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(3) Players 1 and 2 are bargaining over how to split $1. Each player simultaneously and independently claims a share he/she/they would like to have, i.e., player i claims s;, where 0 < s; < 1. If s1 + s2 < 1, then the dollar is divided, each player receiving the share he/she/they claimed. However, if sı + s2 > 1, both players receive zero. (a) What is S;, the set of pure strategies for player i? (b) What is the payoff function U,(s;, s_;) for player i? Write the function in terms of equation(s). (c) What are the pure strategy Nash Equilibria of this game? Is the dollar divided in every Nash Equilibrium?

(3) Players 1 and 2 are bargaining over how to split $1. Each player simultaneously and independently claims a share he/she/they would like to have, i.e., player i claims s;, where 0 < s; < 1. If s1 + s2 < 1, then the dollar is divided, each player receiving the share he/she/they claimed. However, if sı + s2 > 1, both players receive zero. (a) What is S;, the set of pure strategies for player i? (b) What is the payoff function U,(s;, s_;) for player i? Write the function in terms of equation(s). (c) What are the pure strategy Nash Equilibria of this game? Is the dollar divided in every Nash Equilibrium?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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(3) Players 1 and 2 are bargaining over how to split $1. Each player simultaneously and independently claims a share he/she/they would like to have, i.e., player i claims s;, where 0 < s; < 1. If s1 + s2 < 1, then the dollar is divided, each player receiving the share he/she/they claimed. However, if sı + s2 > 1, both players receive zero. (a) What is S;, the set of pure strategies for player i? (b) What is the payoff function U,(s;, s_;) for player i? Write the function in terms of equation(s). (c) What are the pure strategy Nash Equilibria of this game? Is the dollar divided in every Nash Equilibrium?
Transcribed Image Text:(3) Players 1 and 2 are bargaining over how to split $1. Each player simultaneously and independently claims a share he/she/they would like to have, i.e., player i claims s;, where 0 < s; < 1. If s1 + s2 < 1, then the dollar is divided, each player receiving the share he/she/they claimed. However, if sı + s2 > 1, both players receive zero. (a) What is S;, the set of pure strategies for player i? (b) What is the payoff function U,(s;, s_;) for player i? Write the function in terms of equation(s). (c) What are the pure strategy Nash Equilibria of this game? Is the dollar divided in every Nash Equilibrium?
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