“…The uniqueness of the rationalizable solution depends solely on the fundamentals of the model. Strong rationality has been studied as well in terms of the stability of equilibria (Morris and Shin, 1998;Desgranges, 2000;Gauthier, 2002;Chamley, 2004;Ghosal, 2006) and in static and dynamic macroeconomic models (Evans and Guesnerie, 1993, 2003, 2005. 2 In these contributions, however, the definition of the rationalizable solution is usually intuitive and/or context-specific, adapting the original definitions and characterizations of rationalizable strategies to models with a non-atomic set of agents.…”
The concept of rationalizability has been used in the last fifteen years to study stability of equilibria in models with a continuum of agents such as competitive markets, macroeconomic dynamics and currency attacks. However, rationalizability has been formally defined in general settings only for games with a finite number of players. We propose an exploration of rationalizability in the context of games with a continuum of players. We deal with a special class of these games, in which payoff of each player depends only on his own strategy and on an aggregate value: the state of the game, which is obtained from the complete action profile. We define the sets of point-rationalizable states and rationalizable states. For the case of continuous payoffs and compact strategy sets, we characterize these sets and prove their convexity and compactness. We provide as well results on the equivalence of point-and standard-rationalizability.
“…The uniqueness of the rationalizable solution depends solely on the fundamentals of the model. Strong rationality has been studied as well in terms of the stability of equilibria (Morris and Shin, 1998;Desgranges, 2000;Gauthier, 2002;Chamley, 2004;Ghosal, 2006) and in static and dynamic macroeconomic models (Evans and Guesnerie, 1993, 2003, 2005. 2 In these contributions, however, the definition of the rationalizable solution is usually intuitive and/or context-specific, adapting the original definitions and characterizations of rationalizable strategies to models with a non-atomic set of agents.…”
The concept of rationalizability has been used in the last fifteen years to study stability of equilibria in models with a continuum of agents such as competitive markets, macroeconomic dynamics and currency attacks. However, rationalizability has been formally defined in general settings only for games with a finite number of players. We propose an exploration of rationalizability in the context of games with a continuum of players. We deal with a special class of these games, in which payoff of each player depends only on his own strategy and on an aggregate value: the state of the game, which is obtained from the complete action profile. We define the sets of point-rationalizable states and rationalizable states. For the case of continuous payoffs and compact strategy sets, we characterize these sets and prove their convexity and compactness. We provide as well results on the equivalence of point-and standard-rationalizability.
The eductive approach consists of finding solutions consistent with common knowledge of individual rationality and the model. An equilibrium is stable whenever it is the unique outcome consistent with these assumptions. This is a strong stability criterion as it relies on no assumption of prior knowledge of others’ expectations. This review presents various (in)stability results. It focuses on the following method: Rewrite the model as a temporary equilibrium map in which the current economic outcome is determined by expectations and characterize stability by contracting properties of this map. The main insight suggested by these results is due to Guesnerie (2002) : Stability is obtained when the actual outcome is not very sensitive to expectations. Additional insights include that agents’ heterogeneity is a source of instability; the ability of prices to transmit information is limited by the quality of private information; and coordination when agents are infinitely lived is difficult because of the large effect of long-run expectations.
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