Completely Mixed Strategies for Generalized Bimatrix and Switching Controller Stochastic Game

作者：Dubey Dipti; Neogy S K^*; Ghorui Debasish

来源：Dynamic Games and Applications, 2017, 7(4): 535-554.

DOI：10.1007/s13235-016-0211-5

• Generalized bimatrix game
• Completely mixed Strategies
• Switching controller stochastic game
• Vertical linear complementarity problem

In this paper, we revisit a result by Jurg et al. (Linear Algebra Appl 141:61-74, 1990) where the necessary and sufficient condition for a bimatrix game to be weakly completely mixed is given. We present an alternate proof of this result using linear complementarity approach. We extend this result to a generalization of bimatrix game introduced by Gowda and Sznajder (Int J Game Theory 25:1-12, 1996) via a generalization of linear complementarity problem introduced by Cottle and Dantzig (J Comb Theory 8:79-90, 1970). We further study completely mixed switching controller stochastic game (in which transition structure is a natural generalization of the single controller games) and extend the results obtained by Filar (Proc Am Math Soc 95:585-594, 1985) for completely mixed single controller stochastic game to completely mixed switching controller stochastic game. A numerical method is proposed to compute a completely mixed strategy for a switching controller stochastic game.

• 出版日期2017-12