Simultaneous Games - Mixed Strategies I.pdf - mixed strategy = random strategy Simultaneous Games Mixed Strategies I Expected Utility Hypothesis How do

# Simultaneous Games - Mixed Strategies I.pdf - mixed...

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Simultaneous Games - Mixed Strategies I Expected Utility Hypothesis How do people evaluate a gamble? Figures 8A.1-8A.2 Matching Pennies Revisited KID 2 H T KID 1 H 1 , - 1 - 1 , 1 T - 1 , 1 1 , - 1 What is the Nash equilibrium of this game? How will you play the game anyway? What is Row’s best response if Column uses H ? T ? A random strategy ( q -mix)? (Repeat the same analysis for Column.) KID 2 H ( q ) T (1 - q ) q -mix KID 1 H ( p ) 1 , - 1 - 1 , 1 2 q - 1 , - T (1 - p ) - 1 , 1 1 , - 1 1 - 2 q , - p -mix - , 1 - 2 p - , 2 p - 1 - , - 0 0 . 5 1 . 0 0 0 . 5 1 . 0 p q Kid 1’s best response Kid 2’s best response MSNE Best Response Analysis of Matching Pennies How about the minimax approach? 1 -1 -1 1 1 minimax=1 maximin = -1 -> No equilibrium from NE and Minimax theorem Rationlizability H1->T2->T1->H2->H1 using random strategy, use probability mixed strategy = random strategy -1(p)+(1)(1-p) p-mix ^ q= 0.5 p=0.5 q-mix ^ p=0.5 q=0.5 using mix strategy is getting some payoff btw the max. and min. when q =1 , best respose is to set p =1 when q is close to zero, 2q-1 will be close to zero

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