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A Characterization of Stationary Nash Equilibria of Single Controller Constrained Stochastic Games

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Title A Characterization of Stationary Nash Equilibria of Single Controller Constrained Stochastic Games
 
Creator SINGH, VV
HEMACHANDRA, N
 
Subject Constrained stochastic games
constrained Markov decision processes
occupation measure
single controller game
Nash equilibrium
mathematical program
 
Description We consider a two player finite state-action general sum single controller constrained stochastic game with both discounted and average cost criteria. We consider the situation where player 1 has subscription-based constraints and player 2, who controls the transition probabilities, has realization-based constraints which can also depend on the strategies of player 1. It is known that a stationary Nash equilibrium for discounted case exists under strong Slater condition, while, for the average case, stationary Nash equilibrium exists if additionally the Markov chain is unichain. For each case we show that the set of stationary Nash equilibria of this game has one to one correspondence with the set of global minimizers of a certain nonconvex mathematical program. If the constraints of player 2 do not depend on the strategies of player 1, then the mathematical program reduces to a quadratic program. The known linear programs for zero sum games of this class can be obtained as a special case of above quadratic programs.
 
Publisher WORLD SCIENTIFIC PUBL CO PTE LTD
 
Date 2016-01-15T09:53:43Z
2016-01-15T09:53:43Z
2015
 
Type Article
 
Identifier INTERNATIONAL GAME THEORY REVIEW, 17(2SI)
0219-1989
1793-6675
http://dx.doi.org/10.1142/S0219198915400186
http://dspace.library.iitb.ac.in/jspui/handle/100/18302
 
Language en