Econ110_Section9 - Section IX Finitely Repeated Games...

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Section IX: Finitely Repeated Games Daniel Egel November 9, 2008 1 Individually Rational I will start by providing a formal definition and then I will give you a more intuitive definition. Finally, as always, we’ll do a few examples. 1.1 Formal Definition 1 Define player i ’s minmax payoff as v i . A payoff profile w , which includes the payoffs for all n players such that w = ( w 1 ,w 2 ,...,w n ), is individually rational if w i v i for all i . 1.2 Intuitive Definition and Approach for Finding Individually Rational Points Lets consider a game with only two players. The simplest way of writing this that I can think of is as follows: A point is individually rational if the payoffs to both players are at least as good ( ) to the payoff that they would get if they were being minmaxed by the other player 1.3 Some Examples of Individually Rational Payoffs Lets go back to the examples from last week and find the payoff profiles that are individually rational. 1.3.1 Example 1 Let’s do an example together. Consider the following game: Player 1 Player 2 E F G H A 2,5 10,3 4,5 3, 9 B 3,7 1,4 6, 8 7,7 C 1, 1 0,0 0, 3 4,1 D 4, 6 5,5 8, 8 2, 6 1 This following definition is based on that provided in “A Course in Game Theory”, Osborne and Rubinstein (1994) p. 143 1
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1. What is player 1’s minmax payoff? What is the player 2’s minmax payoff?
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This note was uploaded on 12/25/2010 for the course PO 137 taught by Professor Power during the Fall '10 term at Berkeley.

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Econ110_Section9 - Section IX Finitely Repeated Games...

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