Consider the following policy game. The house of representatives (player 1) can propose a new federal minimum wage of x ∈ [10, 20]. The senate (player 2) can either accept the proposal or reject it and maintain the current level. After player 1 proposes x, player 2 observes the proposal and decides whether to accept or reject it. If proposal x is accepted then payoffs are u1(x) = 5+x for player 1 and u2(x) = 20−x for player 2. If player 2 rejects the proposal then both players get a payoff of 7.25. ( a) Draw the game tree. How many subgames does it have? Give an example of a strategy of each player. (b) Find a subgame perfect equilibrium of this game. Is it unique?
Consider the following policy game. The house of representatives (player 1) can propose a new federal minimum wage of x ∈ [10, 20]. The senate (player 2) can either accept the proposal or reject it and maintain the current level. After player 1 proposes x, player 2 observes the proposal and decides whether to accept or reject it. If proposal x is accepted then payoffs are u1(x) = 5+x for player 1 and u2(x) = 20−x for player 2. If player 2 rejects the proposal then both players get a payoff of 7.25. ( a) Draw the game tree. How many subgames does it have? Give an example of a strategy of each player. (b) Find a subgame perfect equilibrium of this game. Is it unique?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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6
Consider the following policy game. The house of representatives (player 1) can propose a new federal minimum wage of x ∈ [10, 20]. The senate (player 2) can either accept the proposal or reject it and maintain the current level. After player 1 proposes x, player 2 observes the proposal and decides whether to accept or reject it. If proposal x is accepted then payoffs are u1(x) = 5+x for player 1 and u2(x) = 20−x for player 2. If player 2 rejects the proposal then both players get a payoff of 7.25. (
a) Draw the game tree. How many subgames does it have? Give an example of a strategy of each player.
(b) Find a subgame perfect equilibrium of this game. Is it unique?
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