolution of total scores over the four subsequent rounds of debate.

	Round Eye'Wana Wana'like Wana'Pass
	1	8	7	10
	2	9	8	8
	3	11	5	9
	4	11	1	13

Table 3 . Evolution of the results of the game after four rounds.

 3

Table 4 . Number of wins per solution over 6 sessions (the total is 7 since there was a draw in one session)

 4

3Arbre des Connaissances website: https://arbre-des-connaissances-apsr.org/ <CoRe/WiP/Practitioner> Paper -<Track Name> Proceedings of the 19th ISCRAM Conference -Tarbes, France 2022

<CoRe/WiP/Practitioner> Paper -<Track Name> Proceedings of the 19th ISCRAM Conference -Tarbes, France 2022

6The game is available for download on their website at https://jeudebat.com/jeux/lintelligence-artificielle/ <CoRe/WiP/Practitioner> Paper -<Track Name> Proceedings of the 19th ISCRAM Conference -Tarbes, France 2022

ACKNOWLEDGEMENTS

The authors would like to thank the Arbre des Connaissances association, in particular Clara Fruchon and Camille Volovich, for their support along the entire game design process and with its distribution6; as well as Marie Jamon for illustrating the game material and booklet. The authors would also like to thank the scientific mediation team of Inria Rhône-Alpes, in particular Florence Polge-Cohen, for financial support and their help with organising the play sessions at Fête de la Science. Finally, we thank all students and teachers who participated in the game sessions.

://www.cnbc.com/


Arnaud Blouin

Jean-Marc Jézéquel

Interacto: A Modern User Interaction Processing Model

ACM Reference Format: Arnaud Blouin and Jean-Marc Jézéquel. 2022. Journa First: Interacto: A Modern User Interaction Processing Model. In Proceedings of The 44th International Conference on Software Engineering (ICSE 2022). , 2 pages.

EXTENDED ABSTRACT

"Anytime you turn on a computer, you're dealing with a user interface" [START_REF] Mijailovic | A Retrospective on User Interface Development Technology[END_REF]. User interfaces (UIs), and the user interactions they supply, pervade our daily lives by enabling users to interact with software systems. The user interactions provided by a UI form a dialect between a system and its users [START_REF] Green | A Survey of Three Dialogue Models[END_REF]: a given user interaction can be viewed as a sentence composed of predefined words, i.e. low-level UI events, such as mouse pressure or mouse move. For example, we can view the execution of a drag-and-drop interaction as a sentence emitted by a user to the system. This sentence is usually composed of the words pressure, move, and release, that are UI events assembled in this specific order. The Human-Computer Interaction (HCI) community designs novel and complex user interactions. As explained by [START_REF] Beaudouin-Lafon | Designing interaction, not interfaces[END_REF], "HCI researchers have created a variety of novel [user] interaction techniques and shown their effectiveness in the lab [...]. Software developers need models, methods, and tools that allow them to transfer these techniques to commercial applications." Currently, to use such novel user interactions in software systems developers must complete two software engineering tasks: (i) They must assemble low-level UI events to build the expected user interaction. For example, a developer must manually assemble the events pressure, move, and release to build a drag-and-drop. (ii) They have to code how to process such UI events when triggered by users.

To do so, developers still use a technique proposed with SmallTalk and the Model-View-Controller (MVC) pattern in the 80's [START_REF] Glenn E Krasner | A description of the model-viewcontroller user interface paradigm in the smalltalk-80 system[END_REF]: the UI event processing model, currently implemented using callback methods or reactive programming [START_REF] Bainomugisha | A survey on reactive programming[END_REF] libraries. This model considers low-level UI events as the first-class concept developers can use for coding and using increasingly complex user interactions not supported off-the-shelf by graphical toolkits. The reason is that interacting with classical widgets (e.g., buttons, lists, menus) is usually one-shot: a single UI event, such as a mouse pressure on a button or menu, has to be processed. For more complex user interactions such as the drag-and-drop, the current event processing model exhibits critical software engineering flaws that hinder code reuse and testability, and negatively affect separation of concerns and code complexity:

• the concept of user interaction does not exist, so developers have to re-define user interactions for each UI by re-coding them using UI events; • the model does not natively support advanced features, such as cancellation (undo/redo), event throttling, or logging; • developers mix in the same code the assembly of UI events and their processing, leading to a lack of separation of concerns; • the use of callbacks to process UI events (1) can lead to "spaghetti" code [START_REF] Myers | Separating Application Code from Toolkits: Eliminating the Spaghetti of Call-backs[END_REF][START_REF] Oney | Interstate: Interaction-oriented language primitives for expressing GUI behavior[END_REF]; ( 2) is based on the Observer pattern that has several major drawbacks [START_REF] Foust | Generating Reactive Programs for Graphical User Interfaces from Multi-way Dataflow Constraint Systems[END_REF][START_REF] Maier | Deprecating the Observer Pattern with Scala[END_REF][START_REF] Salvaneschi | An Empirical Study on Program Comprehension with Reactive Programming[END_REF][START_REF] Salvaneschi | Towards reactive programming for object-oriented applications[END_REF]; (3) can be affected by design smells [START_REF] Blouin | User Interface Design Smell: Automatic Detection and Refactoring of Blob Listeners[END_REF]; To mitigate these flaws, we propose Interacto as a high level user interaction processing model, depicted by Figure 1. Interacto reifies user interactions and UI commands as first-class concerns. Interacto makes it easy to design, implement and test modular and reusable advanced user interactions, and to connect them to commands with built-in undo/redo support.

To demonstrate its applicability and generality, we developed two implementations of Interacto: Interacto-JavaFX with Java and JavaFX [15], a mainstream Java graphical toolkit; Interacto-Angular with TypeScript [START_REF] Bierman | Understanding Type-Script[END_REF] and Angular [8], a mainstream Web graphical toolkits. Both implementations take the form of a fluent API (Application Programming Interface) [START_REF] Fowler | Domain-specific languages[END_REF]. The following TypeScript code is an example of how Interacto-Angular works to use a multi-touch interaction for drawing a rectangle in an SVG canvas. Interacto provides a large set of predefined user interactions, such as the multi-touch interaction (with two touches) selected Line 1. Then, the developer specifies the UI command the execution of the user interaction may produce (Line 2), here the command DrawRect (coded by the developer). The developers then specifies the graphical component on which the user interaction will operate, here the SVG canvas (Line 3). While the user interaction is running (i.e., while the user is performing a multi-touch), the command is updated using the current interaction data (Line 5). The execution of the command is constrained by a predicate (Line 7). Listing 1: Using a multi-touch interaction for drawing a rectangle in an SVG canvas with Interacto-Angular 1 : A user interacts with an interactive object 𝑜 1 of the user interface.

2 : The interactive object then triggers a UI event processed by a running user interaction 𝑖𝑛𝑡𝑒𝑟 1 .

3 4 : Controllers contain Interacto bindings that turns user interaction executions into UI commands. 5 : The running Interacto binding executes the ongoing UI command to modify the state of the system.

Using Interacto, a developers focuses on transforming the execution of a user interaction into UI command instances.

We evaluate Interacto interest:

• on a real world case study: the development of LaTeXDraw, an open-source highly interactive vector drawing editor for L A T E X, downloaded 1.5 k times per month and available on more than 10 Linux distributions. • with a controlled experiment with 44 master students, comparing it with traditional UI frameworks.

The long term experiment shows that the proposal scales for one very interactive and widely-used software system. The experiment conducted with students exhibited several pros and cons of the proposal. The use of Interacto is beneficial, in terms of time and correctness, for students to add undo/redo features to the application. The use of predefined user interactions is also beneficial in terms of time and correctness. However, an entrance barrier to use correctly Interacto may exist.

MAIN CONTRIBUTIONS INTRODUCED IN THE JOURNAL PAPER

Our work makes the following software engineering contributions:

• We propose a novel model, called Interacto, for processing UI events. This model overcomes the growing limits of the current UI event processing model. • We provide Java and TypeScript implementations of this model to target the JavaFX and Angular UI toolkits. Both implementation are open-source and available on NPM and Maven repositories 1 . Source code is freely available on Github 2 . • We detail a real world use case that consists of a the development of highly interactive open-source software system using Interacto. • We conducted an experiment with 44 master students that exhibited several benefits to using Interacto.

ICSE 2022 ,

 2022 May 21-29, 2022, Pittsburgh, PA, USA Author version.

Figure 1 :

 1 Figure 1: Behavior of the proposed user interaction processing model (in bold what differs from the standard UI processing model):

https://www.npmjs.com/package/interacto https://search.maven.org/search?q=interacto

https://github.com/interacto/

POINTER TO THE JOURNAL PAPER

The paper called "Interacto: A Modern User Interaction Processing Model" has been accepted for publication at the IEEE Transaction of Software Engineering Journal on May, the 20th 2021 [4]. It is now available at the following link: https://ieeexplore.ieee.org/document/9440800 We also provide a preprint at the following address: https://hal.inria.fr/hal-03231669/