### 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 C^{k}. 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 language | English (US) |
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Journal | Dynamic Games and Applications |

DOIs | |

State | Accepted/In press - Jan 1 2019 |

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### 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.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Self-consistent Feedback Stackelberg Equilibria for Infinite Horizon Stochastic Games

AU - Bressan, Alberto

AU - Jiang, Yilun

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85070933064&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85070933064&partnerID=8YFLogxK

U2 - 10.1007/s13235-019-00329-9

DO - 10.1007/s13235-019-00329-9

M3 - Article

AN - SCOPUS:85070933064

JO - Dynamic Games and Applications

JF - Dynamic Games and Applications

SN - 2153-0785

ER -