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Behavioral Economics Analyse the following ultimatum game. Player 1 and Player 2 bargain over the distribution of a surplus of size 1. Player 1 moves first and can propose any distribution of the surplus s ∈ [0, 1]. Player 2 observes the proposal and either accepts it or rejects it. If Player 2 accepts the proposal s, then Player 1’s monetary payoff is 1 − s and Player 2’s monetary payoff is s. Otherwise, both receive nothing. a) Assume that both players only care about their own monetary payoff. Describe a pair of pure strategies for Player 1 and Player 2 so that the equal split (s = 0.5) is sustained as a Nash equilibrium outcome of the game. b) Find the subgame-perfect Nash equilibrium of the game if both players only care about their own monetary payoff. c) Assume now that players are inequity averse. State the utility functions of Player 1 and Player 2 when they have Fehr-Schmidt preferences. d) Assume that Player 1’s preferences are characterized by α1 = β1 = 0, while Player 2’s preferences are characterized by α2 = 2 and β2 = 2/3. Assume that players know each other’s preferences. Find the subgame-perfect Nash equilibrium of the game. e) Assume instead that α1 = α2 = 2 and β1 = β2 = 2/3. Assume that players know each other’s preferences. Find the subgame-perfect Nash equilibrium of the game.

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