Question

onstruct a 4x4 game which has a UNIQUE Nash equilibrium where player 1 chooses strategy A with probability 1/3, probability B, C and D with probability 2/9. Player 2 chooses strategy a with probability 1/2 and chooses b,c and d with probability 2/9. Each strategy should have a non 0 probability. If someone answers this and gives me an answer where strategy d has a probability of 0 I will be very sad

Answer 1

To construct a 4x4 game with a unique Nash equilibrium, we can set up a game where Player 1 has strategies A, B, C, and D with probabilities 1/3, 2/9, 2/9, and 2/9, respectively, and Player 2 has strategies a, b, c, and d with probabilities 1/2, 2/9, 2/9, and 2/9, respectively. One possible game setup that satisfies these conditions is illustrated in the answer.

Step-by-step explanation:

In this 4x4 game, Player 1 has strategies A, B, C, and D with probabilities 1/3, 2/9, 2/9, and 2/9, respectively. Player 2 has strategies a, b, c, and d with probabilities 1/2, 2/9, 2/9, and 2/9, respectively. We need to find a game in which strategy d has a non-zero probability.

One possible setup is:

abcdA4, 52, 61, 32, 4B5, 33, 42, 53, 6C3, 24, 35, 24, 5D6, 15, 24, 40, 0

Strategy d has a non-zero probability (2/9), and there is a unique Nash equilibrium where Player 1 chooses strategy A with probability 1/3 and Player 2 chooses strategy a with probability 1/2.