Communication, Information, and Learning

Abstract

The first chapter of this thesis presents robust neologism proofness, an equilibrium refinement that applies to both cheap-talk and costly signaling games. Robust neologism proofness eliminates equilibria that can be undone by a certain kind of credible communication from the sender to the receiver. We show that robust neologism proof equilibria exist both in monotonic signaling games and signaling games where the sender can give a transfer to the receiver. We apply robust neologism proofness to various examples and compare it with other equilibrium refinements, and show that in monotone-concave-supermodular signaling games with transfers, robust neologism proofness selects the sender-optimal separating equilibria.

The second chapter studies justified communication equilibrium (JCE), a different equilibrium refinement for signaling games with cheap-talk communication. A strategy profile must be a JCE to be a stable outcome of non-equilibrium learning when receivers are initially trusting and senders play many more times than receivers. In the learning model, the counterfactual "speeches" that have been informally used to motivate past refinements are messages that are actually sent. Stable profiles need not be perfect Bayesian equilibria, so JCE sometimes preserves equilibria that existing refinements eliminate. Despite this, it resembles the earlier refinements D1 and NWBR, and it coincides with them in co-monotonic signaling games.

The third chapter studies principal-agent settings where the principal has private information, both the principal and agent take actions, and the agent's action is subject to moral hazard. Unlike past work focusing on explicit contracts, we allow the principal to propose contracts that give them flexibility in their choice of future actions. We develop an adaptation of sequential equilibrium called contracting equilibrium for our principal-agent games, and prove its existence. In environments where the principal's type and agent's action are complements, the condition of payoff-plausibility characterizes the outcomes that survive robust neologism proofness as well as the strongly justified communication equilibrium outcomes. The principal-optimal safe outcomes, which are analogs of the sender-optimal separating outcomes of signaling games, are always payoff-plausible contracting equilibrium outcomes. They also provide an important payoff benchmark: Every principal type must obtain a weakly higher payoff from every payoff-plausible equilibrium.