A class of nondegenerate n n bimatrix games is presented that have asymptotically more than 2:414 n = p n Nash equilibria. These are more equilibria than the 2 n ? 1 equilibria of the game where both players have the identity matrix as payoo matrix. This refutes the Quint{Shubik conjecture that the latter number is an upper bound on the number of equilibria of nondegenerate n n games. The rst c...

In two player bi-matrix games with partial monitoring, actions played are not observed, only some messages are received. Those games satisfy a crucial property of usual bi-matrix games: there are only a finite number of required (mixed) best replies. This is very helpful while investigating sets of Nash equilibria: for instance, in some cases, it allows to relate it to the set of equilibria of ...

We show that a proper equilibrium of a matrix game can be found in polynomial time by solving a linear (in the number of pure strategies of the two players) number of linear programs of roughly the same dimensions as the standard linear programs describing the Nash equilibria of the game.

We consider the problem of multivariate multi-objective allocation where no or limited information is available within the stratum variance. Results show that a game theoretic approach (based on weighted goal programming) can be applied to sample size allocation problems. We use simulation technique to determine payoff matrix and to solve a minimax game.

Building a distributed middleware infrastructure that provides the low latency required for massively multiplayer games while still maintaining consistency is non-trivial. Previous attempts have used static partitioning or clientbased peer-to-peer techniques that do not scale well to a large number of players, perform poorly under dynamic workloads or hotspots, and impose significant programmin...

qi = 1, pA ≥ v ≥ Aq. The number v is known as the value of game. The pair (p, q) is known as an equilibrium for the matrix game. As usual, x ≥ 0 means that every entry of the vector x is ≥ 0. We write y ≤ t for a vector y and a number t if every entry of y is ≤ t. We go even further in abusing notation, denoting by y− t the vector obtaining from y by subtracting t from every entry. Similarly we...

A two person zero sum matrix game with fuzzy goals and fuzzy payoffs is considered and its solution is conceptualized using a suitable defuzzification function. Also, it is proved that such a game is equivalent to a primal-dual pair of certain fuzzy linear programming problems in which both goals as well as parameters are fuzzy.

A multi-objective bi-matrix game model based on fuzzy goals is established in this paper. It is shown that the equilibrium solution of such a game model problem can be translated into the optimal solution of a multi-objective, non-linear programming problem. Finally, the results of this paper are demonstrated through a numerical example.

In this paper, we introduce a framework of new mathematical representation of Game Theory, including static classical game and static quantum game. The idea is to find a set of base vectors in strategy space and to define their inner product so as to form them as a Hilbert space, and then form a Hilbert space of system state. Basic ideas and formulas in Game Theory have been reexpressed in such...

In this paper, we present a comunication-integrated reinforcement-learning algorithm for a general-sum Markov game or MG played by independent, cooperative agents. The algorithm assumes that agents can communicate but do not know the purpose (the semantic) of doing so. We model agents that have different tasks, some of which may be commonly beneficial. The objective of the agents is to determin...