Mohamed Amine Berkal

Quentin Palas

Estelle Ricard

Christine Lartigau-Dagron

Luisa Ronga

Jean-Jacques J Toulmé

Corinne Parat

Corinne Nardin
email: corinne.nardin@univ-pau.fr

Glyphosate-exonuclease interactions: reduced enzymatic activity as a route to glyphosate biosensing

Keywords: Glyphosate, oligonucleotide switching structures, enzymatic inhibition, fluorescence spectroscopy, biosensing 2

N-phosphonomethyle-glycine (glyphosate) is the most widely used pesticide worldwide due to its effectiveness in killing weeds at a moderate cost, bringing significant economic benefits. However, owing to its massive use, glyphosate and its residues contaminate surface waters. On site, fast monitoring of contamination is therefore urgently needed to alert local authorities and raise population awareness. We report here the hindrance of the activity of two enzymes, the exonuclease I (Exo I) and the T5 exonuclease (T5 Exo) by glyphosate.

These two enzymes digest oligonucleotides into shorter sequences, down to single nucleotides.

The presence of glyphosate in the reaction medium hampers the activity of both enzymes, slowing down enzymatic digestion. We show by fluorescence spectroscopy that the inhibition of ExoI enzymatic activity is specific to glyphosate, paving the way for the development of a biosensor to detect this pollutant in drinking water at suitable detection limits, i. e. 0.6 nM.

INTRODUCTION

Pesticides and herbicides are essential to agriculture to increase crop yields and to provide sufficient food. Since their launch in the last century, they enabled substantial economic benefits and are thus widely used. [1] Organophosphates are particularly used worldwide since they target a wide variety of pests and weeds, enhancing agricultural production. [2] N-phosphonomethyleglycine (glyphosate) is the most widely used organophosphorus pesticide due to its efficiency in killing weeds. It was introduced by Monsanto in 1970 under the name Roundup. [3] Glyphosate inhibits the 5-enolpyruvylshikimate-3-phosphate synthase enzyme (EPSPS), which is responsible for the biosynthesis of aromatic amino-acids, causing cessation of growth and plant death. [START_REF] Amrhein | ACTION OF THE HERBICIDE GLYPHOSATE[END_REF] Due to its high solubility in water, glyphosate residues accumulate in surface waters causing serious problems in the environment and human health, e. g. the irreversible inhibition of the activity of the acetylcholinesterase enzyme has detrimental effects on the central nervous system. [START_REF] Bera | [END_REF] Besides, several studies demonstrated that glyphosate could affect cell cycle regulation, inhibit steroid hormone secretion in men, and also cause effects adverse to animals and to aquatic vegetation. [6,7] The carcinogenicity of glyphosate remains however under debate. An International Agency for Research on Cancer (IARC) report in 2015 classified glyphosate in category 2A, i.e. "probably carcinogenic for humans". [8] Two years later (2017), the European Food Safety Authority (EFSA) published a report concluding that glyphosate is not likely to be carcinogenic to humans. [9] Since glyphosate carcinogenicity remains to be confirmed, it is therefore regularly evaluated by national and international regulatory agencies. European Directive 98/83/EC set a maximum residue limit (MRL) for each pesticide in drinking water, including glyphosate, at 0.1 µg L -1 . [10] Furthermore, the tolerable daily intake (TDI) of glyphosate under chronic oral exposure and the acute reference dose are estimated at 0.5 mg kg -1 body weight per day. [START_REF]Glyphosate : l'Anses fait le point sur les données de surveillance[END_REF] Although the presence of glyphosate in different waters is already regulated, its low molecular weight, high polarity, and lack of fluorophore or chromophore groups rendered its detection difficult up to now. [12,13] The main means of analysis of glyphosate are therefore chromatographic methods coupled with mass spectrometry (MS), including high pressure liquid chromatography (HPLC), ion exchange chromatography (IEC), ion chromatography (IC) and gas chromatography (GC). [14][15][16] These conventional techniques are sensitive and highly specific, allowing trace analysis of pesticides in environmental samples. However, they require highly qualified operators. Besides that, samples need to be pre-treated and then analyzed in sophisticated off-site laboratories offering these expensive techniques. This mode of detection is thus unsuitable for the survey of flowing waters.

They require on site analysis at a suitable frequency to detect a possible pollution peak to rapidly alert the authorities and population. Most of the technologies used for the detection of glyphosate require high-end low throughput equipment and resources. None of them are adequate for field detection. [17] Increasing efforts are thus devoted to finding sensitive and selective alternative ways to detect glyphosate on site. Biosensors, combining of a biological sensing element and a transducer, are an appealing alternative to conventional laboratory-based methods. Specificity and selectivity are ensured by the biological sensing elements, which could be antibodies, enzymes, aptamers or even cells, [18] while sensitivity is provided by the transducer, which converts the biological interaction into an electrical signal allowing detection of the analyte.

The potential selectivity and sensitivity of optical and electrochemical based biosensors make them attractive for the detection of pesticides. [19][20][21][22] Methods include absorption (UV-Vis) spectroscopy, [23], [24] fluorescence spectroscopy, [25], [26] photoluminescence assay, [27], [28] chemiluminescence assay, [29], [30] surface-enhanced Raman scattering (SERS), [31], [32] potentiometric sensing, [33] impedence sensing, [34], [35] and amperometry. [36], [37] Only a few of these biosensors developed to detect pesticides, have been applied to glyphosate (Table S1) [38][39][40][41][42] . Moreover, none had sensing elements suitable for in situ detection of glyphosate.

Our main objective is thus the identification of a suitable sensing element to develop in the future an electrochemical aptasensor. [43] This biosensor would thus be composed of an aptamer sensing element and of an electrochemical detection platform. Aptamers are oligonucleotide switching structures that form a complex with the target, e.g. small organic molecules, proteins or even cells, with very high affinity and specificity. [44,45] The interaction between glyphosate and its aptamers described in the literature [41,[START_REF]Dna aptamer binding to glyphosate with Specificity[END_REF][START_REF]Aptamer specifically bound with glyphosate and application[END_REF] was thus tested using enzymatic digestion by the T5 exonuclease (T5 Exo) and exonuclease I (Exo I). [START_REF] Alkhamis | [END_REF] The activity of these enzymes is widely used to demonstrate the specific interaction between a ligand and an oligonucleotide switching structure. [49][50][51][52][53] The enzymes digest the aptamer into shorter oligonucleotides and/or mononucleotides. In the presence of the target, an aptamer/target complex is formed which leads to a decrease of enzymatic activity allowing detection of the interaction.

As reported below, we demonstrate the specific inhibition of Exo I and T5 Exo enzymatic activity in a specific buffer by glyphosate, with high potential for the development of an efficient and specific biosensor of glyphosate in the future.

Results and Discussion

2.1.Interaction of Aptamer Candidates with Glyphosate as Assessed by T5 Exo Enzymatic

Digestion followed by Polyacrylamide Gel Electrophoresis (PAGE)

Conventional PAGE [START_REF] Alkhamis | [END_REF] subsequent to T5 Exo digestion was used to assess the interaction between glyphosate and its aptamer candidates. The interaction between glyphosate and potential aptamer candidates reported in the literature, GLY1, [41] GLY2 [START_REF]Dna aptamer binding to glyphosate with Specificity[END_REF] and GLY3, [START_REF]Aptamer specifically bound with glyphosate and application[END_REF] was first tested. In parallel to the use of GLY2 and GLY3 glyphosate specific aptamer candidates, two negative controls, SCR GLY2 and SCR GLY3, were designed in order to further validate the specificity of GLY2 and GLY3 against glyphosate. The main conformations of the aptamers and negative controls are shown in Figure S1. No negative control was designed for the GLY1 aptamer since it is specific not to glyphosate but to two other pesticides, i.e. trichlorfon and malathion. [41] The negative control sequences have the same number of nucleic acid bases and the same GC content as GLY2 and GLY3, but were designed with a random nucleic acid order resulting in a new conformation that prevents target recognition.

Reduced enzymatic activity in the presence of glyphosate was observed with the GLY1 and GLY3 candidates, as well as for the SCR GLY3 negative control (Figure 1). GLY2 and SCR GLY2 (Figure S2) yielded no reduction in enzymatic activity in the presence of glyphosate, throughout the digestion time tested. These results suggest that GLY1 and GLY3 are probably aptamers of glyphosate since a reduction in enzymatic activity is observed, potentially due to the formation of a complex between the aptamer and glyphosate, whereas with this method GLY2 showed no interaction with glyphosate. As expected the SCR GLY2 negative control showed no interaction with glyphosate. However, the negative control SCR GLY3, which should not interact with glyphosate, showed the opposite. To conclude on a potential interaction between glyphosate and SCR GLY3, a rapid detection approach was thus needed to replace PAGE which is a tedious method as it requires several cumbersome steps, namely the preparation of the gel plate, the migration step, the disassembly of the gel plate, the staining step and finally reading of the fluorescence. In addition, enzymatic digestion by T5 Exo is relatively slow (complete digestion of SCR GLY3 is achieved in about ten hours or more, Figure S3) and doesn't allow quantification.

2.2.Quantitative Analysis of the Interaction between Glyphosate and its Aptamer Candidates as Assessed by Fluorescence Spectroscopy

In order to quantify the percentage of digestion and to shorten the analysis time, we resorted to fluorescence spectroscopy. Assays were carried out first with both GLY3 and SCR GLY3 which clearly demonstrated a decrease in T5 Exo activity in the presence of glyphosate by PAGE.

Different conditions of incubation and digestion were tested using both enzymes, T5 Exo and Exo I (Figure S4). The reduction of the enzymatic activity was confirmed with both GLY3 and SCR GLY3 regardless of the incubation time or of the temperature of incubation and/or digestion tested.

As expected, digestion at 37 °C is more efficient than digestion at room temperature. [START_REF] Alkhamis | [END_REF][54][55][56] Digestion at 37 °C with two hours of incubation between GLY3 or SCR GLY3 and glyphosate at 37 °C was thus selected as the reference condition for subsequent studies of interaction specificity as it provides the best digestion efficiency while enabling differentiation between the two conditions, i.e. with or without glyphosate.

In order to shorten the digestion time needed to clearly exhibit enzymatic activity, the digestion kinetics of GLY1, GLY3 and SCR GLY3 were measured (Figure S5). Near-total digestion (in the absence of glyphosate) was achieved with all candidates in only 30 min, demonstrating the acceleration of enzymatic digestion when combining both enzymes. In what follows, we fix the digestion time to 30 min. Contrary to when PAGE was used, no decrease of the enzymatic activity of GLY1 was observed in the presence of glyphosate. This is explained by the fact that fluorescence spectroscopy measures the total fluorescence in a sample. However, it is the shortest sequence hence low fluorescence.

GLY1 led to the same low fluorescence signal and thus to the same percentage of digestion even in the presence of glyphosate (78% and 82% of digestion, Figure 2). On the contrary, with GLY3 and SCR GLY3, the fluorescence intensity after digestion in the presence of glyphosate is clearly higher (24% vs. 12% digestion) than in its absence (92% vs. 95% digestion, Figure 2) because they are protected against digestion.

As observed in Figure 2, for both GLY3 and SCR GLY3 candidates, decreased enzymatic activity in the presence of glyphosate is observed. Similar to PAGE, fluorescence spectroscopy shows reduced activity of the negative control SCR GLY3 in the presence of glyphosate.

Glyphosate inhibits the activity of the enzyme 5-enolpyruvylshikimate-3-phosphate synthase (EPSPS), [START_REF] Amrhein | ACTION OF THE HERBICIDE GLYPHOSATE[END_REF] and inhibition of both Exo I and T5 Exo enzymes activity cannot be ruled out. EPSPS synthase catalyzes the transfer of the carboxyvinyl portion of phosphoenolpyruvate (PEP) regiospecifically to the 5-OH of shikimate 3-phosphate (S3P), forming 5-enolpyruvoylshikimate 3-phosphate (EPSP) and inorganic phosphate [57] (Figure S6a). Glyphosate however mimics the PEP substrate of the enzyme (Figure S6b) which results in a stable complex of EPSPS.S3P.glyphosate leading to the inhibition of EPSPS. [58][59][60][61][62] A similar mechanism could be proposed to understand the inhibition of Exo I by glyphosate. ExoI breaks PEP phosphodiester bonds (Figure S6c). [63] In the presence of glyphosate, a more stable complex of the enzyme with glyphosate instead of one with its substrate, i. e. oligonucleotides, might preferentially form leading to enzymatic inhibition.

Before concluding on the interaction between glyphosate and SCR GLY3, we however investigated the role of sequence composition and of the buffer on the reduction of enzymatic activity by glyphosate.

2.3.Sequence Composition and Reduction of Enzymatic Activity in the Presence of

Glyphosate

By definition, an aptamer is a unique sequence that recognizes a specific target. If SCR GLY3 is an aptamer specific to glyphosate, it must be unique and none of the sequences selected for this assay should interact with glyphosate.

Several oligonucleotides were therefore tested in the same conditions of digestion than as GLY3 and SCR GLY3, namely GLY1 and GLY2, the AA40 library (which contains about 10 15 unique sequences), and ATZ1, [64] ATZ2 [65] which are aptamers developed against atrazine (Figure 3).

% of digestion

With glyphosate Without glyphosate

2.4.Role of the GLY3 Interaction Buffer in Reduction of Enzymatic Activity

We therefore assessed the role of the GLY3 interaction buffer in enzymatic inhibition by the digestion of both the GLY3 and the AA40 library sequences in HEPES buffer, which is used frequently in the development of aptamers at Novaptech (Figure S7).

Neither showed reduction of enzymatic activity in the presence of glyphosate, and both enzymes are active in the HEPES buffer (90 % digestion). These results clearly confirm that the GLY3 interaction buffer is crucial to the reduction of enzymatic activity.

Although it contains few divalent cations (1 mM of Mg 2+ ) it is essential to enzymatic activity.

Indeed, as reported earlier, Mg 2+ concentrations as low as 10 -2 to 10 -3 mM reduce the activity of Exo I by 10 to 20%. [66] Besides, according to the literature, glyphosate has a chelating effect strongly complexing divalent cations, including Mg 2+ . [67] Thus 1 mM of Mg 2+ could be complexed by 1 mM of glyphosate and reduce enzymatic activity. To rule out this effect, GLY3 was digested in its own buffer with or without glyphosate, but with excess of Mg 2+ cations, i. e. 5 mM (instead of 1 mM) (Figure S8). Enzymatic activity was nevertheless reduced implying that enzymatic inhibition is not related to the cation concentration.

To rule out the effect of monovalent cations (K + and Na + ) on enzymatic activity, different concentration ratios were tested in the GLY3 buffer in the same conditions of digestion (Figure S9a). The first is the same as in which enzymatic activity is not reduced. The same test was performed with the HEPES buffer (Figure S9b).

Thus, monovalent cations do not significantly affect enzymatic digestion. It is rather the Tris buffer component, contrary to HEPES, which plays the main role in the reduction of enzymatic activity.

2.5.Glyphosate as an Inhibitor of Enzymatic Activity

We probed separately the inhibition of either Exo I and T5 Exo by the digestion of a random sequence, SUP000, of comparable length to GLY3 (81 nucleotides vs. 84 nucleotides), in GLY3

and HEPES buffers, but without the incubation step of SUP000 with glyphosate. The enzymes were tested separately in order to evaluate their individual behavior in the two buffers.

Being a random sequence, SUP000 is not expected to interact with glyphosate. Therefore, each enzyme solution was prepared with and without glyphosate and the SUP000 sequence was added at the last stage. The whole set was incubated for 30 min at 37 °C.

As observed in Figure 4, and in the HEPES buffer, neither enzyme reduces activity in the HEPES buffer, with or without glyphosate. In the GLY3 buffer, T5 Exo is already inhibited (20% digestion without glyphosate) compared to the HEPES buffer (90% of digestion without glyphosate). Exo I is active in both buffers. However, this test clearly shows that the presence of glyphosate in the GLY3 buffer inhibits the activity of Exo I.

2.6.Specificity of the Reduction of the Enzymatic Activity

Since its activity is inhibited in the GLY3 buffer, the expected enhancement of digestion by T5

Exo is ruled out and therefore its use discarded from studies reported below. Is the reduction of enzymatic activity specific to glyphosate? Other pesticide molecules, especially the main

% of digestion

With glyphosate Without glyphosate metabolite of glyphosate (AMPA), were tested using SUP000 as the substrate for Exo I: simazine, alachlor, atrazine, atrazine-desethyl, and isoproturon (Figure 5). Slight inhibition is observed in presence of AMPA and simazine, (62% and 68% digestion compared to 80% without pesticide). But only glyphosate induces strong inhibition (≈ 6% of digestion), which means that inhibition is specific to glyphosate.

Conclusion

Here we show that glyphosate inhibits the T5 Exo and Exo I, as quantified by fluorescence spectroscopy. Identification of this oligonucleotide digesting enzyme sensing element paves the way to the future development of a biosensor since the activity is specifically inhibited by glyphosate. The outcomes of this study are of high relevance since exonucleases are human enzymes, especially the Exo I enzyme that is required for 5' and 3' mismatch repair in human, [68] further demonstrating that the mechanisms, consequences and danger to human health of this pesticide should be urgently elucidated.

Experimental Section

4.1.Chemicals and Reagents

All the chemicals and reagents were of analytical grade (> 99%) and used without further

Aptamer name Sequence

GLY1 aptamer [41] 5'-AGC-TTG-CTG-CAG-CGA-TTC-TTG-ATC-GCC-ACA-GAG-CT-3'

GLY2 aptamer [START_REF]Dna aptamer binding to glyphosate with Specificity[END_REF] 5'-CGT-ACG-GAA-TTC-GCT-AGC-AGA-GGG-ATG-GTG-TGG-GTG-GCT-GCG-GCT-ATA-GGA-GCG-TAC-CGGATC-CGA-GCT-CCA-CGT-G-3'

GLY3 aptamer [START_REF]Aptamer specifically bound with glyphosate and application[END_REF] 5'-TGC-TAG-ACG-ATA-TTC-GTC-CAT-CCG-AGC-CCG-TGG-CGG-GCT-TTA-GGA-CTC-TGC-GGG-CTT-CGCGGC-GCT-GTC-AGA-CTG-AAT-ATG-TCA-3'

4.3.Design of Negative Controls (DNA Oligonucleotides)

In order to assess the specificity of interaction of the GLY2 and GLY3 aptamer candidates towards glyphosate, two DNA oligonucleotide negative controls, scrambled GLY2 and scramble GLY3 (SCR GLY2, SCR GLY3), were designed and used with the same buffers as GLY2 and GLY3. Two aptamers developed against atrazine, ATZ1 [64] and ATZ2, [65] the thrombin aptamer, [69] the arsenic aptamer, [70] ssDNA, and the AA40 library sequences (which contains about 10 15 unique sequences) were also used as negative controls (Table S2).

4.4.Experimental Conditions

All incubations between glyphosate and its aptamer candidates, as well as enzymatic digestion, were performed using a thermomixer (Eppendorf, Hamburg, Germany).

Enzymatic digestion was performed at room temperature (~20 °C) and at 37 °C with stirring (240 rpm). In each experiment, the buffers described in Table S3 were used with their corresponding aptamer. All experiments were done in duplicate or triplicate. The standard deviations are presented in the form of error bars. The pH of all buffers was measured with a Seveneasy pH-meter (Mettler Toledo, Columbus, Ohio, USA) and was adjusted using either a 1 M NaOH solution or a 0.1 M HCl solution.

4.5.T5 Exonuclease Digestion and Gel Electrophoresis

The interaction between glyphosate and its aptamer candidates described in the literature was done by T5 Exo digestion prior to PAGE. [START_REF] Alkhamis | [END_REF] The T5 Exo enzyme digests double-stranded and singlestranded DNA sequences in the 5' to 3' direction, down to single nucleotides (Figure S10). The working principle of this method is described in Figure S11. Interaction between the aptamer and its target results in delayed digestion of the oligonucleotide due to the formation of an aptamer/target complex impeding the enzymatic digestion. [49][50][51][52][53] For all digestion assays, 1 µL of a 25 µM aptamer solution is added to 22 µL of interaction buffer containing glyphosate at a final concentration of 1 mM. After incubation between glyphosate and their aptamer candidates in the appropriate conditions (Table S4), 0.5 µL of the T5 Exo enzyme at 10 U µL -1 is added to the reaction mixture (at a final concentration of 0.2 U µL -1 ), and the digestion is started at room temperature under gentle stirring. After each digestion period, 5 µL of the reaction mixture are drawn off and added to 15 µL of loading buffer (75% formamide (v/v), 10% glycerol (v/v), 0. 125% SDS (v/v), 10 mM EDTA and a pinch of xylene cyanol) and then loaded into the wells of a previously prepared denaturing polyacrylamide gel plate (final gel concentration = 15%, see preparation in electronic supplementary information ESI). The samples are separated by gel migration using an EPS-300X electric generator (CBS, Paris, France), under the following conditions: applied voltage U = 750 V, intensity I = 300 mA, power P = 20 W and 1 h10 min of migration time.

The gel plate is dismantled and the polyacrylamide gel is immersed in 100 mL of 0.5X TBE containing 1X SYBR Gold, which is an intercalator binding to DNA by insertion between the DNA bases [71] (the absorption spectrum of SYBR Gold as well as calculations of its molar concentration We followed the protocol reported previously. [START_REF] Alkhamis | [END_REF] 1 µL of a 25 µM aptamer solution is added to 22 µL of interaction buffer containing glyphosate at a final concentration of 1 mM. After incubation between glyphosate and aptamer candidates in the appropriate conditions (Table S4), 1.5 µL of both T5 Exo and Exo I at a final concentration of 0.2 U µL -1 and 3.75 U µL -1 respectively were added to the reaction mixture, and the digestion started at 37 °C under gentle stirring. After each incubation period, 5 µL of the reaction mixture were drawn off and loaded into the wells of a black Fluorescence was measured at 545 nm (excitation at 495 nm) (Tecan Infinite M1000 Pro, Männedorf, Suisse).

Supporting information: Supporting Information is available from the Wiley Online Library.

Figure 1 .

 1 Figure 1. Digestion of the GLY1 candidate (a), GLY3 candidate (b) and SCR GLY3 (c) at 1 µM each by T5 Exo (0.2 U/µL) at room temperature in GLY1 and GLY3 buffers, respectively, after 2 h incubation at 37°C with (+) or without (-) glyphosate (1 mM).

Figure 2

 2 Figure2shows the percentage of digestion obtained with GLY1, GLY3 and SCR GLY3, measured

Figure 2 .

 2 Figure 2. Digestion of GLY1, GLY3 and SCR GLY3 at 1 µM by both enzymes, T5 Exo and Exo I, at 37 °C for 30 min, after 2 hours of incubation at 37 °C with or without glyphosate (1 mM) in GLY3 buffer.

Figure 3 .

 3 Figure 3. Digestion of different oligonucleotides at 1 µM by both enzymes, T5 Exo and Exo I, at 37 °C for 30 min after 2 hours of incubation at 37 °C with or without glyphosate (1 mM) in GLY3 buffer.

Figure 4 .

 4 Figure 4. Digestion of SUP000 (1 µM), Exo I and T5 Exo, for 30 min at 37 °C in HEPES and GLY3 buffers with and or glyphosate (1 mM).

Figure 5 .

 5 Figure 5. Digestion of SUP000 at 1 µM by Exo I (0.15 U µL -1 ) at 37 °C for 30 min in GLY3 buffer in the absence or in the presence of different pesticide molecules at 1 mM.

Figure 6 .

 6 Figure 6. (a) Principle of analyzing aptamer/target interaction by T5 Exo and Exo I digestion, followed by fluorescence spectroscopy. (b) The expected percentage of enzymatic digestion in the presence and in the absence of the target.

  384-well microplate (Corning black, Thermo Fischer Scientific) containing 25 µL of stop solution (1.2X SYBR Gold, 12 mM Tris-HCl pH = 7.4, 48% formamide (v/v), 3.75 mM EDTA).

Table 1 .

 1 MilliQ water and the concentrations were measured by UV-Vis spectroscopy using the Nanodrop 2000 spectrometer (Mettler Toledo, Columbus, Ohio, USA). The sequences of the glyphosate aptamer candidates are listed in Table 1. Sequences of glyphosate aptamer candidates

	purification. Tris(hydroxymethyl)aminomethane (Tris-HCl), sodium chloride (NaCl), potassium
	chloride (KCl), hydrochloric acid (HCl), sodium hydroxide (NaOH), magnesium chloride
	hexahydrate (MgCl26H2O), calcium chloride tetrahydrate (CaCl24H2O), formamide,
	ethylenediaminetetraacetic acid (EDTA), glycerol and sodium dodecyl sulfate 4X (SDS) were
	purchased from Euromedex (Strasbourg, France). Ethanol (EtOH), magnesium acetate, sodium
	acetate, potassium acetate, tris(hydroxymethyl)aminomethane, boric acid, EDTA,
	tris(hydroxymethyl)aminomethane and boric acid (TBE), urea and tetramethyl ethylenediamine
	(TEMED) were purchased from VWR Chemicals (Radnor, Pennsylvania, USA). Glyphosate,
	aminomethylphosphonic acid (AMPA), atrazine, xylene cyanol and ammonium persulfate (APS)
	were purchased from Sigma Aldrich (St. Louis, MO, USA). SYBR Gold was purchased from
	Invitrogen (Thermo Fischer Scientific, Waltham, Massachusetts, USA). 4-(2-hydroxyethyl)-1-
	piperazine ethane sulfonic acid (HEPES) was purchased from Pan Reac Application (ITW
	Reagents, Castellar del Vallès, Spain). Exo I (20000 U mL -1 ) and T5 Exo (10000 U mL -1 ) were
	purchased from New England Biolabs (Ipswich, Massachusetts, USA).
	4.2.Oligonucleotides
	All oligonucleotides used in this work were synthesized by Eurogentec (Seraing, Belgium) with
	polyacrylamide gel electrophoresis (PAGE) purification grade. The oligonucleotides were
	dissolved in

Acknowledgments:

We acknowledge grants from the Université de Pau et de Pays de l'Adour through its project Energy and Environment Solutions supported by the Agence National pour la recherche (ANR OPE-2018-0020) and the Communauté d'agglomération de Pau Béarn Pyrénées (CDAPBP, OPE-2020-0032) and from the Région Nouvelle Aquitaine (CONV-2019-0227). R. Brown kindly read the revised manuscript.

.

are shown in Figure S12 and Table S5 respectively). The whole set is incubated for 25 min in the dark under gentle stirring (18 rpm) on a horizontal incubator (See-saw rocker, Stuart-equipment, Waltham, Massachusetts, USA). After incubation, the gel fluorescence is visualized with G-Box (SYNGENE, Synoptics, Cambridge, UK).

4.6.Fluorescence Spectroscopy

To achieve fast, quantitative analysis of the interaction between potential aptamer candidates and glyphosate, a second enzyme, exonuclease I, is combined with T5 Exo, and the analysis is done by measuring the fluorescence intensity of SYBR Gold. The activity of Exo I is indeed complementary to that of the T5 Exo as it digests single-stranded DNA into mononucleotides in the opposite direction to T5 Exo (from 3' to 5', Figure S13). In addition, it digests the products of T5 Exo enzymatic digestion, which accelerates the process. Protection of the aptamer by its target thus translates into a higher fluorescence intensity of SYBR gold than without. Fluorescence intensity is converted to the digestion yield via Equation 1. The yield of digestion is lower when the target protects its aptamer (Figure 6).


Préget R †1

Target versus budget reverse auctions: an online experiment using the strategy method

Keywords: Reverse auctions, Online experiments, Strategy Method, Budget constraint, Target constraint. JEL Classification-C92

Reverse auctions are used in various fields by public or corporate buyers to purchase goods and services from multiple sellers at the best price. Unlike in selling auctions, in reverse auctions a budget constraint rather than a target quantity is often announced by the auctioneer. However, in auction theory no optimal bidding strategy has yet been found in the case when a budget constraint is announced. Here we compare the two auction formats in an online experiment with 329 participants.

We use the strategy method to obtain participants' bidding strategies from which we run exhaustive simulations of auction outcomes. This innovative methodology allows to overcome the issue of randomness of the auction outcome related to bidders' values. When each bidder has a single unit to sell, from the buyer's perspective, we find that, on average, the budget-constrained auction format outperforms the target-constrained auction format.

Introduction

In market design, auctions are often promoted as an alternative to fixed payments to reduce the asymmetry of information between an auctioneer and the bidders. These mechanisms provide an incentive for bidders to bid closer to their reservation value, as they have to trade off between their margin and increasing their probability of winning the auction.

Contrary to standard selling auctions, in reverse or procurement auctions, the auctioneer is the buyer, and the bidders are the sellers. In a multi-unit reverse auction, the buyer can announce the target to the bidders, i.e., the quantity or number of units to be purchased. In such target-constrained auctions (hereafter Target), the buyer accepts the lowest bids until the target is reached. However, in reverse auctions it is quite common that the buyer announces a budget constraint, i.e., his maximum budget for the maximum quantity or number of units. This usually occurs in conservation auctions for example (see. [START_REF] Schilizzi | Conservation tenders: linking theory and experiments for policy assessment[END_REF]. In such budget-constrained auctions (hereafter Budget), the lowest bids are accepted until the budget is exhausted.

In this study, we compare the performance of these two reverse auction formats (Target and Budget) to determine which constraint would enable the auctioneer, on average, to purchase the maximum quantity for the minimum cost. Surprisingly, the question of how the announced constraint affects the efficiency of a reverse auction outcome remains understudied.

Indeed, auction theory has widely been built on the study of selling auctions. Consequently, in the literature, it is always the quantity or number of units that is announced on share auctions or multi-unit auctions [START_REF] Milgrom | Putting auction theory to work[END_REF][START_REF] Klemperer | Auctions: theory and practice[END_REF][START_REF] Krishna | Auction theory[END_REF].

Budget-constrained auctions have received very little attention in the auction literature, yet announcing a budget is relatively common in reverse auctions. In this paper, we attempt to shed some light on this question. We consider the simple case in which each bidder has only one unit to sell and thus competes on price only. All units are identical for the buyer, but the sellers each have independent and private costs to produce their unit. We consider a discriminatory multi-unit reverse auction, i.e., a sealed bid auction where winning bidders are paid their own bid. In a multi-unit target (selling) auction, an optimal bidding strategy exists that is based on maximizing the bidders' expected surplus [START_REF] Harris | Allocation Mechanisms and the Design of Auctions[END_REF][START_REF] Cox | Theory and Behavior of Multiple Unit Discriminative Auctions[END_REF]. [START_REF] Hailu | Assessing the performance of auctions for the allocation of conservation contracts: Theoretical and computational approaches[END_REF] and [START_REF] Liu | Balancing Cost Effectiveness and Incentive Properties in Conservation Auctions : Experimental Evidence from Three Multi-award Reverse Auction Mechanisms[END_REF] extend this result to the reverse auction case in which a target constraint is announced. However, to our knowledge, no optimal bidding strategy has yet been identified for an auction in which a budget has been announced. Therefore, we cannot determine theoretically which format is the most efficient in a reverse auction.

In addition, to make a relevant comparison, we need to define equivalent constraints.

In the Target and Budget cases, respectively, the lower the number of units requested by the buyer or the lower the budget announced by the buyer, the greater the degree of competition. However, we can hardly predict a priori the level of each constraint that equalizes the level of competition between Target and Budget. To overcome this issue, we propose an original method using simulations based on experimental bidding strategies.

Concretely, to ensure some kind of equivalence, we set the target constraint exogenously and then define the budget constraint endogenously according to the results obtained in the Target treatment [START_REF] Schilizzi | Assessing the Performance of Conservation Auctions : An Experimental Study[END_REF]. One of our contributions is the way we calculate the average outcome of the auctions in each treatment. We use the strategy method to obtain the bidding strategy for each subject. The strategy method is a well establish method in experimental economics (see [START_REF] Selten | Die Strategiemethode zur Erforschung des eingeschränkt rationalen Verhaltens im Rahmen eines Oligopolexperiments[END_REF][START_REF] Mitzkewitz | Experimental results on ultimatum games with incomplete information[END_REF][START_REF] Brandts | The strategy versus the direct-response method: A first survey of experimental comparisons[END_REF] which has been used in few auction experiments [START_REF] Rapoport | Bidding Strategies in a Bilateral Monopoly with Two-Sided Incomplete Information[END_REF][START_REF] Selten | Bidding behavior in first-price auctions with directly observed bid functions[END_REF][START_REF] Güth | Bid functions in auctions and fair divisions games: Experimental evidence[END_REF][START_REF] Güth | Learning to bid -An experimental study of bid function adjustments in auctions and fair division games[END_REF][START_REF] Kirchkamp | Outside options: Another reason to choose the first-price auction[END_REF][START_REF] Katuščák | Does feedback really matter in oneshot first-price auctions?[END_REF][START_REF] Mill | Competition between friends and foes[END_REF], but never in the case of reverse auctions. In experimental auctions, the strategy method consists in asking subjects for their entire bidding strategy (for all cost levels) in a single round. Then, we simulate from the subjects' bidding strategies what we call the "average budget", which is used to set the constraint in the Budget treatment. We also simulate the average number of units purchased in the Budget treatment. Finally, if the average number of units purchased in Budget is significantly higher than the number of units announced in Target, Budget has higher budgetary efficiency than Target and vice versa.

To the best of our knowledge, only [START_REF] Schilizzi | Assessing the Performance of Conservation Auctions : An Experimental Study[END_REF] and [START_REF] Boxall | An experimental examination of target based conservation auctions[END_REF] have compared Target and Budget. They use laboratory experiments in the context of conservation auctions in which student subjects play the role of farmers (bidders) whose opportunity costs are set randomly. Subjects take part in repeated auctions with three and 15 periods, respectively. Random costs are reshuffled each period in [START_REF] Schilizzi | Assessing the Performance of Conservation Auctions : An Experimental Study[END_REF] and every five periods in [START_REF] Boxall | An experimental examination of target based conservation auctions[END_REF]. Both experiments are multi-unit auctions, but bidders have one unit to sell in [START_REF] Schilizzi | Assessing the Performance of Conservation Auctions : An Experimental Study[END_REF] and possibly several in [START_REF] Boxall | An experimental examination of target based conservation auctions[END_REF]. Both experiments find that the Target format outperforms the Budget format in the first round but that after several repetitions the auction performance evens out.

Our experiment differs from previous ones in three main ways. First, we propose a totally decontextualized experiment for better control and to allow the results to be extended to any reverse auction. Second, we use the strategy method to obtain subjects' complete bidding strategies from which we simulate exhaustively the possible auction outcomes. Third, we use the above-mentioned exhaustive simulations to compute equivalent target and budget constraints so as to compare both formats in a more rigorous way.

In Section 2, we present some theoretical background underlying our experiment, as well as the equilibrium bidding strategy in the Target format. Then, in Section 3, we introduce our experimental design, based on the strategy method, and its online implementation. Section 3 also details the way we simulate auction outcomes to set equivalent constraints and measure efficiency in Target and Budget. A description of subjects and control variables is conducted in Section 4, while the results are presented in Section 5.

Finally, Section 6 gives some discussions and Section 7 concludes.

Theory of reverse auctions

In this section, we present a theoretical framework which is derived from auction theory (2.1), the two types of announced constraints (2.2) and the symmetric equilibrium bidding strategy in the Target case (2.3).

Auction game

We consider a multi-unit procurement or reverse auction with an auctioneer who is the buyer and with N risk-neutral symmetric bidders who are each sellers of a single unit. Thus, each bidder i proposes a single bid b i which is the selling price for his unit. All the units are homogeneous and perfectly divisible for the auctioneer. Each bidder i produces his unit at a private cost c i . It is common knowledge that costs are identically and independently drawn from the same distribution with a density function f (.) and a cumulative function F (.) on the interval [c, c]. Let b i (c) be the bidder i's bidding function (or bidding strategy), which is assumed to be increasing and differentiable. When a Nuple of costs, (c 1 , ..., c N ), are assigned to bidders, bids b i are ranked by the auctioneer in ascending order of price with rank (r), r = 1, ..., N .

b (1) ≤ b (2) ≤ ... ≤ b (N )
The lowest bids are selected until the announced constraint is reached (see Section 2.2).

The auctioneer can split the last selected unit to meet his constraint or in case of ties.

We consider a discriminatory (or first price) reverse auction, thus the price paid to each winning bidder is defined by the bidder's own submitted bid.

Announced constraint

We distinguish two auction formats: the target-constrained auction (Target) and the budget-constrained auction (Budget). These formats do not impact the payment rule but define differently the limit of the selection rule in a reverse multi-unit auction.

In Target, before the bidders submit their bid, the auctioneer announces the quantity he will buy. Let M T (with 0 < M T < N ) be the targeted number of units. Then, to minimize his expenses, the auctioneer selects the lowest bids until the desired quantity is reached. Thus, he buys the M T least expensive units. Formally, M T may be any real positive number, not only an integer.

In Budget, the auctioneer announces B, the maximum amount of money he will spend to buy the highest possible quantity. Thus, units are purchased in ascending order of price until the available budget is reached or all the N available units for sale are purchased.

In the budget format, it is likely that the announced budget will not fit exactly with the purchase of an integer number of units. This is not a problem, since we consider units to be perfectly divisible. In addition, note that the budget constraint may not be reached, and a balance may remain when the sum of all the bids is lower than the budget announced, i.e., B > N i=1 b i . Announcing one or the other constraint leads to two different auction formats for the bidders which are also based on two different objectives for the auctioneer. In Target his aim is to minimize his expenditure while buying exactly the right number of units (the target). In Budget, his goal is to buy as many units as possible without exceeding his budget.

The choice of the constraint type may be driven by a real constraint or a preferred objective. Of course, in the end, the trade-off between price and quantity can only be solved by setting the buyer's demand function. Nevertheless, to keep the comparison exercise as general as possible, we do not impose a given demand function. Rather, we assume that the buyer does not have any strict constraints: his available budget is unlimited and his marginal utility for each unit until the N th is strictly positive. Thus, we assume that the buyer's objective is to purchase the maximum quantity for the minimum budget.

Equilibrium bidding function

In Target, when M T is a positive integer, bidders seek to maximize their expected gain, expressed as:

E(b i , c i ) = (b i -c i ).P rob(b i < b (M T +1) ), (1)
with b (M T +1) the first rejected bid [START_REF] Müller | Auction Mechanisms for Soil and Habitat Protection Programmes[END_REF].

Considering the symmetric equilibrium of the auction game introduced in Section 2.1, [START_REF] Hailu | Assessing the performance of auctions for the allocation of conservation contracts: Theoretical and computational approaches[END_REF] and [START_REF] Liu | Balancing Cost Effectiveness and Incentive Properties in Conservation Auctions : Experimental Evidence from Three Multi-award Reverse Auction Mechanisms[END_REF] demonstrate that the unique optimal bidding function

b * (c) in Target is: b * (c) = c c uF (u) M T -1 (1 -F (u)) N -M T -1 f (u)du c c F (u) M T -1 (1 -F (u)) N -M T -1 f (u)du . ( 2
)
In Budget, the quantity purchased is unknown to bidders, because it depends on other bids. Therefore, there is no simple equilibrium bidding function [START_REF] Müller | Auction Mechanisms for Soil and Habitat Protection Programmes[END_REF], as strategic interactions can hardly be modelled1 .

Without any theoretical result, we compare the two auction formats in a decontextualized online lab experiment where subjects play the auction game described in Section 2.1.

Online experiment and auction outcome simulations

In the current section we describe the strategy method and the reasons we have adopted it in our online lab experiment (3.1). Next, we present our experimental design (3.2) and explain how we compute experimental outcomes based on participants' complete bidding strategies (3.3). Finally, we show how the online experiment has been implemented (3.4).

Strategy method

In induced value auction experiments, costs are usually assumed to be uniformly distributed across a given interval [c, c]. In practice, only a discrete sample of costs is necessarily considered. Let J be the number of possible values within this interval. In most experiments, one cost per bidder is drawn in order to perform the auction, and several periods are conducted with different sets of costs to generate more data. In these repeated auctions, results may depend on cost draws even if the same set of costs is kept across treatments. A learning process can also occur over periods that may bias the results, even if no feedback is given to the bidders after each period (e.g., [START_REF] Güth | Learning to bid -An experimental study of bid function adjustments in auctions and fair division games[END_REF][START_REF] Lusk | Experimental Auctions[END_REF]. Finally, there may be a wealth effect when several auctions are played and paid for successively.

To overcome these issues, we use the strategy method (or cold strategy) to get the entire bidding strategy of every subject in a single round. In practice, subjects have to fill in a decision table containing the J possible cost values with J corresponding bids. Using the strategy method enables us to easily run an online experiment, since the subjects do not need to be connected at the same time. In each treatment, groups of N bidders are randomly formed ex post, and the N-uple of cost k used to define subjects' earnings among the K = J N possible cost arrangements is also randomly drawn ex post.

Experimental design

We choose a between-subjects design where subjects are randomly assigned to a single treatment to prevent any order effect. Indeed, in a pilot lab experiment with a withinsubject design, a significant order effect has been found.

Comparing the two auction treatments requires setting equivalent constraints. As stated in the introduction and illustrated in Figure 1, we first run the Target treatment with an exogenous constraint set to M T units. In the following section, we will detail how we compute the average budget (B) from the bidding functions obtained in Target to buy M T units. This average budget B is then used as the endogenous constraint in the Budget treatment. Next, we compute the average number of units purchased M B from the bidding functions obtained in Budget. Finally, if M B is higher than M T then Budget outperforms Target and vice-versa.

In the following section (3.3), we explain how we compute exact group-level values of treatment is conducted on several groups of N bidders, so to get independent data, groups need to be independent. Therefore, to compute the average auction outcome at the treatment level, each subject is randomly assigned to a single group of N bidders. There are G T and G B independent groups, respectively, in Target and Budget.

Simulation of auction outcomes

The advantage of having the bidding strategies of all subjects is to be able to simulate the auction outcome for any group g of N subjects and for any cost arrangement k. These simulations generate a very rich data set which allows us to eliminate the randomness related to the drawing of costs. Indeed, simulations can be run on all the K = J N possible cost arrangements.

We define an auction as a group g of N bidders associated to a given N-uple of costs k (corresponding to the k th N-uple of costs). As explained in 2.1, in each group g, bids b igk are ranked by the buyer in ascending order of price: b

(1)gk ≤ b (2)gk ≤ ... ≤ b (N )gk .
Calculation of the average budget B spent in Target to set equivalent constraints: Here we detail how we compute from subjects' bidding strategies the average budget spent in the Target treatment, which is used as the endogenous constraint in the Budget treatment.

In Target, only the M T cheapest units are selected. Therefore, the budget spent in that auction is B gk = M T r=1 b (r)gk . The exact mean of the budget spent B g is computed within each group g (g = 1, ..., G T ) on all the possible cost arrangements k (k = 1, ..., K) such as:

B g = K k=1 B gk K (3)
Thus, the average budget B is the combined mean of the G T exact mean budgets

B g B = G T g=1 B g G T . ( 4
)
Calculation of the average number of units auctioned in Budget to compare auction performance: Cost-effectiveness is measured by comparing the average number of units auctioned in Budget (M B ) with the number of units announced in Target (M T ) for an equivalent average budget B (see Figure 1). As for the average budget, the number of units auctioned M B gk is first defined at the auction level. Define t as a positive integer such as 0 < t < N , then

M B gk =        t + B- t r=1 b (r) b (t+1) if t r=1 b (r) ≤ B < t+1 r=1 b (r) N if B ≥ N r=1 b (r) (5)
Note: there may be a non-null residual budget E gk if the budget B is great enough to purchase all the units.

E gk =        0 if B ≤ N r=1 b (r) B -N r=1 b (r) if B > N r=1 b (r) (6)
Second, exact mean values are computed at the group level g across all cost arrangements k.

M B g = K k=1 M B gk K (7)
These are finally summed up in a single treatment-level value M B . Thus, the average number of units purchased in Budget is given by:

M B = G B g=1 M B g G B ( 8
)
M B is compared to M T , the exogenous number of units purchased in Target. The average residual budget in Budget is also computed as:

E = G B g=1 K k=1 E gk K G B (9)
but, after the game has been played, it is assumed to be lost for both the auctioneer and the bidders.

Calculation of the average allocative efficiency in both formats:

In addition to the number of units purchased from equivalent budget and target constraints, we check the allocative efficiency of each auction. Allocative efficiency is at the maximum level when all purchased units are from the bidders with the lowest costs. Let c (i) be the cost corresponding to the i th unit in ascending order of cost.

c (1) ≤ c (2) ≤ ... ≤ c (N )
In each auction, bids are ranked in order of increasing price and not according to production cost. Therefore, the winning bids do not necessarily correspond to the lowest costs.

To measure the allocative efficiency of a given auction, we use as indicator a dummy variable which is equal to one if the purchased units are those with the lowest costs, and equal to zero otherwise.

In Target, the allocative efficiency of auction k of group g is:

AE T gk = 1 if M T i=1 c i = M T i=1 c (i) 0 else (10)
In Budget, the allocative efficiency of auction k of group g is:

AE B gk =    1 if M B gk i=1 c i + {M B gk } c M B gk = M B gk i=1 c (i) + {M B gk } c ( M B gk ) 0 else (11) with {M B gk } = M B gk -M B
AE T = G T g=1 K k=1 AE T gk K G T (12)
and in Budget as:

AE B = G B g=1 K k=1 AE B gk K G B ( 13
)
The closer these indicators are to one, the greater the allocative efficiency.

Online implementation of the experiment

The experiment was programmed with o-Tree software [START_REF] Chen | oTree-An open-source platform for laboratory, online, and field experiments[END_REF] and implemented online with an instructional video.

In the instructional video, subjects are told they are participating in an experiment in which they are anonymous sellers and that they can earn money depending on their decisions and those of other participants. Indeed, they are randomly assigned to groups of four participants without being able to identify the three other members of their group.

The relatively small number of bidders (N = 4) was chosen to increase the number of independent observations, i.e., the number of groups. Subjects are given the possibility to sell a unit of a good to a single buyer (the experimenter). To participate in the experimental game, subjects must complete a decision table (Fig. 2) containing 21 possible production costs for their unit. The distribution of private costs c i is uniform between e0 and e100 and includes J = 21 possible cost values corresponding to multiples of e5.

We define the exogenous Target M T = N/2 = 22 . For each cost, subjects must choose a selling price above or equal to the corresponding cost and rounded up to the nearest euro.

Figure 2: Decision table

We explain to the subjects that at the end of the experiment, in order to determine earnings, a production cost will be drawn randomly for each participant. Then, for each subject, the bid associated to his/her randomly drawn cost will be collected from his/her decision table. Finally, in each group of four participants, the cheapest units will be bought until the announced constraint is exhausted (according to the auction treatment).

Subjects' gains are defined as follows. If they do not succeed in selling their unit, they gain nothing. If they do succeed in selling their unit, they receive a payment equal to the difference between their selling price and their production cost. Full instructions for the Target treatment 3 are available in the Appendix A.1.

In such an online environment, subjects cannot ask questions; therefore, they must have a perfect understanding of the instructions. To this end, after the video they are required to answer a comprehension questionnaire consisting of True/False questions (see Appendix A.2). After responding to each question, the correct answer appears on the participant's screen. At any time during the experiment, subjects can access a text version of the instructions.

After completing the decision table, subjects answer a short questionnaire (see Appendix A.3). First, we elicit risk aversion with a self-assessment question, as in [START_REF] Dohmen | Individual risk attitudes: Measurement, determinants, and behavioral consequences[END_REF]. As this behavioral characteristic may have an impact on the way subjects bid, it is necessary to ensure that our two treatment groups are balanced with regard to this variable. Second, we assess the difficulty respondents had in proposing selling prices.

We speculate that it is more difficult for subjects to bid in Budget than in Target. Finally, we ask a few socio-demographic questions.

Data

Our experiment was conducted online in June 2021 and involved 329 subjects from the general French population who were registered on the FouleFactory platform 4 . Participants received a standard fee for a 15-minute survey (e2) and a potential extra gain from auction earnings (e2.56 per subject, on average). Participants knew that they would be assigned ex post to a randomly constituted group of four bidders.

50.8% of the subjects were women and the average age was 41 (Std.Dev. = 13). Some

Results

Our main results on the performance comparison between Target and Budget treatments is presented in 5.1. We then analyze the variability of outcomes in each auction format across cost draws (5.2), which is possible because our simulations are exhaustive on the cost arrangements within the groups. Finally, we explain our results by emphasizing both the role of subjects' bidding behavior and the role of the auction formats themselves (5.3).

Main results

The Target treatment results in an average budget B of e72.32 (see Table 2) 5 , which is the amount the auctioneer needs, on average, to purchase M T = 2 units, given the bidding strategies of 128 subjects assigned to G T = 32 groups. This amount was rounded down to e72 to be used as the budget constraint in the Budget treatment 6 . As reported in Table 2, the Budget treatment results in an average purchase of M B = 2.135 units. Note that the Budget treatment also benefits from a positive average balance of E = e0.09. We consider this excess budget to be lost. Overall, the Budget format allows subjects to purchase significantly more units (7% more) on average than the Target format with the same average budget (Wilcoxon signed-rank test, p<0.001) 7 Here, rounding the budget constraint to the nearest lower integer and having a non-null residual budget are 5 To ensure no bias is introduced due to group composition, exhaustive simulations on both cost arrangements and group constitutions were also performed. This even more general mean is: e72.19. 6 We acknowledge that in rounding down the average budget constraint to e72, we potentially underestimate the average number of units purchased in the Budget treatment. However, we were more concerned that giving an overly precise budget (e.g., to the cent) might have seemed strange to the subjects. 7 We use a non-parametric test, since the number of units purchased is not normally distributed (Shapiro-Wilk normality test).

conservative assumptions that support our conclusion that the Budget format outperforms the Target format.

With regard to allocative efficiency, we find a very small difference between the two treatments (0.013 see. Table 3). Not only is this difference not significant (Wilcoxon ranksum test with continuity correction, p-value=0.59), it is so small that it could be ignored.

These results show that the allocation efficiency is relatively high in both auction formats, since the purchased units are from the bidders with the lowest costs in about 85% of the auctions. Finally, contrary to our speculation, it was not more difficult for our respondents to bid in Budget than in Target. According to the self-assessment variable Ease to bid, with values comprised between zero (absolutely no difficulty to bid) and 10 (very difficult to bid), the average values per treatment (6.81 for Target and 6.54 for Budget) are not significantly different (Pearson's chi-square test, p-Value = 0.25)).

Variability of auction outcomes across cost draws

Results presented in the previous section, and their variance, are computed from the exact mean of each group over the K possible cost arrangements. These exact group means are computed with simulations based on the subjects' complete bidding strategies (see Section 3.3) in order to eliminate any bias related to the randomness of cost draws.

Figures 3 and4 illustrate the variability of outcomes within each group by providing (independent) exact group means (B g and M B g , respectively), with intervals corresponding to their standard deviations. The average group-level standard deviation is e38.95 in Target (which represents 53.86% of the average budget computed at the treatment level) and 0.632 units in Budget (29.59% of the average number of units purchased). Therefore, from the auctioneer's point of view, we observe, on average, a lower uncertainty due to the randomness of costs in Budget than in Target. This result could be another advantage of announcing to bidders a budget rather than a target. We see from Figure 3 that the group exact means of budget spent in Target vary according to group by a relatively small amount: around e72 (the average budget denoted by the horizontal dashed line). Indeed, the standard deviation of group exact means is only e6.56 (see Table 2). We also observe a low variability in the exact mean of the groups in Budget (Fig. 4). Here the standard deviation is only 0.099 units. Furthermore, the exact mean of units purchased by group is less than two units (the exogenous target constraint denoted by the horizontal dashed line) in only four groups out of 49, which is consistent with the results presented in Table 2. In this paper, however, independent observations are computed on the basis of exhaustive simulations. This ensures that the comparison of the performance of the two treatments is not related to random cost draws.

Why does Budget outperform Target ?

Budget can outperform Target because the auction constraint format is different but also because bidders bid differently in each treatment. Indeed, an explanation for the higher budgetary efficiency in Budget is that the offers made by the subjects tend to be lower in Budget than in Target. Figure 5 shows the average bids of the auction strategies, by cost level8 .

At this stage, bidding strategies appear similar in the two treatments (with slightly lower price offers in Budget, which could explain its superiority). Note that experimental bids are very different from the optimal bidding strategy in Target, which is consistent with results found by [START_REF] Liu | Balancing Cost Effectiveness and Incentive Properties in Conservation Auctions : Experimental Evidence from Three Multi-award Reverse Auction Mechanisms[END_REF]. To break down the total treatment effect, we consider the average outcome of a fictive treatment, which consists in simulating a Budget constrained auction using subjects' bids from the Target treatment. As illustrated in Figure 6, the comparison of this fictive treatment with the Target treatment allows us to isolate the effect of the constraint format (format effect = 2.086-2 = 0.086 units) since we keep the same bidding strategies (Target bids). We find this effect to be significant only at the 10 percent level (Wilcoxon signed-rank test, p = 0.054). The comparison of the fictive treatment with the Budget treatment allows us to isolate the effect of the subjects' bidding strategies (bid effect = 2.135-2.086=0.049 units) since we keep the same auction

Discussion

We found that the Budget format provides higher budgetary efficiency than Target. This contrasts with results found by [START_REF] Schilizzi | Assessing the Performance of Conservation Auctions : An Experimental Study[END_REF] and [START_REF] Boxall | An experimental examination of target based conservation auctions[END_REF] in the context of conservation auctions. These experimental studies suggest that Target presents greater cost-effectiveness than Budget in the first auction period but that the performance of Target erodes faster with repetitions. Both papers attribute this relative decrease in Target performance to faster learning by participants of the cut-off price in Target, which we cannot test with our current experimental protocol.

Our online experimental results rely on the use of an innovative methodological framework based on the strategy method which is a "cold" procedure where subjects must bid for several possible costs at the same time (see. [START_REF] Brandts | The strategy versus the direct-response method: A first survey of experimental comparisons[END_REF]. This is a key difference from [START_REF] Schilizzi | Assessing the Performance of Conservation Auctions : An Experimental Study[END_REF] and [START_REF] Boxall | An experimental examination of target based conservation auctions[END_REF], who used "hot" or direct-response procedures where one individual cost is drawn per period and subjects must bid directly according to the cost drawn. The strategy method has already been used in some previous studies in the context of selling auctions, but only to analyze individual bidding strategies [START_REF] Rapoport | Bidding Strategies in a Bilateral Monopoly with Two-Sided Incomplete Information[END_REF][START_REF] Selten | Bidding behavior in first-price auctions with directly observed bid functions[END_REF][START_REF] Güth | Bid functions in auctions and fair divisions games: Experimental evidence[END_REF][START_REF] Güth | Learning to bid -An experimental study of bid function adjustments in auctions and fair division games[END_REF][START_REF] Kirchkamp | Outside options: Another reason to choose the first-price auction[END_REF][START_REF] Katuščák | Does feedback really matter in oneshot first-price auctions?[END_REF][START_REF] Mill | Competition between friends and foes[END_REF] and not to exhaustively simulate the exact mean of auction outcomes. An extensive literature compares direct-response and strategy methods in various behavioral games (e.g. [START_REF] Fischbacher | The behavioral validity of the strategy method in public good experiments[END_REF][START_REF] Böhm | Norm shifts under the strategy method[END_REF]. In some cases, a difference was found between the two methods (e.g. [START_REF] Casari | The strategy method lowers measured trustworthy behavior[END_REF], which may be explained by a hypothetical bias related to the strategy method. However, most of the time no or mixed evidence has been found [START_REF] Brandts | The strategy versus the direct-response method: A first survey of experimental comparisons[END_REF][START_REF] Fischbacher | The behavioral validity of the strategy method in public good experiments[END_REF][START_REF] Böhm | Norm shifts under the strategy method[END_REF], in particular in auction experiments [START_REF] Rapoport | Bidding Strategies in a Bilateral Monopoly with Two-Sided Incomplete Information[END_REF][START_REF] Armantier | Subjective probabilities in games: An application to the overbidding puzzle[END_REF]. Moreover, these differences may be explained by learning or wealth effects, which are not present with the strategy method.

We have combined the strategy method with ex post numerical simulations to generate a large number of auctions. With the parameter values in our experiment, it is even possible to simulate exhaustively all possible auction outcomes. A benefit of the strategy method is that our experiment could be conducted online with a large number of subjects without requiring them to be connected at the same time. In addition, we used as independent observations the exact mean of each group computed over all possible induced cost arrangements. This ensures that the comparison of the two treatments is not biased by the randomness of cost draws. Indeed, outcomes may vary considerably according to the cost arrangement considered in each group (see Section 5.2).

Conclusion

To summarize, the aim of this paper was to compare the relative performance of targetconstrained and budget-constrained reverse auctions (in this paper Target and Budget, respectively). To do so, equivalent constraints were set up by determining the budget constraint endogenously from the average budget spent in the Target treatment. We used the strategy method to obtain subjects' complete bidding strategies, which allowed us to make ex post simulations and avoid any potential bias generated by randomly induced costs. We found that the Budget format provides, on average, a greater amount of units for an equivalent budget than the Target format. But, although the difference is significant, it is relatively small in this experiment. Furthermore, we found that both formats performed similarly in terms of allocative efficiency.

This paper fills a gap in the literature, as this is the first decontextualized study to deal with relative performance of Target and Budget reverse auctions. It also introduces a new way to produce and analyze auction experimental data thanks to the combination of the strategy method and a simulation exercise. We believe that this methodology is an important contribution of the paper and may be useful for future experiments on auctions. We acknowledge that in our study many aspects have not been explored, such as the impact of the auction group size N on auction performance, or alternatively, whether one format would better foster sellers' participation than the other (here N is fixed and exogenous). Indeed, participation and risk of collusion are important issues in auctions.

The way the reverse auction is framed and designed may have an important impact on both of these issues, which would nevertheless depend on the context in practice.

The uniform distribution of costs we used for practical considerations could also lead to an overestimation of the variability of outcomes compared with a normal distribution.

Finally, the performance of both formats with repetitions remains beyond the scope of this study. These issues are to be explored in further work, as is the combination of the two constraints in a single auction treatment.

Welcome !

This experiment is being conducted by researchers as part of a public research project to study decision making.

In this experiment you will have the opportunity to earn money in addition to the fixed participation payment.

The additional gain will depend on your decisions, as well as the decisions of other participants involved in this experiment.

We ask you to pay close attention to the instructions provided. They should allow you to understand your role in the experiment.

This survey is entirely anonymous.

The researchers will not be able to link your identity to your decisions.

In this experiment, groups of 4 participants will be randomly formed.

Other participants will not be able to identify you and you will not be able to identify them.

You are a seller and we (the researchers) are the buyer.

7

Once all sellers have completed their table, a production cost will be drawn randomly for each seller.

Example

Once all sellers have completed their table, a production cost will be drawn randomly for each seller.

Then corresponding bid price for this cost will be looked up in their table.

Game rules

The buyer will rank the 4 units offered in your group in ascending order of price (from lowest to highest).

In each group, the buyer will buy the 2 least expensive units.

9 < < < < < <
In case of a tie between several sales prices in the same group, these units will be divided by the buyer.

In this case, he will buy the same fraction of a unit from each of the ties.

Remarks

The cost that will be drawn at the end of the experiment to calculate your earnings does not depend on the cost of the other sellers.

Each production cost in the table has the same chance of being drawn.

12 For each possible production cost, you should ask yourself :

« For this production cost, what is my selling price? » At this point, you do not know the production costs or the prices that the other 3 sellers will offer.

Each price should be rounded to the nearest euro and be greater than or equal to the cost of production.

13 ?

Before filling in the table, please answer 3 questions in order to better understand the experiment.

Your answers to these questions will have no impact on your earnings!

After completing the table, you will be asked to answer a short final questionnaire.

During the experiment you can review the instructions at any time by clicking on this button:

14

Only those who succeed in selling their unit (or fraction of a unit) will receive their earnings. Less than e1100

Between e1100 and e1899

Between e1900 and e2299

Between e2300 and e3099

Between e3100 and e3999

Between e4000 and e6499

More than e6500

Do not wish to answer 7. What is your socio-professional category?

Farmers B Robustness checks using a matching procedure

B.1 Balance across samples

First, we test whether the two samples are well balanced on the control variables of our online experiment. We introduce here the variable Risk aversion, which is a self-evaluated variable with values between zero (no risk aversion) and 10 (high risk aversion). We observe in

B.2 Matching procedure

The objective here was to obtain two well-balanced samples on all the control variables.

The following probit model was used to compute propensity scores (PSs)

T reat i = α 0 + α 1 Riskaversion i + α 2 Incomecontinuous i + α 3 Age i + α 4 F emale i + α 5 Highlyeducated i + α 6 P rof ession i + i , (14)
T reat i being a dummy variable taking the value one if the subject i was in the Budget treatment. In this model, the Highly educated dummy is used in the matching procedure instead of Studies level to avoid generating too much variance whereas Studies level is well balanced in original samples (see Appendix B.1). In order to compute the propensity scores using this model, subjects who did not provide their income had to be removed.

This left 122 subjects in the Target group and 188 in Budget. The two subjects with the lowest PSs from Target, i.e., the lowest predicted probability of being from the Budget treatment, were also removed, as the number of subjects must be a multiple of four.

Then subjects were matched using the Optimal Pair Matching method from the MatchIt R package [START_REF] Stuart | MatchIt: Nonparametric preprocessing for parametric causal inference[END_REF] with a 1:1 ratio. This consists in minimizing the sum of the absolute pair distances in the matched sample. After this procedure, the two samples were balanced on all control variables (see Table 5) including Profession (Pearson's chi-square test, p-Value = 0.77). Using the procedure described in Section 3.3 with matched samples, we found outcome values presented in Table 6. No significant differences were found with respect to the original samples for the average budget (Wilcoxon rank-sum test, p = 0.97) and the average number of units purchased (Wilcoxon rank-sum test, p = 0.26), which supports the validity of our results.

Figure 1 :

 1 Figure 1: Overview of the experimental design

Figure 3 :

 3 Figure 3: Exact means and standard deviations of the budget spent per group in Target (B g )

Figure 4 :

 4 Figure 4: Exact means and standard deviations of the number of units purchased per group in Budget (M B g )

Figure 5 :

 5 Figure 5: Average bids in Target and Budget

Figure 6 :

 6 Figure 6: Breakdown of the treatment effect

  If your entire unit is purchased: gain = price -cost If a fraction of your unit is purchased: gain = fraction × (price -cost) If your unit is not purchased: gain 11 fraction You don't need to pay the cost of producing your unit if you can't sell it.

Table 1 :

 1 socio-demographic categorical variables are shown in Table1, in which we see that 48.9% of our subjects had at least a bachelor's degree and (at least) 43.2% earned e1900 or more per month. On the three comprehension questions, 47.4% of the respondents made no mistakes, 42.9% made only one mistake, 9.7% made two mistakes and none made three.We had 131 participants in Target and 198 in Budget, which allowed us to constitute G T = 32 and G B = 49 groups of four bidders. Three subjects in Target and two subjects in Budget were removed randomly so that the number of subjects was a multiple of four. Although subjects were randomly assigned to the two treatments, we observed (see Appendix B.1) that our treatment samples were not balanced on the Income and Profession variables. However, robustness checks presented in the Appendix B.2 show that this does not impact the validity of our results. Sample description (n=329)

	Variables	Categories	Count % subjects
		No high school diploma		7.3
		High school diploma		18.9
	Studies Level	Associate's degree		24.9
		Bachelor's degree		16.1
		Graduate studies	108	32.8
		Less than e1100		25.2
		Between e1100 and e1899		25.8
		Between e1900 and e2299		14.3
	Income	Between e2300 and e3099 Between e3100 and e3999		17.0 7.9
		Between e4000 and e6499		3.4
		More than e6500	2	0.6
		Do not wish to answer		5.8
		Farmers	2	0.6
		Craftsmen, retailers, entrepreneurs		6.4
		Executives and higher intellectual professions		21.3
	Profession	Employees	129	39.2
		Students		9.4
		Retired		7.6
		Unemployed		15.5

3 Instructions for the Budget treatment are available on request.

4

Participants are paid to complete surveys. See https://www.wirk.io/en/50k-freelancers-in-france/ (former web address: https://www.foulefactory.com/en/)

Table 2 :

 2 Average budget and average nb. of units purchased

	Target	128	32	2	72.32
				(.)	(6.56)
	Budget	196	49	2.135	72
				(0.099)	(.)

Treatment Nb. subjects * Nb. groups Nb. units purchased Empirical budget (e) Standard deviations in parenthesis. * Three subjects in Target and two in Budget were removed randomly to get multiples of four in both treatments. Results are robust across various group configurations.

Table 3 :

 3 Average allocative efficiency

	Treatment Nb. subjects * Nb. groups	Allocative efficiency
	Target	128	32	0.851
				(0.115)
	Budget	196	49	0.838
				(0.161)

Standard deviations in parenthesis.

* Three subjects in Target and two in Budget were removed randomly to get multiples of four in both treatments.

  Table 4 that samples are well balanced on Risk aversion (Wilcoxon rank-sum test), Age (Welch's t-test) and the Female variable (Pearson's chi-squared test). This is true also for the variable Studies level (Pearson's chi-squared test, p-Value = 0.39) and the Highly educated variable (Pearson's chi-squared test), which is a dummy, constructed from the variable Studies level, indicating whether the subject had at least achieved a bachelor's degree.

However, we found that samples were not balanced on the variables Profession (Pearson's chi-squared test, p-Value < 0.01) and the Income continuous variable (Wilcoxon rank-sum test, p-Value = 0.02), which was derived from the midpoints of Income classes and the lower bound for the highest class.

Table 4 also gives more information on the Profession, Studies level and Income variables.

Table 4 :

 4 Description of original samples

	Variables	Dummies	Mean in Target Mean in Budget p-Value
	Risk aversion		5.10	4.84	0.26
	Income continuous		1709.93	2007.32	0.02
	Age		42.04	40.13	0.22
	Female		0.53	0.49	0.43
	Highly educated		0.51	0.47	0.51
		No high school diploma	0.03	0.10	0.02
		High school diploma	0.20	0.18	0.71
	Studies level	Associate's degree	0.26	0.24	0.73
		Bachelor's degree	0.17	0.16	0.78
		Graduate studies	0.34	0.32	0.63
		Less than e1100	0.33	0.20	0.01
		Between e1100 and e1899	0.24	0.27	0.46
		Between e1900 and e2299	0.13	0.15	0.58
	Income	Between e2300 and e3099 Between e3100 and e3999	0.12 0.09	0.20 0.07	0.06 0.49
		Between e4000 and e6499	0.02	0.05	0.14
		More than e6500	0.01	0.01	0.77
		Do not wish to answer	0.07	0.05	0.49
		Farmers	0.00	0.01	0.67
		Craftsmen, retailers, entrepreneurs	0.08	0.06	0.45
		Executives and higher intellectual professions	0.18	0.24	0.18
	Profession	Employees	0.28	0.46	0.00
		Students	0.15	0.06	0.00
		Retired	0.11	0.06	0.09
		Unemployed	0.21	0.12	0.04

Table 5 :

 5 Two sub-samples of 120 subjects

	Variables	Dummies	Mean in Target Mean in Budget p-Value
	Risk aversion		5.07	5.09	0.84
	Income continuous		1729.26	1693.39	0.84
	Age		43.23	42.65	0.74
	Female		0.51	0.48	0.70
	Highly educated		0.51	0.51	1.00
		Farmers	0.00	0.01	1.00
		Craftsmen, retailers, entrepreneurs	0.08	0.06	1.00
		Executives and higher intellectual professions	0.18	0.24	0.52
	Profession	Employees	0.28	0.46	0.34
		Students	0.15	0.06	0.37
		Retired	0.11	0.06	0.39
		Unemployed	0.21	0.12	0.63

Table 6 :

 6 Average budget and average nb. of units purchased (matched samples)

Treatment Nb. subjects Nb. groups Nb. units purchased Empirical budget

		CEE-M Working Papers 1 -2023
	WP 2023-01	Pauline Castaing & Antoine Leblois
		« Taking firms' margin targets seriously in a model of competition in supply functions »
	WP 2023-02	Sylvain Chabé-Ferret, Philippe Le Coënt, Caroline Lefébvre, Raphaële Préget, François Salanié, Julie Subervie & Sophie Thoyer
		« When Nudges Backfire: Evidence from a Randomized Field Experiment to Boost Biological Pest Control »
	WP 2023-03	Adrien Coiffard, Raphaële Préget & Mabal Tidball « Target versus budget reverse auctions: an online experiment using the strategy method »
	Target	120	30	2	72.26
				(.)	(9.32)
	Budget	120	30	2.152	72
				(0.083)	(.)
	Standard deviations in parenthesis.

1 CEE-M Working Papers / Contact : laurent.garnier@inrae.fr  RePEc https://ideas.repec.org/s/hal/wpceem.html  HAL https://halshs.archives-ouvertes.fr/CEE-M-WP/

Note that Latacz-Lohmann and[START_REF] Latacz-Lohmann | Auctioning Conservation Contracts: A Theoretical Analysis and an Application[END_REF] study budget-constrained auctions in a decision theory framework which does not take into account bidders' interactions.

We consider N/2 as an average level of competition between bidders.

Among the 329 bid functions obtained in the experiment, 22 are not monotonic: 14 in Budget and 8 in Target.

A Content of the experiment A.1 Instructional video for Target treatment (Translated slides from French to English)

We are forced to use a neutral and abstract context in order not to influence your answers.

Each participant is invited to sell 1 unit of a good.

unit =

The 4 units offered in each group (1 unit for each seller) are perfectly identical.

= = =

Your task is to propose selling prices (in euros) for your unit based on its production cost.

To this end, you must complete this table which contains all the possible production costs for your unit.

These costs range from to 100 increments.

Once all sellers have completed their