T. Parthasarathy

An orderfield property for stochastic games when one player controls transition probabilities

When the transition probabilities of a two-person stochastic game do not depend on the actions of a fixed player at all states, the value exists in stationary strategies. Further, the data of the stochastic game, the values at each state, and the components of a pair of optimal stationary strategies all lie in the same Archimedean ordered field. This orderfield property holds also for the nonzero sum case in Nash equilibrium stationary strategies. A finite-step algorithm for the discounted case is given via linear programming.

Existence of

In this paper we prove the existence of p-equilibrium stationary strategies for non-zero-sum stochastic games when the reward functions and transitions satisfy certain separability conditions. We also prove some results for positive and discounted zero-sum stochastic games when the state space is infinite.

p

In this paper, we consider positive stochastic games, when the state and action spaces are all infinite. We prove that, under certain conditions, the positive stochastic game has a value and that the maximizing player has an ε-optimal stationary strategy and the minimizing player has an optimal stationary strategy.

-equilibrium and optimal stationary strategies in stochastic games

Preface. Introduction. I: Two-Person Games. Computing Linear Minimax Estimators K. Helmes, C. Srinivasan. Incidence Matrix Games R.B. Bapat, S. Tijs. Completely Mixed Games and Real Jacobian Conjecture T. Parthasarathy, et al. Probability of Obtaining a Pure Strategy Equilibrium in Matrix Games with Random Pay-Offs S. Mishra, T.K. Kumar. II: Cooperative Games. Nonlinear Self Dual Solutions for TU Games P. Sudholter. The Egalitarian Nonpairwise-Averaged Contribution T. Driessen, Y. Funaki. Consistency Properties of the Nontransferable Cooperative Game Solutions E. Yanovskaya. Reduced Game Property of Egalitarian Division Rules for Cooperative Games T. Driessen, Y. Funaki. III: Noncooperative Games. An Implementation of the Nucleolus of NTU Games G. Bergantinos, J.A.M. Potters. Pure Strategy Nash Equilibrium Points in Large Non-Anonymous Games M.A. Khan, et al. Equilibria in Repeated Games of Incomplete Information. The Deterministic Symmetric Case A. Neyman, S. Sorin. On Stable Sets of Equilibria A.J. Vermeulen, et al. IV: Linear Complementarity Problems and Game Theory. A Chain Condition for Qo-Matrices A.K. Biswas, G.S.R. Murthy. Linear Complementarity and the Irreducible Polystochastic Game with the Average Cost Criterion when one Player Controls Transition S.R. Mohan, et al. On the Lipschitz Continuity of the Solution Map in Some Generalized Linear Complementarity Problems R. Sznajder, M.S. Gowda. V: Economic And Or Applications. Pari-Mutuel as a System of Aggregation of Information G. Owen. Genetic Algorithm of the Core of NTU Games H.H. Chin. Some Recent Algorithms for Finding the Nucleolus of Structured Cooperative Games T.E.S. Raghavan. The Characterisation of the Uniform Reallocation Rule Without Pareto Optimality B. Klaus. Two Level Negotiations in Bargaining Over Water A. Richards, N. Singh. Price Rule and Volatility in Auctions with Resale Markets A. Alkhan. Monetary Trade, Market Specialisation and Strategic Behaviour M. Rajeev.

On stochastic games, II

In this paper we give sufficient conditions for the existence of saddle points and Nash equilibrium points in the class of classical and relaxed controls for differential games.

Game-Theoretical Applications to Economics and Operations Research

It is shown that discounted general-sum stochastic games with two players, two states, and one player controlling the rewards have the ordered field property. For the zero-sum case, this result implies that, when starting with rational data, also the value is rational and that the extreme optimal stationary strategies are composed of rational components.