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game - Game Theory 166 Game Theory A Game theory studies...

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Game Theory 166 Game Theory A. Game theory studies strategic interaction, developed by von Neumann and Morgenstern around 1950 B. Howtodepict payoffsof gamefromdifferent strategies 1. two players 2. two strategies 3. example Row Column Left Right Top Bottom a) this depicts a dominant strategy b) each person has a strategy that is best no matter what the other person does c) nice when it happens, but doesn’t happen that often
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Game Theory 167 C. Nash equilibrium 1. what if there is no dominant strategy? 2. in this case, look for strategy that is best if the other player plays his best strategy 3. note the ‘‘circularity’’ of definition 4. appropriate when you are playing against a ‘‘rational’’ opponent 5. each person is playing the best given his expecta- tionsabout theother person’splayand expectations are actually confirmed 6. example: Row Column Left Right Top Bottom a) note (top, left) is Nash; (bottom, right) is also Nash
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Game Theory 168 7. Nash equilibrium in pure strategies may not exist.
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