We have studied two person stochastic di erential games with multiple modes. For the zero-sum game we have established the existence of optimal strategies for both players. For the nonzero sum case we have proved the existence of a Nash equilibrium.

We introduce several methods of decomposition for two player normal form games. Viewing the set of all games as a vector space, we exhibit explicit orthonormal bases for the subspaces of potential games, zero-sum games, and their orthogonal complements which we call anti-potential games and anti-zero-sum games, respectively. Perhaps surprisingly, every anti-potential game comes either from the ...

We study the problem of computing Nash equilibria of zero-sum games. Many natural zerosum games have exponentially many strategies, but highly structured payoffs. For example, in the well-studied Colonel Blotto game (introduced by Borel in 1921), players must divide a pool of troops among a set of battlefields with the goal of winning (i.e., having more troops in) a majority. The Colonel Blotto...

We study a zero sum differential game under strong assumptions of convexity — the cost is convex for one player, and concave for the other. An explicit necessary and sufficient condition for a saddle point of the game is given in terms of convex analysis subgradients of the conjugate of the cost function. A generalized Hamiltonian equation is shown to describe saddle trajectories of the game.

In this paper, we first devise two algorithms to determine whether or not a bimatrix game has strategically equivalent zero-sum game. If so, propose an algorithm that computes the given is game, then approach compute whose saddle-point equilibrium can be mapped well-supported approximate Nash of original We conduct extensive numerical simulation establish efficacy algorithms.

It is shown that in every repeated zero-sum game of incomplete information in which the information to both players is identical, lim v n and v ∞ exist and are equal.

Lines of Action (LOA) is a two-person zero-sum game with perfect information; it is a chess-like game with a connection-based goal. In this note the 6 × 6 variant of LOA is weakly solved. A Proof-Number search method, PN, is used to compute that the game is a win for the first player (Black). Based on the results of solving the boards up to 6× 6, an optimistic time frame is given for solving 7×...

A zero-sum stochastic differential game problem on infinite horizon with continuous and impulse controls is studied. We obtain the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities. We also obtain a verification theorem which provides an optimal strategy of the game. Mathematics Subject Classificati...