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We formally assume that players in a game consider Nash Equilibrium (NE) the behavioral norm. In finite games of perfect information this leads to a refinement of NE: Faithful Nash Equilibrium (FNE). FNE is outcome equivalent to NE of the trimmed game, obtained by restricting the original tree to its NE paths. Thus, it always exists but it need not be unique. Iterating the norm ensures uniqueness of outcome. FNE may violate backward induction when subgame perfection requires play according to the SPE following a deviation from it. We thus provide an alternative view of tenable threats in equilibrium analysis.

International audience; Consumption satisfaction depends on other factors apart from the inherent characteristic ofcommodities. Leibenstein (1950) studies how the consumer's demand reacts to other factorsdifferent from the inherent characteristic of a specific commodity. In particular, he highlights thedesire of some consumers to be "in style", and the attempt by other for exclusiveness. The desireof some people to conform with the others, to be fashionable or stylish provokes a "bandwagoneffect": the demand for a commodity increases due to the fact that others are consuming this samecommodity. Conversely, the desire of some other people to be exclusive, or different from the"common hence" provokes the "snob" effect: the demand for a commodity decreases due to thefact that others are consuming it. This paper analyzes positional concerns and conformism in amodel of private contributions to public good. A positional consumer gets joy when his/her relativecontribution to the public good is higher than the average contribution by others. A conformistconsumers feels better if his behavior fits the average behavior in society, i.e., near the averagecontribution by others. The well-being of a conformist consumer decreases both when hiscontribution is above or below the average contribution by others. We analyze how positionalpreferences and conformism for voluntary contributions to a public good favor players'contributions and under which conditions can lead to social welfare improvements. A two-playerpublic good game between a positional and a conformist is analyzed, first in a one-shot game andlater in a simple dynamic game with inertia, placing particular attention to the transition path.Homogeneous and non-homogeneous individuals are considered regarding the players' valuationof the public good.

International audience; Motivated by recent research on product differentiation, we conduct laboratory experiments to study how demand uncertainty influences firms' incentives to differentiate. We ground our experiment on a discrete version of the standard location-then-price game introduced by \cite{Hotelling_1929}, and we consider different levels of demand uncertainty. We first derive the game equilibrium assuming risk-neutral firms, and obtain the standard prediction that a high level of demand uncertainty generates more differentiation. Second, we extend the analysis to consider non risk-neutral firms and markets with asymmetric risk profiles. We show that the game equilibrium can differ substantially according to the attitude to risk. Third, we compare our predictions with the experimental data and find that demand uncertainty acts as a differentiation force in the context of both symmetric markets composed of risk-neutral or risk-lover subjects and asymmetric markets. We find support also for the agglomeration effect arising from demand uncertainty for sufficiently risk-averse subjects. Overall, these results might explain the opposite product differentiation strategies frequently observed in markets with fast-evolving tastes (i.e. minimum or maximum differentiation). Finally, the data confirm that subjects differentiate to relax price competition and provide evidence of a strong positive relationship between differentiation and prices.

A designer is privately informed about the state and chooses an information-disclosure mechanism to influence the decisions of multiple agents playing a game. We define interim-optimal mechanisms, a subset of incentive-compatible mechanisms that are optimal in the sense that the informed designer cannot credibly find an alternative mechanism that strictly improves his interim payoff. We prove that an interim-optimal mechanism exists and that every interim-optimal mechanism is a perfect Bayesian equilibrium outcome of the informed-designer game. An ex-ante optimal mechanism may not be interim optimal, but it is when it is ex-post optimal. Likewise, the unraveling outcome in disclosure games is interim optimal. We provide a belief-based characterization of interim-optimal mechanisms and compare them with ex-ante optimal ones in common economic environments. In settings with strategic complements and binary actions, every ex-ante optimal mechanism is interim optimal. We compare interim optimality to other solutions of informed-principal problems.

We study the interaction between multiple information designers who try to influence the behavior of a set of agents. When the set of messages available to each designer is finite, such games always admit subgame perfect equilibria. When designers produce public information about independent pieces of information, every equilibrium of the direct game (in which the set of messages coincides with the set of states) is an equilibrium with larger (possibly infinite) message sets. The converse is true for a class of Markovian equilibria only. When designers produce information for their own corporation of agents, pure strategy equilibria exist and are characterized via an auxiliary normal form game. In an infinite-horizon multi-period extension of information design games, a feasible outcome which Pareto dominates a more informative equilibrium of the one-period game is supported by an equilibrium of the multi-period game.

International audience; We study the optimal design of tests with manipulable inputs. Tests take a unidimensional state of the world as input and output, an informative signal to guide a receiver's approve or reject decision. The receiver wishes to only approve states that comply with her baseline standard. An agent with a preference for approval can covertly falsify the state of the world at a cost. We characterize receiver‐optimal tests and show they rely on productive falsification by compliant states. They work by setting a more stringent operational standard, and granting noncompliant states a positive approval probability to deter them from falsifying to the standard. We also study how falsification‐detection technologies improve optimal tests. They allow the designer to build an implicit cost of falsification into the test, in the form of signal devaluations. Exploiting this channel requires enriching the signal space.

International audience; We study repeated zero-sum games where one of the players pays a certain cost each time he changes his action. We derive the properties of the value and optimal strategies as a function of the ratio between the switching costs and the stage payoffs. In particular, the strategies exhibit a robustness property and typically do not change with a small perturbation of this ratio. Our analysis extends partially to the case where the players are limited to simpler strategies that are history independent―namely, static strategies. In this case, we also characterize the (minimax) value and the strategies for obtaining it.

The present study proposes a theoretical model that investigates how R&D productivity influences the relationship between product substitutability and R&D investment in a duopolistic market. We argue that the effects on R&D investment are more complex than the previous literature suggests. We show theoretically that, in unlevelled industries, the laggard’s R&D investment decreases with product substitutability regardless of the R&D productivity level. In sharp contrast, in levelled industries, whether R&D investment increases or decreases with product substitutability depends crucially on the level of the R&D productivity. We choose parameters and formulate testable predictions that we take to the laboratory. We find that subjects’ behavior is largely consistent with the model’s predictions.

We experimentally study how individuals read strategically-transmitted information when they have preferences over what they will learn. Subjects play disclosure games in which Receivers should interpret messages skeptically. We vary whether the state that Senders communicate about is ego-relevant or neutral for Receivers, and whether skeptical beliefs are aligned or not with what Receivers prefer believing. Skepticism is lower when skeptical beliefs are self-threatening than in neutral settings. When skeptical beliefs are self-serving, skepticism is not enhanced compared to neutral settings. These results demonstrate that individuals' exercise of skepticism depends on the conclusions of skeptical inferences.

A set of agents is aware of the existence of an economic opportunity, and compete for the associated prize. We study incentives to communicate about the existence of this economic opportunity to uninformed agents when the winner of the prize shares it with others, through some exogenous sharing rule. Communicating about the opportunity has two conflicting effects: it increases competition, but it can also increase the likelihood of receiving a large share of the prize. We find that, for any sharing rule, there is a minimum equilibrium, which Pareto dominates all other equilibria. We also find that under bilaterally symmetric sharing, more sharing generates more communication. We then discuss these results along several extensions.

International audience; In this article we propose a theoretical model to better comprehend the effect of gun laws on violent property crime. We assume that a violent encounter between a criminal and a victim is costly to both, and we uncover two types of equilibria: a pure strategy violent equilibrium and a mixed strategy equilibrium where the criminal is deterred with strictly positive probability. The effect of a relaxation of gun laws is shown to be conditional on both initial gun laws and on the relative improvement of the victims’ defense capacity relative to the criminals’ offense capacity. We uncover a potentially inverted U-shaped relationship between gun laws leniency and investments in violent activities which helps reconciling seemingly contradictory empirical findings.; Dans cet article nous développons un modèle théorique permettant de mieux comprendre l’effet des lois sur le contrôle des armes à feu sur les crimes violents liés à l’appropriation de propriété privée. Nous supposons qu’une rencontre violente est coûteuse aussi bien pour un criminel que pour sa victime et nous identifions deux types d’équilibres : un équilibre violent en stratégie pure et un équilibre en stratégie mixte dans le cadre duquel le criminel est dissuadé avec une probabilité strictement positive. L’effet d’un assouplissement de la législation sur les armes à feu dépend du niveau des restrictions légales initiales en la matière, ainsi que du gain d’efficacité relatif de la victime et du criminel. Nous mettons au jour une possible relation en U-inversé entre la souplesse des lois sur les armes à feu et les investissements en activités violentes, ce qui permet de réconcilier des résultats empiriques antérieurs contradictoires.

International audience We use the analogy-based expectation equilibrium (Jehiel, 2005) to study cheap talk from a sender who does not perfectly understand all the messages available to him. The sender is endowed with a privately known language competence corresponding to the set of messages that he understands. For the messages that he does not understand, the sender has correct but only coarse expectations about the equilibrium response of the receiver. An analogy-based expectation equilibrium is always a Bayesian solution but usually differs from a standard communication equilibrium and from an equilibrium with language barriers (Blume and Board, 2013). We characterize conditions under which an outcome remains an equilibrium outcome when the sender's competence decreases. Partial language competence rationalizes information transmission and lies in pure persuasion problems, and can facilitate information transmission from a moderately biased sender.

Whether or not to vaccinate one's child is a decision that a parent may approach in several ways. The vaccination game, in which parents must choose whether to vaccinate a child against a disease, is one with positive externalities (herd immunity). In some societies, not vaccinating is an increasingly prevalent behavior, due to deleterious side effects that parents believe may accompany vaccination. The standard game-theoretic approach assumes that parents make decisions according to the Nash behavioral protocol, which is individualistic and non-cooperative. Because of the positive externality that each child’s vaccination generates for others, the Nash equilibrium suffers from a free-rider problem. However, in more solidaristic societies, parents may behave cooperatively –they may optimize according to the Kantian protocol, in which the equilibrium is efficient. We test, on a sample of six countries, whether childhood vaccination behavior conforms better to the individualistic or cooperative protocol. In order to do so, we conduct surveys of parents in these countries, to ascertain the distribution of beliefs concerning the subjective probability and severity of deleterious side effects of vaccination. We show that in all the countries of our sample the Kant model dominates the Nash model. We conjecture that, due to the free-rider problem inherent in the Nash equilibrium, a social norm has evolved, quite generally, inducing parents to vaccinate with higher probability than they would in the non-cooperative solution. Kantian equilibrium offers one precise version of such a social norm.

International audience; Public good games are at the core of many environmental challenges. In such social dilemmas, a large share of people endorse the norm of reciprocity. A growing literature complements this finding with the observation that many players exhibit a self-serving bias in reciprocation: “weak reciprocators” increase their contributions as a function of the effort level of the other players, but less than proportionally. In this paper, we build upon a growing literature on truth-telling to argue that weak reciprocity might be best conceived not as a preference, but rather as a symptom of an internal trade-off at the player level between (i) the truthful revelation of their private reciprocal preference, and (ii) the economic incentives they face (which foster free-riding). In truth-telling experiments, many players misrepresent private information when this is to their material benefit, but to a significantly lesser extent than what would be expected based on the profit-maximizing strategy. We apply this behavioral insight to strategic situations, and test whether the preference revelation properties of the classic voluntary contribution game can be improved by offering players the possibility to sign a classic truth-telling oath. Our results suggest that the honesty oath helps increase cooperation (by 33% in our experiment). Subjects under oath contribute in a way which is more consistent with (i) the contribution they expect from the other players and (ii) their normative views about the right contribution level. As a result, the distribution of social types elicited under oath differs from the one observed in the baseline: some free-riders, and many weak reciprocators, now behave as pure reciprocators.

francaisL’ethique strategique : l’altruisme epure de l’effet de la consideration pour autrui Dans un jeu d’investissement et effort en deux etapes, nous modelisons l’investissement « altruiste » dans la capacite d’un autre agent a beneficier des synergies entre les efforts des deux agents. Notre analyse theorique est developpee en supposant que les agents ne retirent pas une utilite directe de leur investissement « altruiste », c’est-a-dire sans tenir compte des preferences des autres au sein de leur propre utilite. Les resultats d’une experience en laboratoire confirment notre prediction comportementale que, pour un cout d’investissement suffisamment bas, les sujets se coordonnent sur un investissement positif, ce qui, a son tour, augmente leur effort dans la deuxieme etape. Cet effort depend positivement a la fois du propre investissement et de celui de l’autre agent, tel que prevu par notre modele. Ce comportement est observe independamment des preferences des sujets a l’egard du risque et de l’inegalite. EnglishIn a two-stage investment-effort game, we model altruistic investment in another agent’s capacity to benefit from synergies between the two agents’ efforts. We conduct the theoretical analysis of the game by assuming that agents who invest in others have no direct utility from their giving behavior, i.e., without considering other-regarding preferences. Results of a laboratory experiment confirm our behavioral prediction that, for a low enough investment cost, subjects coordinate on a positive complementarity-building investment, which in turn boosts their effort in the second stage. The latter increases in both own and others’ complementarity-building investment, as predicted by our model. All this holds independently of subjects’ risk and inequity aversion.

International audience; This paper studies the standard version of the approval mechanism with two players in a common pool resource (CPR) extraction game. In the case of disapproval, the Nash extraction level is implemented. The paper investigates, experimentally, the extent to which the Nash threat leads to Pareto-improving extraction levels. Through our experiment, we confirm the effectiveness of the Nash threat in reducing CPR over-extraction. Although participants’ behavior is mainly explained by rational thinking, inequity in payoff can also motivate their behavior. Moreover, we show that there is neither an order effect nor a framing effect. Finally, the reduction persists when the Nash threat is no longer in place.

We study how altruism networks affect the adoption of formal insurance. Agents have private CARA utilities and are embedded in a network of altruistic relationships. Incomes are subject to both a common shock and a large idiosyncratic shock. Agents can adopt formal insurance to cover the common shock. We show that ex-post altruistic transfers induce interdependence in ex-ante adoption decisions. We characterize the Nash equilibria of the insurance adoption game. We show that adoption decisions are substitutes and that the number of adopters is unique in equilibrium. The demand for formal insurance is lower with altruism than without at low prices, but higher at high prices. Remarkably, individual incentives are aligned with social welfare. We extend our analysis to CRRA utilities and to a fixed utility cost of adoption.

In ancient Greek polytheism, worshippers could choose which gods they would address, and in doing so they expected some form of benefit in a quid pro quo relationship. We look into the optimal choice of which god to worship as a function of the presumed strategy of the gods for returning favors to the worshippers, and relate it to a form of divine efficiency measure. At the equilibrium the model also shows that the least-worshipped god receives at least a certain volume of devotion. We propose two different approaches that may account for the assumed divine efficiency measure, one based on projecting characteristics of human performance onto the gods, and the other based on a random growth model for the benefits of addressing each god. Both approaches imply that observed acts of worship would follow a type of power law. We gathered data from a large volume of epigraphic and literary sources on actual acts of worships from the ancient Greeks, and it allows us to show that the distributions of these acts at the polis level effectively follow power laws with a particularly high degree of regularity. The number of votive acts towards the least-worshipped gods also match the model's prediction. We test the extent to which the known characteristics of the poleis affect the shape of these distributions, and find little explanatory power. The shape of the distribution of votive acts across gods hence appears to have followed a general law for the Ancient Greeks.

We study zero-sum repeated games where the minimizing player has to pay a certain cost each time he changes his action. Our contribution is twofold. First, we show that the value of the game exists in stationary strategies, depending solely on the previous action of the minimizing player, not the entire history. We provide a full characterization of the value and the optimal strategies. The strategies exhibit a robustness property and typically do not change with a small perturbation of the switching costs. Second, we consider a case where the minimizing player is limited to playing simpler strategies that are completely history-independent. Here too, we provide a full characterization of the (minimax) value and the strategies for obtaining it. Moreover, we present several bounds on the loss due to this limitation.

We consider a sender-receiver game, in which the sender has finitely many types and the receiver's decision is a real number. We assume that utility functions are concave, single-peaked and single-crossing. After the cheap talk phase, the receiver makes a decision, which requires the sender's approval to be implemented. Otherwise, the sender "exits". At a perfect Bayesian equilibrium without exit, the receiver must maximize his expected utility subject to the participation constraints of all positive probability types. This necessary condition may not hold at the receiver's prior belief, so that a non-revealing equilibrium may fail to exist. Similarly, a fully revealing equilibrium may not exist either due to the sender's incentive compatibility conditions.We propose a constructive algorithm that always achieves a perfect Bayesian equilibrium without exit.

This letter investigates games played on bipartite networks by introducing a team production function allowing for any pattern of cross effects between projects and cross effects between agents. By using a new representation of a bipartite network through a multilayers network, we are able to characterise interior equilibrium efforts as a function of agents centralities in the multilayers network.

We study an auction that maximizes the expected social surplus under an upper-bound constraint on the seller’s expected revenue, which we call a revenue cap. Such a constrained-efficient auction may arise, for example, when (i) the auction designer is “pro-buyer”, that is, he maximizes the weighted sum of the buyers’ and seller’s auction payoffs, where the weight for the buyers is greater than that for the seller; (ii) the auction designer maximizes the (unweighted) total surplus in a multiunit auction in which the number of units the seller owns is private information; or (iii) multiple sellers compete to attract buyers before the auction. We characterize the mechanisms for constrained-efficient auctions and identify their important properties. First, the seller sets no reserve price and sells the good for sure. Second, with a nontrivial revenue cap, “bunching” is necessary. Finally, with a sufficiently severe revenue cap, the constrained-efficient auction has a bid cap, so that bunching occurs at least “at the top,” that is, “no distortion at the top” fails.

We study a class of sender–receiver disclosure games in the lab. Our experiment relies on a graphical representation of sender's incentives in these games, and permits partial disclosure. We use local and global properties of the incentive graph to explain behavior and performance of players across different games. Sender types whose interests are aligned with those of the receiver fully disclose, while other types use vague messages. Receivers take the evidence disclosed by senders into account, and perform better in games with an acyclic graph. Senders perform better in games with a cyclic graph. The data is largely consistent with a non-equilibrium model of strategic thinking based on the iterated elimination of obviously dominated strategies.

Performance evaluation (“rating”) systems not only provide information to users but also motivate the rated worker. This article solves for the optimal (effort-maximizing) rating within the standard career concerns framework. We prove that this rating is a linear function of past observations. The rating, however, is not a Markov process, but rather the sum of two Markov processes. We show how it combines information of different types and vintages. An increase in effort may adversely affect some (but not all) future ratings.

We study how voting rules shape voter coordination in large three-candidate elections. We consider three rules, varying according to the number of candidates that voters can support in their ballot: Plurality (one), Anti-Plurality (two) and Approval Voting (one or two). We show that the Condorcet winner—a normatively desirable candidate—can always be elected at equilibrium under Approval Voting. We then numerically study a dynamic process of political tâtonnement. Monte-Carlo simulations of the process deliver rich insights on election outcomes. The Condorcet winner is virtually always elected under Approval Voting, but not under the other rules. The dominance of Approval Voting is robust to alternative welfare criteria and to the introduction of expressive voters.

We study the value of network information in a context of monopoly pricing in the presence of local network externalities. We compare a setting in which all players, i.e. the monopoly and consumers, know the network structure and consumers' private preferences with a setting in which players only know the joint distribution of preferences, in-degrees and out-degrees. We give conditions under which network information increases profit or/and consumer surplus. The analysis reveals the crucial role played by four properties: degree assortativity, homophily (in preferences), preference-degree assortativity and preference-Bonacich centrality assortativity.

We consider a single psychological agent whose utility depends on his action, the state of the world, and the belief that he holds about that state. The agent is initially informed about the state and decides whether to memorize it, otherwise he has no recall. We model the memorization process by a multi-self game in which the privately informed first self voluntarily discloses information to the second self, who has identical preferences and acts upon the disclosed information. We identify broad categories of psychological utility functions for which there exists an equilibrium in which every state is voluntarily memorized. In contrast, if there are exogenous failures in the memorization process, then the agent memorizes states selectively. In this case, we characterize the partially informative equilibria for common classes of psychological utilities. If the material cost of forgetting is low, then the agent only memorizes good enough news. Otherwise, only extreme news are voluntarily memorized.

A designer is privately informed about the state and chooses an information disclosure mechanism to influence the decisions of multiple agents playing a game. We define an intuitive class of incentive compatible information disclosure mechanisms which we coin interim optimal mechanisms. We prove that an interim optimal mechanism exists, and that it is an equilibrium outcome of the interim information design game. An ex-ante optimal mechanism may not be interim optimal, but it is whenever it is ex-post optimal. In addition, in leading settings in which action sets are binary, every ex-ante optimal mechanism is interim optimal. We relate interim optimal mechanisms to other solutions of informed principal problems.

Over the last half century, violent conflicts between ethno-religious organizations and states have shaped the political and economic development context in developing countries. However, global empirical evidence on the dynamic and strategic underpinnings of these phenomena is lacking. Here, we investigate the dynamic violent relationships between the organizations that represent minorities at risk and the governments in Middle-Eastern and North African countries. Our estimates of dynamic panel data models of discrete strategic responses reveal dampened cycles of violence between states and insurgent politico-ethnic organizations due to violent mutual responses. However, such cycles are absent when the organizations target civilians instead, which is more likely after an insurgency spell. Finally, we provide an original game-theoretical interpretative framework for our results, which allows us to identify, on average and under sensible restrictions, the Stag Hunt game as an appropriate representation of the (possibly reduced-form) general strategic situations that link states and minority organizations in MENA.This is at odds with the frequent use of the prisoner's dilemma setting in the literature, or of other ad hoc strategic hypotheses, to analyze conflicts.

International audience; Lacan’s contribution in applying and promoting game theory in the early 1950s is mostly ignored in the history of game theory. Yet his early analyses of logical reasoning made him one of the first social scientists to consider the importance of the hypothesis of common knowledge. By retracing Lacan’s path in his discovery of game theory, we show how much he has been a precursor in applying it. While accommodating a narrative approach, he demonstrated rigour and originality. Soliciting mathematicians open to interdisciplinarity, he introduced as early as 1945 modes of reasoning which corresponds to reasoning based on common knowledge.

We consider sender–receiver games in which the sender has finitely many types and the receiver makes a decision in a compact set. The new feature is that, after the cheap talk phase, the receiver makes a proposal to the sender, which the latter can reject in favor of an outside option. We focus on situations in which the sender’s approval is absolutely crucial to the receiver, namely, on equilibria in which the sender does not exit at the approval stage. A nonrevealing equilibrium without exit may not exist. Our main results are that if the sender has only two types or if the receiver’s preferences over decisions do not depend on the type of the sender, there exists a (perfect Bayesian Nash) partitional equilibrium without exit, in which the sender transmits information by means of a pure strategy. The previous existence results do not extend: we construct a counter-example (with three types for the sender and type-dependent utility functions) in which there is no equilibrium without exit, even if the sender can randomize over messages. We establish additional existence results for (possibly mediated) equilibria without exit in the three type case.

We study public goods games played on networks with possibly non-reciprocal relationships between players. Examples for this type of interactions include one-sided relationships, mutual but unequal relationships, and parasitism. It is well known that many simple learning processes converge to a Nash equilibrium if interactions are reciprocal, but this is not true in general for directed networks. However, by a simple tool of rescaling the strategy space, we generalize the convergence result for a class of directed networks and show that it is characterized by transitive weight matrices. Additionally, we show convergence in a second class of networks; those rescalable into networks with weak externalities. We characterize the latter class by the spectral properties of the absolute value of the network's weight matrix and show that it includes all directed acyclic networks., Comment: 44 pages

Experimental evidence shows that the rational expectations hypothesis fails to characterize the path to equilibrium after an exogenous shock when actions are strategic complements. Under identical shocks, however, repetition allows adaptive learning, so that inertia in adjustment should fade away with experience. If this finding proves to be robust, inertia in adjustment may be irrelevant among experienced agents. The conjecture in the literature is that inertia would still persist, perhaps indefinitely, in the presence of real-world complications such as nonidentical shocks. Herein, we empirically test the conjecture that the inertia in adjustment is more persistent if the shocks are nonidentical. For both identical and nonidentical shocks, we find persistent inertia and similar patterns of adjustment that can be explained by backward-looking expectation rules. A reformulation of naïve expectations with similarity-based learning approach is found to have a higher predictive power than rational and trend-following rules.

International audience; We contribute to the ongoing debate in the psychological literature on the role of thin slices of observable information in predicting others' social behavior, and its generalizability to cross-cultural interactions. We experimentally assess the degree to which subjects, drawn from culturally dierent populations (France and Japan), are able to predict strangers' trustworthiness based on a set of visual stimuli (mugshot pictures, neutral videos, loaded videos, all recorded in an additional French sample) under varying cultural distance to the target agent in the recording. Our main nding is that cultural distance is not detrimental for predicting trustworthiness in strangers, but that it may aect the perception of dierent components of communication in social interactions.

International audience; I consider multi-round cheap talk communication environments in which, after a lie, the informed party has no memory of the content of the lie. I characterize the equilibria with forgetful liars in such settings assuming that a liar's expectation about his past lie coincides with the equilibrium distribution of lies aggregated over all possible realizations of the states. The approach is used to shed light on when the full truth is almost surely elicited, and when multiple lies can arise in equilibrium. Elaborations are proposed to shed light on why non-trivial communication protocols are used in criminal investigations.

Motivated by recent discussions about the issue of risk perceptions for climate change related events, we introduce a non-cooperative game setting where agents manage a common pool resource under a potential risk, and agents exhibit different risk perception biases. Focusing on the effect of the polarization level and other population features, we show that the type of bias (overestimation versus underestimation biases) and the resource quality level before and after the occurrence of the shift have first-order importance on the qualitative nature of behavioral adjustments and on the pattern of resource conservation. When there are non-uniform biases within the population, the intra-group structure of the population qualitatively affects the degree of resource conservation. Moreover, unbiased agents may react in nonmonotone ways to changes in the polarization level when faced with agents exhibiting different types of bias. The size of the unbiased agents’ sub-population does not qualitatively affect how an increase in the polarization level impacts individual behavioral adjustments, even though it affects the magnitude of this change. Finally, it is shown how perception biases affect the comparison between centralized and decentralized management.

We propose and study a strategic model of hiding in a network, where the network designer chooses the links and his position in the network facing the seeker who inspects and disrupts the network. We characterize optimal networks for the hider, as well as equilibrium hiding and seeking strategies on these networks. We show that optimal networks are either equivalent to cycles or variants of a core-periphery networks where every node in the periphery is connected to a single node in the core., 27 pages

International audience; Dynamic pricing of new products has been extensively studied in monopolistic and oligopolistic markets. But, the optimal control and differential game tools used to investigate the pricing behavior on markets with a finite number of firms are not well-suited to model competitive markets with an infinity of firms. Using a mean-field games approach, this paper examines dynamic pricing policies in competitive markets, where no firm exerts market power. The theoretical setting is based on a diffusion modeì a la Bass. We prove both the existence and the uniqueness of a mean-field game equilibrium, and we investigate mean tendencies and firms dispersion in the market. Numerical simulations show that the competitive market splits into two separate groups of firms depending on their production experience. The two groups differ in price and profit. Thus, high prices and profits do not have to signal anticompetitive practices, stimulating the debate on market regulation.

Achieving an ambitious goal frequently requires succeeding in a sequence of intermediate tasks, some being critical for the final outcome, and others not. However, individuals are not always able to provide a level of effort sufficient to guarantee success in all such intermediate tasks. The ability to manage effort throughout the sequence of tasks is therefore critical when resources are limited. In this paper we propose a criterion that defines the importance of a task and identifies how an individual should optimally allocate a limited stock of exhaustible efforts over tasks. We test this importance criterion in a laboratory experiment that reproduces the main features of a tennis match. We show that our importance criterion is able to predict the individuals’ performance and it outperforms the Morris importance criterion that defines the importance of a point in terms of its impact on the probability of achieving the final outcome. We also find no evidence of choking under pressure and stress, as proxied by electrophysiological measures.

We analyze risk-taking regulation when financial institutions are linked through shareholdings. We model regulation as an upper bound on institutions' default probability, and pin down the corresponding limits on risk-taking as a function of the shareholding network. We show that these limits depend on an original centrality measure that relies on the cross-shareholding network twice: (i) through a risk-sharing effect coming from complementarities in risk-taking and (ii) through a resource effect that creates heterogeneity among institutions. When risk is large, we find that the risk-sharing effect relies on a simple centrality measure: the ratio between Bonacich and self-loop centralities. More generally, we show that an increase in cross-shareholding increases optimal risk-taking through the risk-sharing effect, but that resource effect can be detrimental to some banks. We show how optimal risk-taking levels can be implemented through cash or capital requirements, and analyze complementary interventions through key-player analyses. We finally illustrate our model using real-world financial data and discuss extensions toward including debt-network, correlated investment portfolios and endogenous networks.

We study choices and reaction times of respondents in an impunity game with unfair offers. The non-private impunity game features two roles, proposer and respondent, who are both aware whether the pie size is small or large. Proposers decide among three more or less unfair offers; respondents can accept or reject the offer, in which case it is lost for them. Whatever the responder decides is communicated to the proposer. 240 proposers took part in a traditional laboratory; 24 respondents were in an fMRI setup where they confronted all 240 proposals elicited from proposers. Responses were sent via email to proposers. Proposers revealed little concern for respondents. Respondents overwhelmingly rejected small offers, especially from a large pie. Surprisingly and in contrast with most of the literature and the Social Heuristic Hypothesis, we find that on average acceptances took longer than rejections. This result is driven by individual heterogeneity. The rich response data allow us to distinguish different respondent types, finding a remarkable consistency: subjects mainly accepting (rejecting) take more time to reject (accept). We attribute this finding to heterogeneity in self-priming. Our results suggest a primary role for individual heterogeneity in experiments testing the intuitive or deliberate status of cooperation and altruism.

This paper addresses the problem of utility maximization under uncertain parameters. In contrast with the classical approach, where the parameters of the model evolve freely within a given range, we constrain them via a penalty function. We show that this robust optimization process can be interpreted as a two-player zero-sum stochastic differential game. We prove that the value function satisfies the Dynamic Programming Principle and that it is the unique viscosity solution of an associated Hamilton-Jacobi-Bellman-Isaacs equation. We test this robust algorithm on real market data. The results show that robust portfolios generally have higher expected utilities and are more stable under strong market downturns. To solve for the value function, we derive an analytical solution in the logarithmic utility case and obtain accurate numerical approximations in the general case by three methods: finite difference method, Monte Carlo simulation, and Generative Adversarial Networks., Comment: 25 figures

International audience; We analyze the robustness of equilibria in sequential games when there is almost common certainty of payoffs. We show that a generic extensive-form game may have no robust equilibrium behavior, but has at least one robust equilibrium outcome, which is induced by a proper equilibrium in its normal-form representation. Therefore, backward induction leads to a unique robust outcome in a generic perfect-information game. We also discuss close relation between robustness to incomplete information and strategic stability. Finally, we present the implications of our results for the robustness of subgame-perfect implementation.

National audience; I examine how incentives for refutation affect publication quality. I build a sequential model of public experimentation with two scientists, a researcher and a refuter. The researcher chooses when to publish a result confirming a hypothesis, with a probability that the result has type I error. The publication quality corresponds to the probability that the hypothesis is valid, which is the complement of the probability of type I error. Once the result is published, the refuter starts experimenting but, unlike the researcher, he can choose between working on refutation or on an outside safe option at any time. When scientists are initially pessimistic about the hypothesis' confirmation and when refutation is costly for the researcher, the higher the refutation rewards, the lower the equilibrium publication quality in case the researcher is more efficient than the refuter. The opposite result holds when the refuter is more efficient. In an extension, when the researcher's experimentation is private, I prove that the publication quality is lower than in the public experimentation case, suggesting that transparency improves research quality

International audience; This paper examines how voluntary contributions to a public good are affected by the contributors' heterogeneity in beliefs about the uncertain impact of their contributions. It assumes that contributors have Savagian preferences that are represented by a two-state-dependent expected utility function and different beliefs about the benefit that will result from the sum of their contributions. We establish general comparative statics results regarding the effect of specific changes in the distribution of beliefs on the (unique) Nash equilibrium provision of the public good, under certain conditions imposed on the preferences. We specifically show that the equilibrium public good provision is increasing with respect to both first- and second-order stochastic dominance changes in the distribution of beliefs. Hence, increasing the contributors' optimism about the uncertain benefit of their contributions increases aggregate public good provision, as does any homogenization of these beliefs around their mean.

International audience; In this paper, we revisit the theory of spatial externalities. In particular, we depart in several respects from the important literature studying the fundamental pollution free riding problem uncovered in the associated empirical works. First, instead of assuming ad hoc pollution diffusion schemes across space, we consider a realistic spatiotemporal law of motion for air and water pollution (diffusion and advection). Second, we tackle spatiotemporal non-cooperative (and cooperative) differential games. Precisely, we consider a circle partitioned into several states where a local authority decides autonomously about its investment, production and depollution strategies over time knowing that investment/production generates pollution, and pollution is transboundary. The time horizon is infinite. Third, we allow for a rich set of geographic heterogeneities across states while the literature assumes identical states. We solve analytically the induced non-cooperative differential game under decentralization and fully characterize the resulting long-term spatial distributions. We further provide with full exploration of the free riding problem, reflected in the so-called border effects. In particular, net pollution flows diffuse at an increasing rate as we approach the borders, with strong asymmetries under advection, and structural breaks show up at the borders. We also build a formal case in which a larger number of states goes with the exacerbation of pollution externalities. Finally, we explore how geographic discrepancies affect the shape of the border effects.

We consider agents organized in an undirected network of local complementarities. A principal with a limited budget offers costly bilateral contracts in order to increase the sum of agents' effort. We study excess-effort linear payment schemes, i.e. contracts rewarding effort in excess to the effort made in absence of principal. The analysis provides the following main insights. First, for all contracting costs, the optimal unit returns offered to every targeted agent are positive and generically heterogeneous. This heterogeneity is due to the presence of outsiders, who create asymmetric interaction between contracting agents. Second, when contracting costs are low, it is optimal to contract with everyone and optimal unit returns are identical for all agents. Third, when contracting costs are sufficiently high, it becomes optimal to target a subset of agents, and optimal targeting can lead to NP-hard problems. In particular, when the intensity of complementarities is sufficiently low, a correspondence is established between optimal targeting and the densest k subgraph problem. Overall, the optimal targeting problem involves a trade-off between centrality and budget spending-central agents are influential, but are also more budget-consuming. These considerations can lead the principal to not target central agents.

International audience; We develop a spatial resource model in continuous time in which two agents/players strategically exploit a mobile resource in a two-region setup. To counteract the overexploitation of the resource (the tragedy of commons) that occurs when players are free to choose where to fish/hunt/extract/harvest, the regulator can establish a series of spatially structured policies. We compare the equilibria in the case of a common resource with those that emerge when the regulator either creates a natural reserve, or assigns Territorial User Rights to the players. We show that, when the discount rate is close to its "critical value", i.e. when technological and preference parameters dictate a low harvesting intensity/effort, the policies are ineffective in promoting the conservation of the resource and, in addition, they lead to a lower payoff for at least one of the players. Conversely, in a context of harsher harvesting intensity, the intervention can help to safeguard the resource, preventing extinction while also improving the welfare of both players.

Why do farm households inefficiently allocate resources across the plots they cultivate? We explore how these production inefficiencies relate to consumption decisions and information sharing within the household. In a lab-in-the-field experiment, male producers allocate too few inputs to their wife's plot, failing to maximize household aggregate profits. They do transfer more inputs when the returns from that plot are higher. Experimental manipulation of information on these returns triggers heterogeneous responses across households. We provide a theoretical framework that rationalizes these findings and further leads to sharp predictions. Joint contribution to a household public good compels spouses to make efficient production decisions. Only households who are in a separate-sphere regime experience inefficiency in farm production and are unable to effectively communicate on returns to avoid extra losses. Consistent with this framework, when we experimentally offer an ex post information verification mechanism, additional losses due to information asymmetries are prevented.

International audience; We experimentally investigate how much value people put in observable information about others in strategic interactions. The incentivized experimental task is to predict an unknown target player's trustworthiness in an earlier hidden action game. In Experiment 1, we vary the source of information about the target player (neutral picture, neutral video, video containing strategic content). The observed prediction accuracy rates then serve as an empirical measure of the objective value of information. In Experiment 2, we elicit the subjective value of information using the standard stated preferences method (willingness to accept). While the elicited subjective values are ranked in the same manner as the objective ones, subjects attach value to information which does not help predict target behavior, and exaggerate the value of helpful information.