The traditional theory of games imposes a very high rationality requirement upon agents. This requirement originates in the development of the theory of utility which provides game theory’s underpinnings (see Luce and Raiffa, 1957, for an introduction). For example, in order to be able to assign a cardinal utility function to individual agents, one typically assumes that each agent has a well-defined, consistent set of preferences over the set of “lotteries” over the outcomes which may result from individual choice. Since the number of different lotteries over outcomes is uncountably infinite, this requires each agent to have a well-defined, consistent set of uncountably infinitely many preferences.