What are the welfare effects of enhanced dissemination of public information through the media and disclosures by market participants with high public visibility? We examine the impact of public information in a setting where agents take actions appropriate to the underlying fundamentals, but they also have a coordination motive arising from a strategic complementarity in their actions. When the agents have no socially valuable private information, greater provision of public information always increases welfare. However, when agents also have access to independent sources of information, the welfare effect of increased public disclosures is ambiguous.

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.4. Goyal (1996) uses a rich set of examples to examine the effect of changes in the local interaction system.

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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 and explain over-reaction to (noisy) public information. * This is a much revised version of the paper with the longer title "Beauty Contests, Bubbles and Iterated Expectations in Asset Markets". We thank seminar participants at the LSE, the Bank of England, the IMF, Stanford, the accounting theory mini-conference at Chicago GSB, and the Gerzensee finance meetings for their comments. We thank Mehul Kamdar for capable research assistance. We are grateful to the editor, Maureen O'Hara and a referee for their guidance.

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Creditors of a distressed borrower face a coordination problem. Even if the fundamentals are sound, fear of premature foreclosure by others may lead to pre-emptive action, undermining the project. Recognition of this problem lies behind corporate bankruptcy provisions across the world, and it has been identified as a culprit in international financial crises, but has received scant attention from the literature on debt pricing. Without common knowledge of fundamentals, the incidence of failure is uniquely determined provided that private information is precise enough. This affords a way to price the coordination failure. Comparative statics on the unique equilibrium provides several insights on the role of information and the incidence of inefficient liquidation.

A number of papers have shown that a strict Nash equilibrium action pro¯le of a game may never be played if there is a small amount of incomplete information (see, for example, Carlsson and van Damme (1993a)). We 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 payo®s almost always given by the complete information game has an equilibrium which generates behavior close to the Nash equilibrium. We show that an open set of games has no robust equilibrium and examine why we get such di®erent results from the re¯nements literature. We show that if a game has a unique correlated equilibrium, it is robust. Finally, a natural many-player many-action generalization of risk dominance is shown to be a su±cient condition for robustness. ¤ We are grateful to Eddie Dekel, Drew Fudenberg and George Mailath for valuable comments.

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