Econ110_Section9

# 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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