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Nash consistent representation of effectivity functions through lottery models
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Abstract
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.microeconomics ;