Robust Equilibria under Non-Common Priors

This paper considers the robustness of equilibria to a small amount of incomplete information, where players are allowed to have heterogenous priors. An equilibrium of a complete information game is robust to incomplete information under non-common priors if for every incomplete information game where each player's prior assigns high probability on the event that the players know at arbitrarily high order that the payoffs are given by the complete information game, there exists a Bayesian Nash equilibrium that generates behavior close to the equilibrium in consideration. It is shown that for generic games, an equilibrium is robust under non-common priors if and only if it is the unique rationalizable action profile. Set-valued concepts are also introduced, and for generic games, a smallest robust set is shown to exist and coincide with the set of a posteriori equilibria

Robust Equilibria under Non-Common Priors

This paper considers the robustness of equilibria to a small amount of incomplete information, where players are allowed to have heterogenous priors. An equilibrium of a complete information game is robust to incomplete information under non-common priors if for every incomplete information game where each player's prior assigns high probability on the event that the players know at arbitrarily high order that the payoffs are given by the complete information game, there exists a Bayesian Nash equilibrium that generates behavior close to the equilibrium in consideration. It is shown that for generic games, an equilibrium is robust under non-common priors if and only if it is the unique rationalizable action profile. Set-valued concepts are also introduced, and for generic games, a smallest robust set is shown to exist and coincide with the set of a posteriori equilibria

Robust implementation under alternative information structures

In this paper we consider a model in which agents have complete information about their neighbours and, possibly, incomplete information about the rest of the economy. We consider two different informational frameworks. In the first, agents do not have priors about what is going on in the rest of the economy. In the second, agents are supposed to have priors about the unknown characteristics. We present a mechanism which any social choice correspondence satisfying monotonicity and no veto powet in both informational settings for every possible prior thus requiring little knowledge from the point of view of the designer of the information possesed by agents about the economy

Secure implementation

Strategy-proofness, requiring that truth-telling be a dominant strategy, is a standard concept in social choice theory. However, this concept has serious drawbacks. In particular, many strategy-proof mechanisms have multiple Nash equilibria, some of which produce the wrong outcome. A possible solution to this problem is to require double implementation in Nash equilibrium and in dominant strategies, i.e., secure implementation. We characterize securely implementable social choice functions and investigate the connections with dominant strategy implementation and robust implementation. We show that in standard quasi-linear environments with divisible private or public goods, there exist surplus-maximizing (non-dictatorial) social choice functions that can be securely implemented.Nash implementation, robust implementation, secure implementation, strategy-proofness

Robustness to incomplete information in repeated games

This paper extends the framework of Kajii and Morris (1997) to study the question of robustness to incomplete information in repeated games. We show that dynamically robust equilibria can be characterized using a one-shot robustness principle that extends the one-shot deviation principle. Using this result, we compute explicitly the set of dynamically robust equilibrium values in the repeated prisoners' dilemma. We show that robustness requirements have sharp intuitive implications regarding when cooperation can be sustained, what strategies are best suited to sustain cooperation, and how changes in payoffs affect the sustainability of cooperation. We also show that a folk theorem in dynamically robust equilibria holds, but requires stronger identifiability conditions than the pairwise full rank condition of Fudenberg, Levine and Maskin (1994).Robustness to incomplete information, one-shot robustness principle, repeated Prisoners' Dilemma, selective punishment, folk theorem

On the Strategic Impact of an Event under Non-Common Priors

This paper studies the impact of a small probability event on strategic behavior in incomplete information games with non-common priors. It is shown that the global impact of a small probability event (i.e., its propensity to affect strategic behavior at all states in the state space) has an upper bound that is an increasing function of a measure of discrepancy from the common prior assumption. In particular, its global impact can be arbitrarily large under non-common priors, but is bounded from above under common priors. These results quantify the different implications common prior and non-common prior models have on the (infinite) hierarchies of beliefs.common prior assumption; higher order belief; rationalizability; contagion; belief potential

Robust implementation under alternative information structures.

In this paper we consider a model in which agents have complete information about their neighbors and, possibly, incomplete information about the rest of the environment. We consider two different informational frameworks. In the firts, agents do not have priors about the relevant characteristics in the rest of the environment. In the second, agents are supposed to have priors about the unknown characteristics. We present a mechinism which implements any social choice correspondence satisfying monotonicity and no veto powe in both informational settings for every possible prior thus requiring little knowledge from the point of view ofthe desinner of the information possessed by agents about the environment.Nash implementation; Incomplete information; Local information;

Private value preturbations ad informational advantage in common value auctions

We analyze the value of being better informed than one’s rival in a two bidder, second price common value auction. In order to do so, we must pare down the continuum of equilibria that typically exists in this setting. We propose selecting an equilibrium that is robust to perturbing the common value of the object with small private value components. Under this selection, we show that having better information about the common value will frequently hurt rather than help a bidder and that the ratio of private value to common value information held by a bidder has a significant effect on the value of information