Nash Consistent Representation of Effectivity Functions through Lottery Models

Authors: 
Bezalel Peleg and Hans Peters
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 equal chance 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 consistent representation. 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 lotteries are evaluated by their expected utility. No additional condition on the original effectivity function is needed.

Date: 
September, 2005
Published in: 
Games and Economic Behavior 65 (2009), 503-515.
Number: 
404