Coursenotes_ECON301

Well call this point c and th payoffs a 25263 he are

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online