A simple axiomatics of dynamic play in repeated games

This paper proposes an axiomatic approach to study two-player infinitely repeated games. A solution is a correspondence that maps the set of stage games into the set of infinite sequences of action profiles. We suggest that a solution should satisfy two simple axioms: individual rationality and collective intelligence. The paper has three main results. First, we provide a classification of all repeated games into families, based on the strength of the requirement imposed by the axiom of collective intelligence. Second, we characterize our solution as well as the solution payoffs in all repeated games. We illustrate our characterizations on several games for which we compare our solution payoffs to the equilibrium payoff set of Abreu and Rubinstein (1988). At last, we develop two models of players' behavior that satisfy our axioms. The first model is a refinement of subgame-perfection, known as renegotiation proofness, and the second is an aspiration-based learning model.Axiomatic approach, repeated games, classification of games, learning, renegotiation

Sentiments and rationalizability

Sentiments are characteristics of players' beliefs. I propose two notions of sentiments, confidence and optimism, and I study their role in shaping the set of rationalizable strategy profiles in (incomplete information) games with complementarities. Confidence is related to a player's perceived precision of information; optimism is the sentiment that the outcome of the game will be ``favorable.'' I prove two main results on how sentiments and payoffs interact to determine the size and location of the set of rationalizable profiles. The first result provides an explicit upper bound on the size of the set of rationalizable strategy profiles, relating complementarities and confidence; the second gives an explicit lower bound on the change of location, relating complementarities and optimism. I apply these results to four areas. In models of currency crisis, the results suggest that the most confident investors may drive financial markets. In models of empirical industrial organization, the paper provides a classification of the parameter values for which the model is identified. In non-Bayesian updating, the results clarify the strategic implications of certain biases. Finally, the results generalize and clarify the uniqueness result of global games.Rationalizable strategy profiles; complementarities; sentiments; confidence; optimism

Beliefs and rationalizability in games with complementarities

We propose two characteristics of players' beliefs and study their role in shaping the set of rationalizable strategy profiles in games with incomplete information. The first characteristic, type-sensitivity, is related to how informative a player thinks his type is. The second characteristic, optimism, is related to how "favorable" a player expects the outcome of the game to be. The paper has two main results: the first result provides an upper bound on the size of the set of rationalizable strategy profiles, the second gives a lower bound on the change of location of this set. These bounds have explicit and relatively simple expressions that feature type-sensitivity, optimism, and properties of the payoffs. Our results generalize and clarify the well-known uniqueness result of global games (Carlsson and van Damme (1993)). They imply new uniqueness results and allow to study rationalizability in new environments. We provide applications to supermodular mechanism design (Mathevet (2010)) and non-Bayesian updating (Epstein (2006)).Complementarities, rationalizability, beliefs, type-sensitivity, optimism, global games, equilibrium uniqueness

Supermodular mechanism design

This paper introduces a mechanism design approach that allows dealing with the multiple equilibrium problem, using mechanisms that are robust to bounded rationality. This approach is a tool for constructing supermodular mechanisms, i.e. mechanisms that induce games with strategic complementarities. In quasilinear environments, I prove that if a social choice function can be implemented by a mechanism that generates bounded strategic substitutes - as opposed to strategic complementarities - then this mechanism can be converted into a supermodular mechanism that implements the social choice function. If the social choice function also satisfies some efficiency criterion, then it admits a supermodular mechanism that balances the budget. Building on these results, I address the multiple equilibrium problem. I provide sufficient conditions for a social choice function to be implementable with a supermodular mechanism whose equilibria are contained in the smallest interval among all supermodular mechanisms. This is followed by conditions for supermodular implementability in unique equilibrium. Finally, I provide a revelation principle for supermodular implementation in environments with general preferences.Implementation, mechanisms, learning, strategic complementarities, supermodular games

A Contraction Principle for Finite Global Games

I provide a new proof of uniqueness of equilibrium in a wide class of global games. I show that the joint best-response in these games is a contraction. The uniqueness result then follows as a corollary of the contraction property. Furthermore, the contraction mapping approach provides a revealing intuition for why uniqueness arises: Complementarities in games generate multiplicity of equilibria, but the global games structure dampens complementarities so that only one equilibrium exists. I apply my result to show that uniqueness is obtained through contraction in currency crises and Diamond’s search models

Nomination Processes and Policy Outcomes

We provide a set of new models of three different processes by which political parties nominate candidates for a general election: nominations by party leaders,nominations by a vote of party members, and nominations by a spending competition among potential candidates. We show that more extreme outcomes can emerge from spending competition than from nominations by votes or by party leaders, and that non-median outcomes can result via any of these processes. When voters (and potential nominees) are free to switch political parties, then median outcomes ensue when nominations are decided by a vote but not when nominations are decided by spending competition

Tractable dynamic global games and applications

We present a family of tractable dynamic global games and its applications. Agents privately learn about a fixed fundamental, and repeatedly adjust their investments while facing frictions. The game exhibits many externalities: payoffs may depend on the volume of investment, on its volatility, and on its concentration. The solution is driven by an invariance result: aggregate investment is (in a pivotal contingency) invariant to a large family of frictions. We use the invariance result to examine how frictions, including those similar to the Tobin tax, affect equilibrium. We identify conditions under which frictions discourage harmful behavior without compromising investment volume

Beliefs and rationalizability in games with complementarities

We propose two characteristics of players' beliefs and study their role in shaping the set of rationalizable strategy profiles in games with incomplete information. The first characteristic, type-sensitivity, is related to how informative a player thinks his type is. The second characteristic, optimism, is related to how "favorable" a player expects the outcome of the game to be. The paper has two main results: the first result provides an upper bound on the size of the set of rationalizable strategy profiles, the second gives a lower bound on the change of location of this set. These bounds have explicit and relatively simple expressions that feature type-sensitivity, optimism, and properties of the payoffs. Our results generalize and clarify the well-known uniqueness result of global games (Carlsson and van Damme (1993)). They imply new uniqueness results and allow to study rationalizability in new environments. We provide applications to supermodular mechanism design (Mathevet (2010)) and non-Bayesian updating (Epstein (2006))

A simple axiomatics of dynamic play in repeated games

This paper proposes an axiomatic approach to study two-player infinitely repeated games. A solution is a correspondence that maps the set of stage games into the set of infinite sequences of action profiles. We suggest that a solution should satisfy two simple axioms: individual rationality and collective intelligence. The paper has three main results. First, we provide a classification of all repeated games into families, based on the strength of the requirement imposed by the axiom of collective intelligence. Second, we characterize our solution as well as the solution payoffs in all repeated games. We illustrate our characterizations on several games for which we compare our solution payoffs to the equilibrium payoff set of Abreu and Rubinstein (1988). At last, we develop two models of players' behavior that satisfy our axioms. The first model is a refinement of subgame-perfection, known as renegotiation proofness, and the second is an aspiration-based learning model

Sentiments and rationalizability

Sentiments are characteristics of players' beliefs. I propose two notions of sentiments, confidence and optimism, and I study their role in shaping the set of rationalizable strategy profiles in (incomplete information) games with complementarities. Confidence is related to a player's perceived precision of information; optimism is the sentiment that the outcome of the game will be ``favorable.'' I prove two main results on how sentiments and payoffs interact to determine the size and location of the set of rationalizable profiles. The first result provides an explicit upper bound on the size of the set of rationalizable strategy profiles, relating complementarities and confidence; the second gives an explicit lower bound on the change of location, relating complementarities and optimism. I apply these results to four areas. In models of currency crisis, the results suggest that the most confident investors may drive financial markets. In models of empirical industrial organization, the paper provides a classification of the parameter values for which the model is identified. In non-Bayesian updating, the results clarify the strategic implications of certain biases. Finally, the results generalize and clarify the uniqueness result of global games