Continuous Implementation

It is well-known that mechanism design literature makes many simplifying infor- mational assumptions in particular in terms of common knowledge of the environment among players. In this paper, we introduce a notion of continuous implementation and characterize when a social choice function is continuously implementable. More specif- ically, we say that a social choice function is continuously (partially) implementable if it is (partially) implementable for types in the model under study and it continues to be (partially) implementable for types "close" to this initial model. We ?rst show that if the model is of complete information a social choice function is continuously (partially) implementable only if it satis?es Maskin?s monotonicity. We then extend this result to general incomplete information settings and show that a social choice function is continuously (partially) implementable only if it is fully implementable in iterative dominance. For ?nite mechanisms, this condition is also su¢ cient. We also discuss implications of this characterization for the virtual implementation approach.High order beliefs, robust implementation

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

A Characterization of Stochastically Stable Networks

Jackson and Watts [J. of Econ. Theory 71 (2002), 44-74] have examined the dynamic formation and stochastic evolution of networks. We provide a refinement of pairwise stability, p-pairwise stability, which allows us to characterize the stochastically stable networks without requiring the "tree construction" and the computation of resistance that may be quite complex. When a 1/2-pairwise stable network exists, it is unique and it coincides with the unique stochastically stable network. To solve the inexistence problem of p-pairwise stable networks, we define its set-valued extension with the notion of p-pairwise stable set. The 1/2-pairwise stable set exists and is unique. Any stochastically stable network is included in the 1/2-pairwise stable set. Thus, any network outside the 1/2-pairwise stable set must be considered as a nonrobust network. We also show that the 1/2-pairwise stable set can contain no pairwise stable network and we provide examples where a set of networks is more "stable" than a pairwise stable network.Network formation, Pairwise stability, Stochastic stability

Implementation with Evidence: Complete Information

We study full-implementation in Nash equilibrium under complete information. We generalize the canonical model (Maskin, 1977) by allowing agents to send evidence or discriminatory signals. A leading case is where evidence is hard information that proves something about the state of the world. In this environment, an implementable social choice rule need not be Maskin-monotonic. We formulate a weaker property, evidence-monotonicity, and show that this is a necessary condition for implementation. Evidence-monotonicity is also sufficient for implementation if there are three or more agents and the social choice rule satisfies two other properties—no veto power and non-satiation—that are reasonable in various settings, including “economic environments”. We discuss how natural conditions on the cost of discriminatory signals yield possibility results, in contrast with traditional negative results. Additional results are provided for the case of one and two agents.

The cutting power of preparation

In a strategic game, a curb set [Basu and Weibull, Econ. Letters 36 (1991) 141] is a product set of pure strategies containing all best responses ro every possible belief restricted to this set. Prep sets [Voorneveld, Games Econ. Behav. 48 (2004) 403] relax this condition by only requiring the presence of at least one best response to such a belief. The purpose of this paper is to provide economically interesting classes of games in which minimal prep sets give sharp predictions, whereas in relevant subclasses of these games, minimal curb sets have no cutting power whatsoever and simply consist of the entire strategy space. These classes include potential games, congestion games with player-specific payoffs, and supermodular games.curb sets; prep sets; potential games; congestion games; supermodular games

Sélection d'équilibre par l'information incomplète

Un certain nombre d'articles récents montrent qu'en relâchant l'hypothèse standard de connaissance commune des paiements d'un jeu, il est possible de faire émerger un unique équilibre. Dans cet article, nous chercherons à comprendre les mécanismes à l'œuvre dans cette littérature. Nous nous focaliserons sur un exemple représentatif qui nous permettra de séparer notre analyse entre étude de la structure d'information et étude de la structure des paiements. Nous étudierons les sens dans lesquels on peut considérer ces jeux comme relâchant " faiblement " l'hypothèse de connaissance commune des paiements. Puis nous tâcherons de voir quel type d'équilibre est sélectionné par cette approche. - See more at: http://rei.revues.org/338#sthash.a5C9HI6h.dpu

Implementation with evidence

We generalize the canonical problem of Nash implementation by allowing agents to voluntarily provide discriminatory signals, i.e. evidence. Evidence can either take the form of hard information or, more generally, have differential but non-prohibitive costs in different states. In such environments, social choice functions that are not Maskin-monotonic can be implemented. We formulate a more general property, evidence-monotonicity, and show that this is a necessary condition for implementation. Evidence-monotonicity is also sufficient for implementation in economic environments. In some settings, such as when agents have small preferences for honesty, any social choice function is evidence-monotonic. Additional characterizations are obtained for hard evidence. We discuss the relationship between the implementation problem where evidence provision is voluntary and a hypothetical problem where evidence can be chosen by the planner as part of an extended outcome space.Mechanism design, costly signaling, verifiable information, Nash implementation

Rationalizable Implementation

We consider the implementation of social choice functions under complete information in rationalizable strategies. A strict (and thus stronger) version of the monotonicity condition introduced by Maskin (1999) is necessary under the solution concept of rationalizability. Assuming the social choice function is responsive (i.e., it never selects the same outcome in two distinct states), we show that it is also sufficient under a mild "no worst alternative" condition. In particular, no economic condition is required. We also discuss how our results extend when the social choice function is not responsive.Implementation, Complete information, Rationalizability, Maskin monotonicity

Log-linear dynamics and local potential

We show that local potential maximizer ([15]) with constant weights is stochastically stable in the log-linear dynamics provided that the payoff function or the associated local potential function is supermodular. We illustrate and discuss, through a series of examples, the use of our main results as well as other concepts closely related to local potential maximizer: weighted potential maximizer, p-dominance. We also discuss the log-linear processes where each player's stochastic choice rule converges to the best response rule at different rates. For 2 x 2 games, we examine a modified log-linear dynamics (relative log-linear dynamics) under which local potential maximizer with strictly positive weights is stochastically stable. This in particular implies that for 2 x 2 games a strict (p1,p2)-dominant equilibrium with p1+p2<1 is stochastically stable under the new dynamics