• Endogenous Clustering and Analogy-based Expectation Equilibrium (with Philippe Jehiel)  - Accepted, Review of Economic Studies

Presented at the ESSET 2023 (presenter P. Jehiel) and the Barcelona Summer Forum 2024 (presenter G. Weber).

Abstract: Normal-form two-player games are categorized by players into K analogy classes so as to minimize the prediction error about the behavior of the opponent. This results in Clustered Analogy-Based Expectation Equilibria in which strategies are analogy-based expectation equilibria given the analogy partitions and analogy partitions minimize the prediction errors given the strategies. We distinguish between environments with self-repelling analogy partitions in which some mixing over partitions is required and environments with self-attractive partitions in which several analogy partitions can arise, thereby suggesting new channels of belief heterogeneity and equilibrium multiplicity. Various economic applications are discussed.

• Coarse Agents and Intergroup Phenomena [draft available upon request]

Presented at the Transatlantic Theory Workshop 2024 (CREST - IP Paris and HEC Paris, co-organized by Bocconi, Oxford, and Northwestern)

Abstract: This paper proposes a framework for analyzing intergroup phenomena. A set of heterogeneous agents is divided into two groups. Agents are paired, and each pair plays a simultaneous-move game under complete information. When the opponent belongs to the same group ("in-group"), players form correct expectations about the opponent's behavior in equilibrium. Conversely, players form coarse expectations when their opponent is from the "out-group".  In equilibrium, such coarse expectations must coincide with the aggregate behavior of the out-group. We apply this framework to an organizational setting where the groups represent subdivisions, and each game corresponds to a team task. These tasks are identical and exhibit strategic complementarities. An omniscient designer sorts agents into pairs so as to maximize the overall probability of task success. The analysis of the optimal assignment emphasizes the role of coarse expectations: by pairing efficient agents in-group and less efficient agents out-group, the designer can induce the latter to overexert effort in equilibrium. Further economic applications are discussed.

• Evolutionarily Stable Analogy-based Expectation Equilibrium (with Laure Goursat and Philippe Jehiel) [preliminary draft available upon request]

Abstract. We develop an evolutionary approach to endogenize the choice of analogy partitions in the analogy-based expectation equilibrium (Jehiel, 2005) in environments consisting of multiple (possibly many) symmetric normal-form games with identical action spaces and a categorization (or analogy partition) with more classes comes with a higher fitness cost. In an evolutionarily stable analogy-based expectation equilibrium (ESABEE), we require that analogy partitions and strategies satisfy two conditions: (i) given an analogy partition, the associated strategy is a best response to the corresponding analogy-based expectations; and (ii) analogy partitions that arise with positive probability induce the highest overall fitness among all possible partitions. We show that an ESABEE (possibly involving distributions over analogy partitions) always exists in finite environments, and we establish that they are the steady states of dynamic systems in which analogy partitions are reproduced proportionally to their fitness in each period (as in the replicator dynamics), and strategies are adjusted by moving in the direction of the best responses induced by the partitions (as in belief-based learning models). We illustrate the concept using a family of Hawk-Dove games, for which we establish quite generally that some mixing across analogy partitions must arise when there are many such games, and note several properties that ESABEE must satisfy in such applications such that assigning positive probabillity to coarse partitions irrespective of the fitness costs associated with having finer partitions. We also consider an investment application in which the decision maker observes his cost type and need to form expectations about the benefit which can take multiple values and we assume that the decision maker can use at most k categories. We characterize when the first-best can be obtained as an ESABEE, and we contrast the analysis with that obtained with rational expectations and an optimal  information partition about the benefit realization (as in Dow, 1991) or an optimal information partition about the state (allowing for the case in which the decision maker would not be informed of his cost type) as in the information design literature.

• On Moral Hazard with Reciprocal Monitoring and Collusion among Peers