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Unformatted text preview: ggest payo and Juliet wants to be with Ro off) o omeo watch hing the soc ccer match (her bigge payoff). est Rom and Juliet must sim meo multaneous choose ( sly (without hav ving agreed upon d wher to meet) which venu to arrive at. re ue e We r represented this game in both the extensive form and t normal form as d e e e the follow ws: at! ey Grea Now the have no problem, right? ONG! The Nash equilibria only happen if on of the tw players d ne wo decides to WRO go to the event that they don't want to go to. o o 312 So w we've still go a problem Now, let's suppose that they a both un ot m! e are nable to learn from their past exper n riences (a r realistic pro oblem in som couples and this me s) same situation presents its every s e self single time t that they ag gree to mee et. ote 's g hat mixes as R (M, ) and d Deno Romeo' payoffs from playing M given th Juliet m also denote Romeo's payo from pla offs aying S giv that Juli mixes as R (S, ). ven iet s . Now, let's consi ider Romeo payoff fr o's rom playing M... g R (M, ) = (60) + (5 (1 ) 5) R (M, ) = 60 + 5 5 R (M, ) = 55 + 5 and w what about Romeo's p t payoff from playing S... ... R (S, ) = (0 + (40) (1 ) 0) R (S, ) = 40 4 40 t omeo indiffe erent betwe playing M or S she must een e Now, for Juliet to make Ro choo the that makes R ose Romeo's pa ayoffs the same for M and S (i.e. R (M, ) = R (S )). S, 313 So... ... R (M, ) = R (S ) S, 55 + 5 = 40 40 95 9 = 35 (1 ) = 12 / 19 = 7 / 19 Deno Juliet's payoffs from playing M given tha Romeo m ote at mixes as J (, M) and also denote Juliet's payoffs from play s ying S given that Rome mixes as J (, S). n eo s Now, let's consi ider Juliet's payoff from playing M s m M... J (, M) = (2 + (0) (1 ) 20) J ( M) = 20 , and w what about Juliet's payoff from playing S... t J (, S) = (5 + (80) (1 ) 5) ) J (, S) = 5 + 80 - 80 75 J (, S) = 80 - 7 Now, for Romeo to make J o Juliet indiffe erent betwe playing M or S he must een ose Juliet's payo the sam for M an S (i.e. J (, M) = J offs me nd choo the that makes J (, S S)). ... So... J (, M) = J (, S) , 20 = 80 - 75 95 9 = 80 = 16 / 19 (1 = 3 / 19 ) This results in a Mixed Stra ategy Nash Eq...
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.
- Spring '10