On the genericity of the finite number of equilibria in multicriteria games: a counterexample

The famous Harsanyi's (1973) Theorem states that a generic finite game has an odd number of Nash equilibria in mixed strategies. In this paper, counterexamples are given showing that for finite multicriteria games (games with vector-valued payoffs) this kind of result does not hold. In particular, it is shown that it is possible to find balls in the space of games such that every game in this set has uncountably many equilibria. This result then formalises the intuitive idea that games with uncountable sets of equilibria are not non-generic in the multicriteria case.