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国外博弈论课件lecture11.ppt

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国外博弈论课件lecture11

June 3, 2003 73-347 Game Theory--Lecture 11 June 3, 2003 Lecture 11 Static (or Simultaneous-Move) Games of Complete Information Mixed Strategy Nash Equilibrium Outline of Static Games of Complete Information Introduction to games Normal-form (or strategic-form) representation Iterated elimination of strictly dominated strategies Nash equilibrium Review of concave functions, optimization Applications of Nash equilibrium Mixed strategy Nash equilibrium Today’s Agenda Review of previous class Exercise 138.1 of Osborne Review HW1 Exercise 138.1 of Osborne We first consider pure-strategy Nash equilibria. How many can you find? In order to find all Nash equilibria, we need to consider 15 more cases by Theorem 4 of Lecture 10! We first consider complicated cases. Some cases are very easy. Exercise 138.1 of Osborne Case 1: check whether there is a mixed strategy in which p110, p120, p210, p220, p230 By theorem 4, we should have 2?p11+2? p12= 3?p11+1? p12 = 3?p11+2? p12 and p11+p12=1. We should have 2?p21+0? p22+1? p23 =3?p21+1? p22+0? p23 and p21+ p22+ p23 = 1 Solve these equations. If we can get a solution that satisfies p110, p120, p210, p220, p230 then we have a mixed strategy Nash equilibrium. Otherwise, if we can not find a solution or we find a solution that does not satisfies p110, p120, p210, p220, p230, then we do not have such a mixed strategy Nash equilibrium. Exercise 138.1 of Osborne Case 2: check whether there is a mixed strategy in which p110, p120, p210, p220, p23=0 By theorem 4, we should have 2?p11+2? p12= 3?p11+1? p12 ? 3?p11+2? p12 and p11+p12=1. We should have 2?p21+0? p22+1? p23 =3?p21+1? p22+0? p23 and p21+ p22+ p23 = 1 Solve these. If we can get a solution that satisfies p110, p120, p210, p220, p23=0 then we have a mixed strategy Nash equilibrium. Otherwise, if we can not find a solution or we find a solution that does not satisfies p110, p120, p210, p220, p23=0, then we do not have such a mixed strategy Nash equilibrium. Exercis

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