• 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 [Job Market Paper]

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). The environment consists of multiple (possibly many) symmetric normal-form games with identical action spaces, and having a categorization (or analogy partition) with more classes entails a higher fitness cost. In an evolutionarily stable analogy-based expectation equilibrium (ESABEE), analogy partitions and strategies must 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 yield the highest overall fitness among all possible partitions. We show that an ESABEE (possibly involving distributions over partitions) always exists in finite environments. Moreover, we establish that ESABEEs are the steady states of dynamic systems in which analogy partitions are reproduced proportionally to their fitness in each period (as in replicator dynamics), while 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 show that some mixing across partitions must generally arise when there are many such games. We also identify properties that ESABEE must satisfy in such applications, including that coarse partitions receive positive probability irrespective of the fitness costs of finer partitions. Finally, we consider an investment application in which the decision maker observes his cost type and must form expectations about a benefit that can take multiple values, assuming that at most k categories can be used. We characterize when the first-best can be achieved as an ESABEE and contrast this analysis with that obtained under 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 is not informed of his cost type), as in the information design literature.

• On Moral Hazard with Reciprocal Monitoring and Collusion among Peers

Abstract: I consider a Principal-Agent model under moral hazard and limited liability with identical risk-neutral agents. The principal seeks to implement high effort in a team task with stochastic output. Agents choose effort simultaneously and observe each other's choices afterwards, while the principal observes only the task outcome. Although effort is not contractible, the principal can propose contracts based on both output and agents' reports of effort. With a "shoot-the-liar" mechanism, the principal can weakly implement high effort by asking agents to report both their own effort and that of their teammates. This requires compensating agents only for their effort costs (first-best if efforts were observable). If agents are allowed to collude at the reporting stage, the principal can still implement high effort by aligning one agent's incentives with her own, while the other agents are merely compensated for their effort costs. This is less costly for the principal than incentivizing all agents to exert high effort solely through monetary rewards while ignoring the reports (second-best with unobservable effort and no reports). Thus, the principal can exploit the fact that agents observe each other's effort by breaking symmetry and designating one agent as a "monitor," whose reports, together with the output, determine payments.