Self-consistent Feedback Stackelberg Equilibria for Infinite Horizon Stochastic Games

Alberto Bressan () and Yilun Jiang ()
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Alberto Bressan: Penn State University
Yilun Jiang: Penn State University

Dynamic Games and Applications, 2020, vol. 10, issue 2, No 2, 328-360

Abstract: 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 $$\mathcal{C}^k$$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.

Keywords: Non-cooperative game; Stackelberg equilibrium; Feedback strategy (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s13235-019-00329-9

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