Economics > QUESTIONS & ANSWERS > ECON/MGEC 333 Game Theory And Strategy Midterm Examination II Solutions and Questions 2010 (All)
1. (30pts.) Find the set of pure strategy Nash equilibria and subgame perfect equilibria of the following game: 1 2 1 1 Out In F A F A F A 0, 20 −5, −5 −1, 8 8, 5 10, 10 (40pts.) Two partners... are trying to dissolve their partnership. Player 1 currently owns a share s ∈ (0, 1) of the partnership and player 2 owns 1 − s. The value of owning the whole partnership is vi ∈ [0, 1] for player i = 1, 2. Player 1 moves first by choosing a price p ≥ 0. Player 2 can either buy player 1’s share at ps, in which case the payoffs of player 1 and 2 are ps and v2 − ps, respectively, or he may sell his share at p(1 − s), in which case the payoffs are v1 − p(1 − s) and p(1 − s). The game can be depicted as in Figure 1. 1 2 ps, v2 − ps v1 − p(1 − s), p(1 − s) p B S Figure 1: Partnership Game (a) (15pts.) First assume that v1 = v2 = v, and that this is common knowledge. What is the subgame perfect equilibrium strategy of player 1? [Show More]
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