Date of Award
Doctor of Philosophy (PhD)
Chair and Committee
David K Levine
This dissertation studies self-referential games in which agents can learn (perfectly and imperfectly) about an opponents' intentions from a private signal. In the first chapter, my main focus is on the interaction of two sources of information about opponents' play: direct observation of an opponent's code of conduct and indirect observation of the same opponent's play in a repeated setting. Using both sources of information I prove a folk theorem for repeated self-referential games with private monitoring. In the second chapter, I investigate the impact of self-referentiality on bad reputation games in which the long-run player must choose specific actions to make short-run players participate in the game. Since these particular actions could be interpreted as evidence of perverse behavior, the long-run agent attempts to separate himself from other types and this results in efficiency losses. When players identify intentions perfectly, I show that inefficiencies and reputational concerns due to a bad reputation disappear. In the case of imperfect observation, I find that self-referentiality and stochastic renewal of the long-run player together overcome inefficiencies because of bad reputation. In the third chapter, I address the timing of signals in self-referential games. These models typically suppose that intentions are divined in a pre-play phase; however, in many applications this may not be the case. For games with perfect information when players observe signals in advance, I show that any subgame perfect equilibria of an infinite-horizon game coincides with a Nash equilibrium of the self-referential finite-horizon approximation of the original game. Then, I focus on two specific classes of games. First, in finitely repeated games with discounting I show that a version of the folk theorem holds regardless of the time at which signals are observed. Second, I examine exit games in which players can terminate the game at any stage. In contrast to repeated games, I find that the equilibrium outcome of the self-referential exit game is unique if signals arrive after the first stage, whereas a folk theorem results only if they occur before the first stage. Finally, I explore asynchronous monitoring of intentions where players may not receive signals simultaneously. With asynchronicity, a folk theorem continues to apply for repeated games; however, for exit games there is a unique equilibrium outcome independent of signal timing, or indeed, independent of having a signal.
Block, Juan Ignacio, "Essays on Self-Referential Games" (2014). All Theses and Dissertations (ETDs). 1220.