Each player in an infinite population interacts strategically with a finite subset of that population. Suppose each player's binary choice in each period is a best response to the population choices of the previous period. When can behaviour that is initially played by only a finite set of players spread to the whole population? This paper characterizes when such contagion is possible for arbitrary local interaction systems. Maximal contagion occurs when local interaction is sufficiently uniform and there is low neighbour growth, i.e. the number of players who can be reached in k steps does not grow exponentially in k.

'No trade' theorems have shown that new information will not lead to trade when agents share the same prior beliefs. This paper explores the structure of no trade theorems with heterogeneous prior beliefs. It is shown how different notions of efficiency under asymmetric information--ex ante, interim, ex post--are related to agents' prior beliefs as well as incentive compatible and public versions of those efficiency concepts. These efficiency results are used to characterize necessary and sufficient conditions on agents' beliefs for no trade theorems in different trading environments.

An important question in political economy concerns the form of transfers to special interests. The Chicago view is that political competition leads politicians to make such transfers efficiently. The Virginia position is that lack of information on the part of voters leads politicians to favor inefficient "sneaky" methods of redistribution. This paper analyzes the form of transfers in a model of political competition in which politicians have incentives to make transfers to special interests. It shows that when voters have imperfect information about both the effects of policy and the predispositions of politicians, inefficient methods of redistribution may be employed.

Given a game with uncertain payoffs, information design analyzes the extent to which the provision of information alone can influence the behavior of the players. Information design has a literal interpretation, under which there is a real information designer who can commit to the choice of the best information structure (from her perspective) for a set of participants in a game. We emphasize a metaphorical interpretation, under which the information design problem is used by the analyst to characterize play in the game under many different information structures. We provide an introduction to the basic issues and insights of a rapidly growing literature in information design. We show how the literal and metaphorical interpretations of information design unify a large body of existing work, including that on communication in games (Myerson 1991), Bayesian persuasion (Kamenica and Gentzkow 2011), and some of our own recent work on robust predictions in games of incomplete information.

A social choice function is robustly implementable if there is a mechanism under which the process of iteratively eliminating strictly dominated messages lead to outcomes that agree with the social choice function for all beliefs at every type profile. In an interdependent-value environment with single-crossing preferences, we identify a contraction property on the preferences which together with strict ex post incentive compatibility is sufficient to guarantee robust implementation in the direct mechanism. Strict ex post incentive compatibility and the contraction property are also necessary for robust implementation in any mechanism, including indirect ones. The contraction property requires that the interdependence is not too high. In a linear signal model, the contraction property is equivalent to an interdependence matrix having all eigenvalues smaller than one.

An informed advisor wishes to convey her valuable information to an uninformed decision maker with identical preferences. Thus she has a current incentive to truthfully reveal her information. But if the decision maker thinks that the advisor might be biased in favor of one decision and the advisor does not wish to be thought to be biased, the advisor has a reputational incentive to lie. If the advisor is sufficiently concerned about her reputation, no information is conveyed in equilibrium. In a repeated version of this game, the advisor will care (instrumentally) about her reputation simply because she wants her valuable and unbiased advice to have an impact on future decisions. I.

A number of papers have shown that a strict Nash equilibrium action profile of a game may never be played if there is a small amount of incomplete information. The authors present a general approach to analyzing the robustness of equilibria to a small amount of incomplete information. A Nash equilibrium of a complete information game is said to be robust to incomplete information if every incomplete information game with payoffs almost always given by the complete information game has an equilibrium which generates behavior close to the Nash equilibrium. The authors show that many games with strict equilibria have no robust equilibrium and examine why they get such different results from existing refinements. If a game has a unique correlated equilibrium, it is robust. A natural many-player many-action generalization of risk dominance is a sufficient condition for robustness.

We study the informational events that trigger equilibrium shifts in coordination games with incomplete information. Assuming that the distribution of the changes in fundamentals has fat tails, we show that majority play shifts either if fundamentals reach a critical threshold or if there are large common shocks, even before the threshold is reached. The fat-tail assumption matters because it implies that large shocks make players more unsure about whether their payoffs are higher than others. This feature is crucial for large shocks to matter.

An Ascending Auction for Interdependent Values: Uniqueness and Robustness to Strategic Uncertainty by Dirk Bergemann and Stephen Morris. Published in volume 97, issue 2, pages 125-130 of American Economic Review, May 2007