2. Split the dollar Players 1 and 2 are bargaining over how to split one dollar.

Question

2. Split the dollar Players 1 and 2 are bargaining over how to split one dollar. Both players simultaneousl name shares they would like to keep s and s2. Furthermore, players' choices have to be in incre- ments of 25 cents, that is, s E 0,0.25,0.50,0.75,1.00] and s2 [0,0.25,0.50, 0.75, 1.00. If sit s2 1, then player 1 gets si and player 2 gets s2. If sit > 1, then both players get 0. (3.1) Write down the normal form of the game (the bimatrix of strategies and payoffs) (3.2) Find the Nash Equilibria of this game WIL

Explanation / Answer

3.1

The payoff matrix for player 1 and 2 is given below. Each payoff is shown as (1,2) where 1 represents payoff for player 1 and 2 represents payoff for player 2.

3.2

Finding Nash Equlibria of this game.

Step 1 - Determine the row's player (player 1) best response to each of column's player (player 2) possible strategies. The best strategies are shown in bold.

Step 2 - Determine the column's player (player 2) best response to each of row's player (player 1) possible strategies. The best strategies are shown in bold.

Step 3 : Any outcome that is a best response for both players is a Nash Equilibrium

So, the Nash Equilibria are (1,0), (0.75,0.25), (0.5,0.5), (0.25, 0.75), (0,1) and (0,0)

Player 1 Player2 0 0.25 0.5 0.75 1 0 (0,0) (0,0.25) (0,0.5) (0,0.75) (0,1) 0.25 (0.25,0) (0.25,0.25) (0.25,0.5) (0.25, 0.75) (0,0) 0.5 (0.5,0) (0.5,0.25) (0.5,0.5) (0,0) (0,0) 0.75 (0.75,0) (0.75,0.25) (0,0) (0,0) (0,0) 1 (1,0) (0,0) (0,0) (0,0) (0,0)

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