Use the following payoff matrix for a simultaneous-move one-shot game to answer the accompanying questions. Player...

Use the following payoff matrix for a simultaneous-move one-shot game to answer the accompanying questions. Player 2 Strategy C D E F Player 1 A 25,15 4,20 16,14 28,12 B 10,10 5,15 8,6 18,13 a. What is player 1’s optimal strategy? Why? b. Determine player 1’s equilibrium payoff.

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Answer :

(a). player 1’s optimal strategy.

Optimal strategy is a strategy which gives clear advantage to the player without any need to consider the other players moves.

Here we can say that Player 1 has better payoff by choosing strategy A, but if player 2 chooses strategy D than P1 receives the lowest. So there is no optimal strategy for player 1.

Then is no dominant or optimal strategy for player 1.

Player 1 can take decision by considering or predicting the player 2 strategy, player 2 has a clear dominant strategy, here he receives maximum pay off by adopting strategy D.

player 2 dominant ( optimal strategy) is D, based on this Player 1 will take his decision, if player 2 adopts D, than player 1 has to take strategy B which gives him more payoff.

Player 1 chooses strategy B

(b).player 1’s equilibrium payoff.

The strategy for player 1 is dependent on player 2 as he is not having a dominant strategy. Player 2 dominant strategy is D, Then Player 1 will choose B giving him an equilibrium payoff of 5

Equilibrium pay off for player 1 is 5. and player 2 is 15

Equilibrium payoff for Player 1 and 2 are (5,15)

Rahul Sunny answered 1 year ago

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