This paper introduces a class of non-additive anonymous games where agents are assumed to be uncertain (in the sense of Knight) about opponents’ strategies and about the initial distribution over players’ characteristics in the game. These uncertainties are modelled by non-additive measures or capacities. The Cournot-Nash equilibrium existence theorem is proven for this class of games. It is shown that the equilibrium distribution can be symmetrized under milder conditions than in the case of additive games. In particular, it is not required for the space characteristics to be atomless under capacities. The set-valued map of the Cournot-Nash equilibria is upper-semicontinuous as a function of initial beliefs of the players for non-additive anonymous games
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