Nash consistent representation of effectivity functions through lottery models

Effectivity functions for finitely many players and alternatives are considered. It is shown that every monotonic and superadditive effectivity function can be augmented with equalchance lotteries to a finite lottery model---i.e., an effectivity function that preserves the original effectivity in terms of supports of lotteries---which has a Nash consistentrepresentation. In other words, there exists a finite game form which represents the lottery model and which has a Nash equilibrium for any profile of utility functions, where lotteriesare evaluated by their expected utility. No additional condition on the original effectivity function is needed.