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Fudenberg, Drew

This paper introduces stochastic games with imperfect public signals. It provides a sufficient condition for the folk theorem when the game is irreducible, thus generalizing the results of Dutta (1995) and Fudenberg, Levine, and Maskin (1994). To do this, the paper extends the concept of self-generation (Abreu, Pearce, and Stacchetti, 1990) to “return generation,” which explicitly tracks actions and incentives until the next time the state returns to its current value, and asks that players not wish to deviate given the way their continuation payoffs from the time of this return depend on the public signals that have been observed.

One of the main problems impeding the evolution of cooperation is partner choice. When information is asymmetric (the quality of a potential partner is known only to himself), it may seem that partner choice is not possible without signaling. Many mutualisms, however, exist without signaling, and the mechanisms by which hosts might select the right partners are unclear. Here we propose a general mechanism of partner choice, "screening," that is similar to the economic theory of mechanism design. Imposing the appropriate costs and rewards may induce the informed individuals to screen themselves according to their types and therefore allow a noninformed individual to establish associations with the correct partners in the absence of signaling. Several types of biological symbioses are good candidates for screening, including bobtail squid, ant-plants, gut microbiomes, and many animal and plant species that produce reactive oxygen species. We describe a series of diagnostic tests for screening. Screening games can apply to the cases where by-products, partner fidelity feedback, or host sanctions do not apply, therefore explaining the evolution of mutualism in systems where it is impossible for potential symbionts to signal their cooperativeness beforehand and where the host does not punish symbiont misbehavior.

We study the perfect type-contingently public ex-post equilibrium (PTXE) of repeated games where players observe imperfect public signals of the actions played, and both the payoff functions and the map from actions to signal distributions depend on an unknown state. The PTXE payoffs when players are patient are determined by the solutions to a family of linear programming problems. Using this characterization, we develop conditions under which play can be as if the players have learned the state. We provide a sufficient condition for the folk theorem, and a characterization of the PTXE payoffs in games with a known monitoring structure.

Di erent discrete time triangular arrays representing a noisy signal of players' activities can lead to the same limiting di usion process yet lead to di erent limit equilibria. Whether the limit equilibria are equilibria of the limiting continuous time game depends on the limit properties of test statistics for whether a player has deviated. We provide an estimate of the tail probabilities along these arrays that allows us to determine the asymptotic behavior of the best test and thus of the best equilibrium.

Nash equilibrium takes optimization as a primitive, but suboptimal behavior can persist in simple stochastic decision problems. This has motivated the development of other equilibrium concepts such as cursed equilibrium and behavioral equilibrium. We experimentally study a simple adverse selection (or “lemons”) problem and find that learning models that heavily discount past information (i.e. display recency bias) explain patterns of behavior better than Nash, cursed or behavioral equilibrium. Providing counterfactual information or a record of past outcomes does little to aid convergence to optimal strategies, but providing sample averages (“recaps”) gets individuals most of the way to optimality. Thus recency effects are not solely due to limited memory but stem from some other form of cognitive constraints. Our results show the importance of going beyond static optimization and incorporating features of human learning into economic models.

We examine the long-term implication of two models of learning with recency bias: recursive weights and limited memory. We show that both models generate similar beliefs and that both have a weighted universal consistency property. Using the limited-memory model we produce learning procedures that both are weighted universally consistent and converge with probability one to strict Nash equilibrium.

Consider a model of location choice by two sorts of agents, called “buyers” and “sellers”: In the first period agents simultaneously choose between two identical possible locations; following this, the agents at each location play some sort of game with the other agents there. Buyers prefer locations with fewer other buyers and more sellers, and sellers have the reverse preferences. We study the set of possible equilibrium sizes for the two markets, and show that two markets of very different sizes can co-exist even if larger markets are more efficient. This extends the analysis of Ellison and Fudenberg [2003. Quart. J. Econ. 118, 1249–1278], who ignored the constraint that the number of agents of each type in each market should be an integer, and instead analyzed the “quasi-equilibria” where agents are treated as infinitely divisible.

Costly punishment can facilitate cooperation in public-goods games, as human subjects will incur costs to punish non-cooperators even in settings where it is unlikely that they will face the same opponents again. Understanding when and why it occurs is important both for the design of economic institutions and for modeling the evolution of cooperation. Our experiment shows that subjects will engage in costly punishment even when it will not be observed until the end of the session, which supports the view that agents enjoy punishment. Moreover, players continue to cooperate when punishment is unobserved, perhaps because they (correctly) anticipate that shirkers will be punished: Fear of punishment can be as effective at promoting contributions as punishment itself.

Jean Tirole was awarded the 2014 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel for his analysis of market power and regulation. This paper provides an overview of some of that work, and of his related contributions to game theory.

We derive a simplified version of the model of Fudenberg and Levine, 2006 and Fudenberg and Levine, 2011 and show how this approximate model is useful in explaining choice under risk. We show that in the simple case of three outcomes, the model can generate indifference curves that “fan out” in the Marschak–Machina triangle, and thus can explain the well-known Allais and common ratio paradoxes that models such as prospect theory and regret theory are designed to capture. At the same time, our model is consistent with modern macroeconomic theory and evidence and generates predictions across a much wider set of domains than these models.