# Coordination and Private Information Revelation  
[PERSON]  
strategic complementarities arise due to peculiarities in the production and demand functions, as well as models where the presence of private information and search costs result in coordination failures and over-reactions to aggregative shocks. Ref [7] discusses strategic complementarities in a multi-sector imperfectly competitive economy resulting in coordination failure. Turning to the formal model, we consider a framework with two agents, call them A and B, with both having an \"idea\" of their own. They obtain a payoff from their own idea, as well as an additional amount in case there is coordination on a single idea. Furthermore, the type of one of the agents, say agent A, is private information. We consider a two stage game where, in Stage 1, agent A can reveal her type1, and then in Stage 2 they play a battle-of-the sexes game where they decide on which idea to adopt. In line with much of the literature on persuasion games, information is taken to be hard. Footnote 1: For the sake of clarity, we assume feminine gender for agent/player A and masculine gender for B. Our central result is that disclosure of private information is linked with the possibility of coordination failure-_to wit_, equilibria with full disclosure exist in the absence of any coordination failure; whereas in the presence of coordination failure, there exists an equilibrium with no information revelation. We begin by examining two different scenarios where there is complete information disclosure. In the first, the agents play a pure strategy equilibrium, coordinating on \(A\) if agent A's type had been revealed to be'sufficiently high', and coordinating on \(B\) otherwise. In the second, we allow for correlated equilibria in the coordination stage. In neither of these cases are there coordination failures, and, consistent with our intuition, there exist equilibria with full disclosure. We next examine equilibria with coordination failure in Stage 2, with this failure being captured by the fact that while agent A plays a cut-off strategy, adopting \(A\) if and only if her type is'sufficiently high', agent B plays a completely mixed strategy. We find that in the presence of such strategic uncertainty [PERSON] never reveals her own type. This non-revelation result is in contrast to the early literature on persuasion games which uses an unraveling argument to demonstrate that there would be full disclosure. Our analysis traces the non-revelation result to the possibility of strategic uncertainty over coordination possibilities. Thus this result adds to the subsequent literature that examines economic environments where the revelation argument needs to be qualified. One can mention, among others, ref [8], who finds partial revelation in the presence of costly revelation of private information; ref [9], who argue that in the presence of asymmetric information over the preference of the information providers there is no information revelation; and [10], who study sufficient conditions for complete revelation of private information, when such disclosure is a strategic choice. However, the latter rule out strategic uncertainty in coordination by abstracting from 'coordination equilibria', whereby there can be multiple pure strategy equilibria in the stage following information communication. The intuition for the non-revelation result has to do with coordination possibilities in the second stage game. Why, for example, should an agent with a valuable private idea not want to reveal? We find that the non-revelation argument holds whenever the continuation game in the coordination stage involves strategic uncertainty, formalized through a mixed-strategy equilibrium. An important aspect of the mixed-strategy equilibrium in a coordination game is that, in order to keep the opponent indifferent between her two actions, a player has to play the action associated with a lower-payoff coordinated outcome with a higher probability than the action associated with a higher-payoff coordinated outcome.