Algorithms for Stochastic Games

In this paper, we present algorithms for the solution of finite discounted stochastic games, without special structure. Three equilibrium concepts are considered: saddle points in two-person zero-sum games, Nash equilibrium points in N-person non-cooperative games and finally Stackelberg equilibrium in two-person games.

[1]  A. Haurie,et al.  Sequential Stackelberg equilibria in two-person games , 1985 .

[2]  M. Pollatschek,et al.  Algorithms for Stochastic Games with Geometrical Interpretation , 1969 .

[3]  Jerzy A. Filar,et al.  A finite algorithm for the switching control stochastic game , 1983 .

[4]  J. Filar.  Ordered field property for stochastic games when the player who controls transitions changes from state to state , 1981 .

[5]  R. Karp,et al.  On Nonterminating Stochastic Games , 1966 .

[6]  Stef Tijs,et al.  Fictitious play applied to sequences of games and discounted stochastic games , 1982 .

[7]  J. Wal.  Discounted Markov games: Generalized policy iteration method , 1978 .

[8]  C. E. Lemke,et al.  Equilibrium Points of Bimatrix Games , 1964 .

[9]  Philip E. Gill,et al.  User's guide for SOL/QPSOL: a Fortran package for quadratic programming , 1983 .

[10]  Gerard van der Laan,et al.  On the Computation of Fixed Points in the Product Space of Unit Simplices and an Application to Noncooperative N Person Games , 1982, Math. Oper. Res..

[11]  T. Parthasarathy,et al.  An orderfield property for stochastic games when one player controls transition probabilities , 1981 .

[12]  J. Cruz,et al.  On the Stackelberg strategy in nonzero-sum games , 1973 .

[13]  T. E. S. Raghavan,et al.  Algorithms for stochastic games — A survey , 1991, ZOR Methods Model. Oper. Res..

[14]  Michael A. Saunders,et al.  User''s guide for NPSOL (Ver-sion 4.0): A FORTRAN package for nonlinear programming , 1984 .

[15]  Stef Tijs,et al.  Stochastic games with state independent transitions and separable rewards , 1984 .

[16]  E. Denardo.  CONTRACTION MAPPINGS IN THE THEORY UNDERLYING DYNAMIC PROGRAMMING , 1967 .

[17]  L. Shapley,et al.  Stochastic Games* , 1953, Proceedings of the National Academy of Sciences.

[18]  O. J. Vrieze,et al.  On stochastic games with additive reward and transition structure , 1985 .

[19]  T. Başar.  Dynamic games and applications in economics , 1986 .