On Information Design in Games

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 (2011). 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.