ECON/MGEC 333 Game Theory And Strategy Midterm Examination II Solutions and Questions 2010

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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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