Information provision in games influences behavior by affecting agents' beliefs about the state as well as their higher-order beliefs. We first characterize the extent to which a designer can manipulate agents' beliefs by disclosing information. We then describe the structure of optimal belief distributions, including a concave-envelope representation that subsumes the single-agent result of Kamenica and Gentzkow. This result holds under various solution concepts and outcome selection rules. Finally, we use our approach to compute an optimal information structure in an investment game under adversarial equilibrium selection.We are grateful to the editor, Emir Kamenica, and to three anonymous referees for their comments and suggestions, which significantly improved the paper. Special thanks are due to Anne-Katrin Roesler for her insightful comments as a discussant at the 2016 Cowles
A designer commits to a signal distribution that is informative about a payoff-relevant state. Conditional upon the privately observed signals, agents take actions that affect their payoffs as well as those of the designer. We show how to derive the (designer) optimal information structure in static finite environments. We fully characterize it in a symmetric binary setting for a parameterized game. In this environment, conditionally independent private signals are never strictly optimal. (JEL C72, D78, D82, D83)
In reality, the organizational structure of information -describing how information is transmitted to its recipients -is as important as its content. In this paper, we introduce families of (indirect) information structures, namely meeting schemes and delegated hierarchies, that capture the horizontal and vertical dimensions of realworld transmission. We characterize the outcomes that they implement in general (finite) games and show that they are optimal in binary-action environments with strategic complementarities. Our application to classical regime-change games illustrates the variety of optimal meeting schemes and delegated hierarchies as a function of the objective.
This paper studies supermodular mechanism design in environments with finite type spaces and interdependent valuations. In such environments, it is difficult to implement social choice functions in ex-post equilibrium, hence Bayesian Nash equilibrium becomes the appropriate equilibrium concept. The requirements for agents to play a Bayesian equilibrium are strong, so we propose mechanisms that are robust to bounded rationality and help guide agents towards an equilibrium. In quasi-linear environments that allow for informational and allocative externalities we show that any mechanism that implements a social choice function can be converted into a supermodular mechanism that implements the original social choice function's decision rule. We show that the supermodular mechanism can be chosen in a way that minimizes the size of the equilibrium set and provide two sets of sufficient conditions: for general decision rules and for decision rules that satisfy a certain requirement. This is followed by conditions for supermodular implementation with a unique equilibrium.
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