Open AccessA nonzero-sum risk-sensitive stochastic differential game in the orthant
Author(s) -
Mrinal K. Ghosh,
Somnath Pradhan
Publication year - 2022
Publication title -
mathematical control and related fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.658
H-Index - 21
eISSN - 2156-8472
pISSN - 2156-8499
DOI - 10.3934/mcrf.2021025
Subject(s) - orthant , ergodic theory , mathematics , nash equilibrium , markov chain , mathematical economics , correlated equilibrium , best response , risk dominance , markov process , differential game , mathematical optimization , combinatorics , game theory , epsilon equilibrium , pure mathematics , statistics , repeated game , equilibrium selection
We study a nonzero-sum risk-sensitive stochastic differential game for controlled reflecting diffusion processes in the nonnegative orthant. We treat two cost evaluation criteria, namely, discounted cost and ergodic cost. Under certain assumptions, we establish the existence of Nash equilibria. Also, we completely characterize a Nash equilibrium for the ergodic cost criterion in the space of stationary Markov strategies.