Game theory: Nash equilibrium in asymetric payoff matrix I have a utility function describing the desirability of an outcome state. I weigh the expected utility with the probability of the outcome state occuring. I find the expected utility of an action, a, with $EU(a) = \sum\limits_{s'} P(Result(a) = s' | s)U(s'))$ where Result(a) denotes the outcome state after executing a. There is no global set of actions, the set of actions available to each agent are not identical. 
Player1 / Player2 | Action C      | Action D        |
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Action A          |  (500,-500)   |  (-1000,1000)   |
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Action B          |  (-5,-5)      |  ** (200,20) ** |
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Is this a valid approach? All examples of nash equilibriums i can find uses identical action sets for both agents.

Set of concepts aimed at decision making in situations of competition and conflict (as well as of cooperation and interdependence) under specified rules. Game theory employs games of strategy (such as chess) but not of chance (such as rolling a dice). A strategic game represents a situation where two or more participants are faced with choices of action, by which each may gain or lose, depending on what others choose to do or not to do. The final outcome of a game, therefore, is determined jointly by the strategies chosen by all participants.
http://en.docsity.com/answers/68695/what-type-of-study-is-the-game-theory
