A central question in game theory and artificial intelligence is how a rational agent should behave in a complex environment, given that it cannot perform unbounded computations. We study strategic aspects of this question by formulating a simple model of a game with additional costs (computational or otherwise) for each strategy. First we connect this to zero-sum games, proving a counter-intuitive generalization of the classic min-max theorem to zero-sum games with the addition of strategy costs. We then show that potential games with strategy costs remain potential games. Both zero-sum and potential games with strategy costs maintain a very appealing property: simple learning dynamics converge to equilibrium.
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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number
1439.
Length: Date of creation: Nov 2006 Date of revision: Handle: RePEc:nwu:cmsems:1439
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