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Unformatted text preview: uccessive elimination of (weakly dominate strategie n y) ed es... [i] ma not yield a unique o ay d outcome, [ii] re equires com mmon know wledge, and s for dominated strategies ( (after all, th player is he [iii] is particularly dubious f weakly d indiff ferent). Now let's do thr rough anoth exercise using the successive eliminatio of her e e on (wea akly) domina ated strateg gies... 300 Cons sider a two player gam in strateg form giv as: me gic ven Now, let's illustr rate the "inf formation lo oss" we exp perience by analysing a game in y the s strategic for rm. Take a few minutes to draw an extensive form re e w epresentati of the tw player ion wo strate egic form game above Is your representati the only possible e g e. ion y extensive form game for this payoff m matrix? BLE TEGIES AN NASH E ND EQUILIBRIA A RATIONALIZAB STRAT Defin nition: A str rategy, s, is a "best res s sponse" for player i to his rival's s r strategies if the payoff f f to pla ayer i from playing s is greater th the payoff to playe i from any other s han er y strate (taking the rival's strategies a given). egy as 301 Defin nition: A Na Equilibr ash rium in pure strategies is a set of strategies, one for ea player, e s ach such that each player's str h rategy maxi imizes their payoff tak r king the othe player's er strate egies as giv (i.e. mu ven utual best r response). Let's see how th works... s his ...consider th following two perso game in strategic he g on form: How do we find these "mutual best re esponses"? First, let's take as given that player 1 will choose his pure s a e strategy T. What is playe 2's best response to this inform er o mation? en payoffs When player 1 plays T, the player 2 can choose L, C, or R with his p g being 4 for L, 2 for C, and 3 for R. Clearly, when player 1 play T the be response from play 2 is to p p ys est yer play L. Now, we need to check if T is player 1's best res t sponse if pl layer 2 play L. ys en B, offs When player 2 plays L, the play...
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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