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Unformatted text preview: 2 (, H) = - + 1 2 (, H) = 1 - 2 and what about Player 2's payoff from playing T... 2 (, T) = (1) + (- 1) (1 ) 2 (, T) = 1 + 2 (, T) = 2 1 Now, for Player 1 to make Player 2 indifferent between playing H or T they must choose the that makes Player 2's payoffs the same for H and T (i.e. 2 (, H) = 2 (, T)). So... 2 (, H) = 2 (, T) 1 2 = 2 1 4 = 2 = Person 1's choice to play a mixed strategy depends on Person 2's choice of B. For example, if Person 2 chooses to mix using = as above, then Player 1 will mix on his pure strategies since he is indifferent between them (moreover, Person 1 will mix such that Person 2 is indifferent between the pure strategies available to her). This results in a Mixed Strategy Nash Equilibrium of the form: [(, (1 )), (, (1 ))] or in this case... (( , ), ( , )) where the expected payoffs from these strategies are: 1 (H, ) = 2 1 1 (T, ) = 1 2 2 (, H) = 1 - 2 2 (, T) = 2 1 2( ) 1 = 0 1 2( ) = 0 1 2( ) = 0 2( ) 1= 0 311 Here of course, the individ e, dual outcom of each individual p me play is still u unknown but b mixing st by trategies as above, ea player is ensuring themselves the best s ach s payo in a large number o repeated trials. off e of TTLE OF TH SEXES HE BAT Let's quickly ref s fresh our m memory with respect to Romeo an Juliet's s h o nd situation. They are separa y ated by ma miles w no way of commun any with nicating. Th last time he e that t they saw ea other th agreed to go out o Saturday night but they could ach hey d on y not a agree to wh hich event th would a hey attend befo they were separate ore ed. Juliet wants to go to the Manchester United gam (soccer = sports, de g me enoted as S) bu she know that Rom wants t go to see the Londo Philharm ut ws meo to e on monic Orch hestra (mus denoted as M). sic, d Of co ourse, Rom and Juliet are quite taken with each othe and would prefer to meo e er o be to ogether than to be sep parate, how wever, each of them wo ould derive more pleas sure by being together at the eve that they prefer. ent y For e example, Romeo want to be with Juliet liste R ts h ening to mu usic (his big...
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- Spring '10