Matrix games with uncertain entries: A robust approach

In classical game theory, a conflict of two opponents can be modelled as an equilibrium-based matrix game. We assume a conflict of two non-cooperative antagonistic opponents with a finite number of strategies with zero-sum or constant sum pay-offs. In the same time, we suppose that the elements of the payoff matrix describing the game are not fixed and are allowed to change within a specified interval. Supposing that some of the elements of the payoff matrix are uncertain, it is evident that this would influence the utilities of both players at the same time and moreover, such entropy of the model would eventually influence the position of equilibria or its very existence. We propose a modelling approach that allows one to find a solution of the game with either pure or mixed strategies of opponents with the guaranteed payoffs under the assumption that a specified number of unspecified entries would attain different values than expected. The chosen robust approach is presented briefly as well as the necessary circumstances of matrix game solutions. Our novelty approach follows and is accompanied by an explanatory example in the end of the paper.