Two players bargain over $20. Player 1 first proposes a split of (n, 20 - n), where n is an integer in {0, 1, ..., 20}. Player 2 can either accept or reject this proposal. If player accepts it, player 1 obtains $n and player 2 obtains $(20 - n). If player 2 rejects it, the money is taken away from them and both players will get $0. Find one Nash equilibrium that is NOT a subgame perfect Nash equilibrium. Explain why it is a Nash equilibrium and why it is not subgame perfect.

Two players bargain over $20. Player 1 first proposes a split of (n, 20 - n), where n is an integer in {0, 1, ..., 20}. Player 2 can either accept or reject this proposal. If player accepts it, player 1 obtains $n and player 2 obtains $(20 - n). If player 2 rejects it, the money is taken away from them and both players will get $0. Find one Nash equilibrium that is NOT a subgame perfect Nash equilibrium. Explain why it is a Nash equilibrium and why it is not subgame perfect.

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter15: Strategic Games

Section: Chapter Questions

Problem 2MC

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Two players bargain over $20. They proceed as follows. Player 1 first proposes a split(n; 20-n); where n is an integer in {0, 1,.... 20 }. Player 2 can either accept or reject this proposal. If player 1 accepts it, player 1 obtains $n and player 2 obtains $(20-n) If player 2 rejects it, the money is taken away from them and both players will get $0 Find two subgame perfect Nash equilibria of this game and state clearly each player's equilibrium strategies (recall that in a dynamic game, a player's strategy is a complete-contingent plan). Explain why the strategy profiles form a subgame perfect equilibrium.
Two players bargain over $20. They proceed as follows. Player 1 first proposes a split(n; 20-n); where n is an integer in {0, 1,.... 20 }. Player 2 can either accept or reject this proposal. If player 1 accepts it, player 1 obtains $n and player 2 obtains $(20-n) If player 2 rejects it, the money is taken away from them and both players will get $0 Find one Nash equilibrium that is not a subgame perfect Nash equilibrium. Explain why it is a Nash equilibrium and why it is not subgame perfect.
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