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Probability distribution over the strategies of the

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Unformatted text preview: r i is a probability distribution over the strategies of the other players (JW) I If S i is the set of all probability distributions over the strategies of all the other players then any element ✓ i 2 S i is a belief If there are two players, 1 and 2, then ✓2 (s2 ) is the probability (according to P1’s beliefs) that P2 plays s2 I I I This notation can be ambiguous when there are more than two players because ✓2 could in principle refer to the beliefs that P1 has about P2’s strategies or about the beliefs of P3; the notation ✓ 1 is clearly about P1’s beliefs about all other players Given that ✓2 represents a probability distribution, P 0 for all s2 2 S2 s2 2 S2 ✓2 (s2 ) = 1 and ✓2 (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...
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