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# slides5 - Lecture 5 Solution concepts 14.12 Game Theory...

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Lecture 5 Solution concepts 14.12 Game Theory Muhamet Yildiz Road Map 1. Dominant-strategy equilibrium 2. Rationalizability 3. Nash Equilibrium 1

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1 Dominance s -i =(s 1 ,…, s i-1 ,s i+1 ,…,s n ) Definition: A pure strategy s i * strictly dominates s i if and only if s s u i ) > s s u i ) s i . ( i * , ( i , i i A mixed strategy σ i strictly dominates s i iff σ ( s s u s ) + L + σ ( s s u s ) > s s u ) s i i i 1 ) i ( i 1 , i i ik ) i ( ik , i i ( i , i A rational player never plays a strictly dominated strategy. Prisoners’ Dilemma 2 Cooperate Defect Cooperate (5,5) (0,6) Defect (6,0) (1,1) 2
Weak Dominance Definition: A pure strategy s i * weakly dominates s i if and only if s s u i ) s s u ) s i ( i * , ( i , i i i and at least one of the inequalities is strict. A mixed strategy σ i * weakly dominates s i iff i i i i ik i ik i i i i i i s s u s s u s s s u s + + ) , ( ) , ( ) ( ) , ( ) ( 1 1 σ σ L i s and at least one of the inequalities is strict.

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slides5 - Lecture 5 Solution concepts 14.12 Game Theory...

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