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February 2005
Game theory traditionally specifies players' numerical payoff functions. Following the concept of utility invariance in modern social choice theory, this paper explores what is implied by specifying equivalence classes of utility function profiles instead. Within a single game, utility transformations that depend on other players' strategies preserve players' preferences over their own strategies, and so most standard non-cooperative solution concepts. Quantal responses and evolutionary dynamics are also considered briefly. Classical concepts of ordinal and cardinal non-comparable utility emerge when the solution is required to be invariant for an entire class of "consequentialist game forms'' simultaneously.