We consider the following three-player strategic form game, where Alice's strategies are U, C, and D, and Bob's strategies are L, M, and R, and Carol's strategies are A and B. Carol's strategy consists of choosing which table will be used for the payoffs, Table A or Table B. Table A is below, where for each cell the first number is Alice's payoff, the second number is Bob's payoff and the third number is Carol's payoff.
We consider the following three-player strategic form game, where Alice's strategies are U, C, and D, and Bob's strategies are L, M, and R, and Carol's strategies are A and B. Carol's strategy consists of choosing which table will be used for the payoffs, Table A or Table B.
Table A is below, where for each cell the first number is Alice's payoff, the second number is Bob's payoff and the third number is Carol's payoff.
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| L | M | R | |
| U | 8,11,14 | 3,13,9 | 0,5,8 |
| C | 9,9,8 | 8,7,7 | 6,5,7 |
| D | 0,8,12 | 4,9,2 | 0,4,8 |
| Table A |
Table B is below, where again, for each cell, the first number is Alice's payoff, the second number is Bob's payoff and the third number is Carol's payoff.
.
| L | M | R | |
| U | 14,1,0 | 13,2,11 | 1,3,2 |
| C | 0,0,2 | 7,2,3 | 14,3,2 |
| D | 7,12,11 | 12,12,0 | 2,11,2 |
| Table B |
This game may not have any Nash equilibrium in pure strategies, or it may have one or more equilibria.
How many Nash equilibria does this game have?
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