Robust Multiple Objective Game Theory

In this paper, we propose a distribution-free model instead of considering a particular distribution for multiple objective games with incomplete information. We assume that each player does not know the exact value of the uncertain payoff parameters, but only knows that they belong to an uncertainty set. In our model, the players use a robust optimization approach for each of their objective to contend with payoff uncertainty. To formulate such a game, named robust multiple objective games here, we introduce three kinds of robust equilibrium under different preference structures. Then, by using a scalarization method and an existing result on the solutions for the generalized quasi-vector equilibrium problems, we obtain the existence of these robust equilibria. Finally, we give an example to illustrate our model and the existence theorems. Our results are new and fill the gap in the game theory literature.