Two players, two strategies. Payoffs are given by the...

Two players, two strategies. Payoffs are given by the following matrix: Player 2 A B Player 1 A 100, 50 125, 100 B 50, 100 75, 75 a. (10 points) Does player 1 have a dominant strategy? If yes, indicate it! b. (20 points) What is the solution of the game using Nash equilibrium?

Transcript

00:01 Hello, today we have the following payoff matrix and we have to answer a few questions, ultimately finding the nash equilibrium.

00:09 So firstly, does player one have a dominant strategy? so a dominant strategy is where, no matter what the other player chooses, one strategy has a better payoff for player one.

00:22 So in this instance, we'll look at player one strategies.

00:26 So if player one chooses strategy a, they will either make a hundred, 100, their payoff will be 100 or 125, depending on what player 2 chooses.

00:38 So if player 1 chooses strategy b, they will either make 50 or 75 depending on what player 2 chooses their strategy to be.

00:48 So let's just do a direct comparison of what would happen depending on what player two chooses.

00:55 So if player chooses strategy a, player one will either make 100 or 50.

01:00 So, in the first instance, 100 is greater than 50, meaning strategy a is better.

01:07 Now, if player two goes with strategy b, player one will either make 125 or 75.

01:16 So once again, 125 is greater than 75, meaning strategy a is better.

01:21 So player one does indeed have a dominant strategy, and that would be strategy a, because no matter what player two chooses, strategy a will always grant a greater payoff for player one.

01:36 So with that said, we know that since strategy a is dominant for player 1, player 1 is never going to choose strategy b.

01:48 So we can kind of cross this out, and we'll go into the next question.

01:53 So now we're looking for the solution of the game using the nash equilibrium.

01:57 So we already have player one's dominant strategy, which is a...

Question

Two players, two strategies. Payoffs are given by the following matrix: Player 2 A B Player 1 A 100, 50 125, 100 B 50, 100 75, 75 a. (10 points) Does player 1 have a dominant strategy? If yes, indicate it! b. (20 points) What is the solution of the game using Nash equilibrium?

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