Self-consistent Feedback Stackelberg Equilibria for Infinite Horizon Stochastic Games

Alberto Bressan, Yilun Jiang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The paper introduces a concept of “self consistent” Stackelberg equilibria for stochastic games in infinite time horizon, where the two players adopt feedback strategies and have exponentially discounted costs. The analysis is focused on games in continuous time, described by a controlled Markov process with finite state space. Results on the existence and uniqueness of such solutions are provided. As an intermediate step, a detailed description of the structure of the best reply map is achieved, in a “generic” setting. Namely: for all games where the cost functions and the transition coefficients of the Markov chain lie in open dense subset of a suitable space Ck. Under generic assumptions, we prove that a self-consistent Stackelberg equilibrium exists, provided that either (i) the leader is far-sighted, i.e., his exponential discount factor is sufficiently small, or (ii) the follower is narrow-sighted, i.e., his discount factor is large enough.

Original languageEnglish (US)
Pages (from-to)328-360
Number of pages33
JournalDynamic Games and Applications
Volume10
Issue number2
DOIs
StatePublished - Jun 1 2020

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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