Self-consistent Feedback Stackelberg Equilibria for Infinite Horizon Stochastic Games

Alberto Bressan, Yilun Jiang

Research output: Contribution to journalArticle

1 Citation (Scopus)

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)
JournalDynamic Games and Applications
DOIs
StateAccepted/In press - Jan 1 2019

Fingerprint

Stackelberg Equilibrium
Discount Factor
Stochastic Games
Infinite Horizon
Markov processes
Game
Feedback
Existence and Uniqueness of Solutions
Cost functions
Markov Process
Cost Function
Continuous Time
Horizon
Markov chain
State Space
Subset
Costs
Coefficient
Concepts
Strategy

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

Cite this

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Self-consistent Feedback Stackelberg Equilibria for Infinite Horizon Stochastic Games. / Bressan, Alberto; Jiang, Yilun.

In: Dynamic Games and Applications, 01.01.2019.

Research output: Contribution to journalArticle

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