(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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