It is proved that if it is NP hard to solve the linear complemen tarity problemwith P matrix or to compute a Nash equilibrium point in a player game then NP coNP

this paper shows how game theory can be applied to modeling the interaction between government and manufacturer in implementation of cleaner production. a generic game model based upon ‘two-person non-cooperative’ static game is created to allow various strategic actions being tested by stages, and aid decision making by selecting optimal strategy for both manufacturer and policy maker to reduc...

In this paper we present an appropriate singular, zero-sum, linear-quadratic differential game. One of the main features game is that weight matrix minimizer’s control cost in functional singular. Due to singularity, cannot be solved either by applying Isaacs MinMax principle, or Bellman–Isaacs equation approach. As application, introduced interception with regularized and developed dual repres...

It is proved that if it is NP-hard to solve the linear complemen-tarity problemwith P-matrix or to compute a Nash-equilibrium point in a 2-player game, then NP = coNP.

The rank of a bimatrix game (A,B) is the rank of the matrix A + B. We give a construction of rank-1 games with exponentially many equilibria, which answers an open problem by Kannan and Theobald (2010).

The article presents a mathematical model of multi-stage game the process safe control transport object in possible collision situations with other encountered objects, containing description state variables, and constraints, sets permissible strategies. Multi-criteria optimization tasks were formulated form positional matrix games under conditions playing non-cooperative cooperative as well no...

Ravindra Bapat We consider two-person zero-sum games, or matrix games, in which the pure strategies of the players are the vertices, or the edges of a graph, and the payoff is determined by the incidence structure. We identify some cases where the value and the optimal strategies can be explicitly determined. In particular, we consider the incidence matrix game in which the payoff matrix is the...

Robustness has long been recognized as an important parameter for evaluating game-theoretic results, but talk of ‘robustness’ generally remains vague. What we offer here is a graphic measure for a particular kind of robustness (‘matrix robustness’), using a three-dimensional display of the universe of 2×2 game theory. In such a measure specific games appear as specific volumes (Prisoner’s Dilem...