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.

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.

Even though self-fulfilling currency attacks lead to multiple equilibria when fundamentals are common knowledge, we demonstrate the uniqueness of equilibrium when speculators face a small amount of noise in their signals about the fundamentals. This unique equilibrium depends not only on the fundamentals, but also on financial variables, such as the quantity of hot money in circulation and the costs of speculative trading. In contrast to multiple equilibrium models, our model allows analysis of policy proposals directed at curtailing currency attacks.

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.

In a financial market where traders are risk averse and short lived and prices are noisy, asset prices today depend on the average expectation today of tomorrow's price. Thus (iterating this relationship) the date 1 price equals the date 1 average expectation of the date 2 average expectation of the date 3 price. This will not, in general, equal the date 1 average expectation of the date 3 price. We show how this failure of the law of iterated expectations for average belief can help understand the role of higher-order beliefs in a fully rational asset pricing model.

Players receive a return to investment that is increasing in the proportion of others who invest and the state and incur a small cost for acquiring information about the state. Their information is reflected in a stochastic choice rule, specifying the probability of a signal leading to investment. If discontinuous stochastic choice rules are infinitely costly, there is a unique equilibrium as costs become small, in which actions are a best response to a uniform (Laplacian) belief over the proportion of others investing. Infeasibility of discontinuous stochastic choice rules captures the idea that it is impossible to perfectly distinguish states that are arbitrarily close together and is both empirically documented and satisfied by many natural micro-founded cost functionals on information. Our results generalize global game selection results and establish that they do not depend on the specific additive noise information structure.

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.