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Unformatted text preview: uilibrium of the for h m rm: [(, (1 )), (, (1 ))] or in this case... ... ((16/19 , 3/19), (7/19 , 12/19)) ( 314 wher the expected payoff from thes strategie are: re fs se es R (M, ) = 55 + 5 0 R (S, ) = 40 40 J (, M) = 20 M J (, S) = 80 75 S 5 55 5(7/19) + 5 = 480/19 40 40(7/19 = 480/19 0 9) 20 0(16/19) = 3 320/19 80 75(16/19) = 320/19 0 9 (or 25.2 263) (or 25.2 263) (or 16.8 842) (or 16.8 842) Why does Romeo get a hig gher expec cted payoff than Juliet? ? Why can Romeo mix with = 16 / 19 on music a only 3 / 19 on spo and orts? Does Romeo ha some a s ave advantage o power in this game? or n ? If Ro omeo and Juliet mix strategies the their pay en yoffs will be in the inte e erior of their r utility possibility frontier. y y Cons sider the sit tuation whe they alw ere ways both g to the orc go chestra (M, M). We'll , call t this point A and the pa ayoffs are (6 20). 60, Also, consider the situation where the always g to the so , t n ey go occer match (S, S). h We'll call this po B and t payoffs are (40, 80 l oint the 0). Furth conside the mixe strategy Nash Equilibrium that we just figu her, er ed ured out ((16/ , 3/19), (7/19 , 12/1 /19 19)). We'll call this point C and th payoffs a (25.263 he are 3, 16.84 42). should be able to see (even witho the diag a out gram that fo ollows) that point C is We s interi to the ut ior tility possibilities create by conn ed necting poin A and point B with a nt line s segment. pose that th agree th if they w hey hat went to spo last time then the n orts e next time Supp they would go to the music concert. T o c Then over r repeated tr rials they wo ould go to each venue half of the time and be gu h f e uaranteed t meet. to 315 Their expected utility would then beco r d ome: E ( ROMEO) = (60) + (40) = 50 (U E ( JULIET) = (20) + (80) = 50 (U Let's call this po D wher the payof are (50, 50). s oint re ffs Now, just to be clear, it doe esn't need to be a fair split to be efficient (i.e on the r e. UPF). Supp pose that th agree th they wo...
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- Spring '10