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Unformatted text preview: hey hat ould go to s sports twice in a row and then to e musi once (in an exactly repeated pa ic a attern). Th hen, over tim they wo me, ould go to sport 2/3 of the time and music conc ts e certs 1/3 of the time. Their expected utility would then beco r d ome: E (UROM ) = 1/3 (60) + 2/3 (4 = 46.66 40) 6666 MEO E (UJUL ) = 1/3 (2 + 2/3 (8 = 66.66666 20) 80) LIET s oint re ffs 66666, 66.6 66666). Let's call this po E wher the payof are (46.6 The key thing to recognize is that points A, B, D, E constitu situation where o e ute ns Rom and Juliet commun meo nicate and a agree on a pattern of meeting be ehaviours wher reas point C is the mix strategy Nash outc xed y come in a s situation of uncertainty y abou their mee ut eting behaviours. The f following diagram sug ggests that w when they can commu unicate and agree, d they can reach the bounda of their utility possi ary ibility set...w when there e's unce ertainty they can't. 316 This results in three pure s strategy Na equilibri They ar (t, T), (b, T), and (b, ash ia. re , B). We w want to dev velop a way to eliminat the "risky pure stra y te y" ategy Nash equilibria from this game. Can you s which t . see two pure strategy Nas equilibria are sh a "risky y"? Of co ourse, the "risky" Nash equilibria are (t, T) and (b, B). If one of the players " h e misc calculates or misreport their strat o ts tegy then th worst ca scenario may arise he ase e wher both play re yers get -50 as their pa 0 ayoff. can roblem by re efining our pure strate equilibria using the egy e We c fix this possible pr conc cept of Perfe Nash E ect Equilibrium. Defin nition: A completely mixed strateg for a pla gy ayer is one t that attache a strictly positive es y probability to ev very pure st trategy for t that player. Defin nition: An epsilon-perfe equilibr ect rium of a no ormal form g game is the equilibrium that e m resul from com lts mpletely mixed strateg gies for all p players whe the prob en bability of pl...
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- Spring '10