Continuous-time Repeated Games with Imperfect Information: Folk Theorems and Explicit Results

• Author / Creator

  Bernard, Benjamin

• This thesis treats continuous-time models of repeated interactions with imperfect public monitoring. In such models, players do not directly observe each other's actions and instead see only the impacts of the chosen actions on the distribution of a random signal. Often, there are two reasons why this signal imperfectly reflects the chosen actions: (a) information is continuously available but it is noisy, or (b) events are observable but occur only at intermittent occasions. In a continuous-time setting, these two different types of information can be cleanly distinguished, where Brownian motion is used to model noise in the continuous information and Poisson processes indicate the arrival of informative events with an intensity that depends on players' actions. The first major result of this thesis is a folk theorem for continuous-time repeated games even when players receive only noisy information about past play. The folk theorem gives sufficient conditions such that players achieve asymptotic efficiency as they get arbitrarily patient. Because more outcomes are sustainable in equilibrium when more information is observed, this result also applies when players receive both aforementioned types of imperfect information. In the proof, we restrict ourselves to strategies that are adjusted only at identical copies of certain stopping times. This has two important implications: (1) despite the possibility of switching actions infinitesimally fast, players do not need to do so to attain asymptotic efficiency, and (2) continuous-time equilibria can be attained as limits of equilibria in discrete-time repeated games where the length of the time period is random, rather than fixed. The other main result of this thesis is a characterization of all payoffs that are attainable in equilibrium in such games with two finitely patient players. Relating optimal actions and incentives to the boundary of the equilibrium payoff set, we obtain a differential equation describing the curvature of the set at almost every point. The equilibrium payoff set is obtained from an iterative procedure, which is similar to that known for discrete-time repeated games but leads to an explicit characterization in our setting. Our result shows that the two types of information have drastically different impacts on the equilibrium payoff set. This is due to the fundamental difference in which the two types of information are used to provide incentives: while the continuous information can be used only to transfer value between players, the discontinuous information may be used to transfer or destroy value upon the arrival of an infrequent event. The quantitative nature of the result makes it possible to precisely measure the impact of abrupt information on the efficiency of players' payoffs in equilibrium. Thus, one can compare the value of additional information to the cost of procuring or providing it, which may lead to interesting applications in mechanism design and information disclosure.

• Subjects / Keywords

  • Equilibrium characterization
  • Intertemporal incentives
  • Continuous-time games
  • Folk theorem
  • Imperfect observability
  • Repeated games
  • Game theory

• Graduation date

  Spring 2016

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3M03Z29D

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.