Essays on games and information.

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The first two chapters of my dissertation contribute to two relatively unexplored topics at the intersection of information economics and applied game theory. The same piece of information is not necessarily equally informative for all parties. I call a piece of information equivocal if its owner is unable to predict how a receiver would interpret it: different receivers might interpret it either positively or negatively. The first chapter studies strategic information transmission between equivocally informed senders, and an uninformed receiver. Upon reception, the receiver has the ability to understand the information at a cost, and use it to take a decision that affects all parties. In particular, I analyze the effects of competition between equivocally informed senders. The second chapter develops a model of contest between teams. It uses techniques from the literature on large coordination games with private and public information to solve for the equilibrium of the game. Situations combining strategic interactions within and across groups have rarely been analyzed in the theoretical literature, but have received more attention from the experimental literature. The last chapter is a note on the simplification of message spaces in mechanisms and games.;In the traditional analysis of situations where an informed sender tries to persuade an uninformed receiver to take a certain action by selectively communicating hard information, all the relevant information is revealed in equilibrium because any action of the sender can be outguessed by the receiver. If the sender is unable to interpret her own information, however, this classical unraveling argument breaks down. When, in the absence of information, the receiver is sufficiently inclined to act as the sender wishes, the sender has no incentive to inform her. My first chapter examines whether full disclosure can be restored when there is competition between multiple senders. In the model, the senders compete for a limited number of prizes allocated by the receiver. Full disclosure can be restored only in the presence of weak candidates. With sufficiently many weak candidates, it is always possible to ensure full disclosure.;My second chapter studies a model of social contest between two large teams Individuals can choose whether to actively support their team. They become active supporters if they expect their team to win with a sufficiently high probability. The identity of the winning team is decided according to a deterministic social rule which is a function of the teams' strengths and activity rates. Agents have imperfect and heterogeneous information about the strength of the other team, from both public and private sources with known precisions. I show that no modification of the information structure gives an unambiguous advantage to one particular team. The effects of private and public precisions on equilibrium outcomes are always opposed. Increasing the precision of public information for a team has the same effect as increasing the sensitivity of the social rule to the activity rate of that team, illustrating the idea that public information favors collective action. For a particular example of the social rule, the paper characterizes the information structure that would arise endogenously in a game where at the outset, two team leaders choose the precision of the public signal that will be sent to the other team.;The last chapter provides necessary and sufficient conditions for the simplification of a mechanism or a game is tight. Indeed Milgrom proposes to simplify mechanisms by restricting their message space. This makes it easier to implement them in practice. When simplifying message spaces, it is important not to create new Nash equilibria. A tight simplification is one that does not create any new Nash equilibrium, a strongly tight simplification is one that does not create any new epsilon-Nash equilibrium. I offer characterizations of tightness and strong tightness for any preference domain, based on the observation that in order not to create new equilibria, a simplification needs to preserve at least one deviation to any remaining strategy profile that is not an equilibrium. When the preference domain is that of continuous utility functions on the outcome space, I show that tightness and strong tightness are equivalent, and are also equivalent to the outcome closure property of Milgrom .