# 5 i i the probabilities must sum to one and all be

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Unformatted text preview: is the function ✓2 with ✓2 (C ) = ✓2 (D ) = 0.5 I I The probabilities must sum to one and all be nonnegative The set of all such functions is denoted by S2 Beliefs for nomal form games — example Prisoners’ dilemma D 12C C 2,2 0,3 D 3,0 1,1 I The function ✓2 with ✓2 (C ) = 0.25 and ✓2 (D ) = 0.75 (and zero everywhere else) is a belief of P1 about the strategies of P2, as is the function ✓2 with ✓2 (C ) = ✓2 (D ) = 0.5 I The probabilities must sum to one and all be nonnegative I The set of all such functions is denoted by I With two players ✓ I With three players (not graphed) ✓ 1 = (✓2 , ✓3 ) and the collection of all such vectors ✓ 1 1 = ✓2 and S 1 = S2 S2 S 1 is Mixed versus pure strategies I With a mixed strategy a player randomizes over strategies according to a probability distribution I I For instance, poker players sometimes roll a die to decide whether or not to call With a pure strategy a player chooses one particular strategy with certainty Expected payo↵ I With a mixed strategy and/or if P1 is uncertain about the strategy of P2 there is uncertainty about the...
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## This note was uploaded on 03/27/2014 for the course ECON 402 taught by Professor Krishna,vijayxu,haiqing during the Spring '09 term at Pennsylvania State University, University Park.

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