微觀經(jīng)濟(jì)學(xué)趙耀輝第28章-資料下載頁(yè)
2025-05-19 17:01本頁(yè)面
【導(dǎo)讀】“Up”and“Down”.“Left”and“Right”.
【正文】 2) (0,4) (0,5) (3,2) L,pL R,1pL U, D, 5352.)1(01 LLL p?p???p?Player B Mixed Strategies Player A p pL L? ?3 1( )If then A would play only Up. But there are no Nash equilibria in which A plays only Up. (1,2) (0,4) (0,5) (3,2) L,pL R,1pL U, D, 5352Player B Mixed Strategies Player A If Down. But there are no Nash equilibria in which A plays only Down. p pL L? ?3 1( )then A would play only (1,2) (0,4) (0,5) (3,2) L,pL R,1pL U, D, 5352Player B Mixed Strategies Player A So for there to exist a Nash equilibrium, A must be indifferent between playing Up or Down。 . p pL L? ?3 1( )(1,2) (0,4) (0,5) (3,2) L,pL R,1pL U, D, 5352Player B Mixed Strategies Player A So for there to exist a Nash equilibrium, A must be indifferent between playing Up or Down。 . p p pL L L? ? ? ?3 1 3 4( ) / .(1,2) (0,4) (0,5) (3,2) L,pL R,1pL U, D, 5352Player B Mixed Strategies Player A So for there to exist a Nash equilibrium, A must be indifferent between playing Up or Down。 . p p pL L L? ? ? ?3 1 3 4( ) / .(1,2) (0,4) (0,5) (3,2) L, R, U, D, 53524341Player B Mixed Strategies Player B Player A So the game’s only Nash equilibrium has A playing the mixed strategy (3/5, 2/5) and has B playing the mixed strategy (3/4, 1/4). (1,2) (0,4) (0,5) (3,2) U, D, 5352L, R, 43 41Mixed Strategies Player B Player A The payoffs will be (1,2) with probability 3534920? ?(1,2) (0,4) (0,5) (3,2) U, D, L, R, 43 4153529/20 Mixed Strategies Player B Player A The payoffs will be (0,4) with probability 3514320? ?(0,4) (0,5) (3,2) U, D, L, R, 43 415352(1,2) 9/20 3/20 Mixed Strategies Player B Player A The payoffs will be (0,5) with probability 2534620? ?(0,4) (0,5) U, D, L, R, 43 415352(1,2) 9/20 3/20 6/20 (3,2) Mixed Strategies Player B Player A The payoffs will be (3,2) with probability 2514220? ?(0,4) U, D, L, R, 43 415352(1,2) 9/20 3/20 (0,5) (3,2) 6/20 2/20 Mixed Strategies Player B Player A (0,4) U, D, L, R, 43 415352(1,2) 9/20 3/20 (0,5) (3,2) 6/20 2/20 Mixed Strategies Player B Player A A’s expected Nash equilibrium payoff is 1 920 0 320 0 620 3 220 34? ? ? ? ? ? ? ? .(0,4) U, D, L, R, 43 415352(1,2) 9/20 3/20 (0,5) (3,2) 6/20 2/20 Mixed Strategies Player B Player A A’s expected Nash equilibrium payoff is 1 920 0 320 0 620 3 220 34? ? ? ? ? ? ? ? .B’s expected Nash equilibrium payoff is 2 920 4 320 5 620 2 220 165? ? ? ? ? ? ? ? .(0,4) U, D, L, R, 43 415352(1,2) 9/20 3/20 (0,5) (3,2) 6/20 2/20 Mixed Strategies ?For games with multiple pure strategies, there also exists mixed strategies. ?Example: Chicken game. The probability that each player plays straight is 189。. How Many Nash Equilibria? ?A game with a finite number of players, each with a finite number of pure strategies, has at least one Nash equilibrium. ?So if the game has no pure strategy Nash equilibrium then it must have at least one mixed strategy Nash equilibrium.
教學(xué)課件相關(guān)推薦
鄂ICP備17016276號(hào)-1