Solving a Co-operative Two-person Game under Uncertainty Using Multiple Criteria Optimization

In this communication we consider a two person cooperative game involving unknown parameters. In our model, we suppose that the players know the domain where these parameters can take their values but completely ignore their behaviour., we propose a solution, which is based on the notion of Pareto optimality and takes into account the two aspects involved in this game: cooperation between the two players and the problem of decision making under uncertainty in the case of complete ignorance. We transform the problem of determination of this solution into the problem of determination of a couple of Pareto optimal solutions a special couple of dependent multiple criteria problems. We then give sufficient conditions for the existence of such couples and study the problem of their determination.