课程名称︰赛局论 课程性质︰选修 课程教师︰古慧雯 开课学院：社科院 开课系所︰经济系 考试日期（年月日）︰101.05.11 考试时限（分钟）：10:20-11:30 (70mins) 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1.Consider the following game. The first (second) element of the payoff vector is the payoff to the row (column) player. │ slow│ speed ───┼───┼─── slow│ 2,2│ 0,3 ───┼───┼─── speed│ 3,0│ -1,-1 (a)(3 points) Find out all the Nash equilibrium. (b)(5 points) Consider this game to be repeated twice. Find 3 subgame perfect equilibrium which yield an expected patoff of 3 to each player. 2.(10 points) Consider the simplified Parchessi game of section 3.8.1 (as attached) with the modification that, when a counter is exactly one square from the winning square, then only the throw of a tail permits it to be advanced. Other rules remain unchanged. Positions 1 and 2 of figure 3.17 no longer have the value 1. Let their values be g and h respectively. Prove that d < g. 3.Consider a two person zero-sum game with a payoff matrix M which specifies the payoff to the row player. Let [m lower bar] ([m bar]) denote the row (column) player's security level when both players consider to use only pure strategies, and let [v lower bar] ([v bar]) denote the row (column) player's security level when both players consider to use mixed strategies. (a)(4 points) Please compare [m lower bar] and [v lower bar.] (Give the mathematical forms of [m lower bar] and [v lower bar,] and analyze their their difference rigorously.) (b)(3 points) Suppose [m lower bar] = [m bar.] Prove that the row player's security level is [m lower bar] when both players consider to use mixed strategies. (You could quote the result that [v bar] > [v lower bar.] Other than that any claim has to be provided with a detailed proof.) --

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