Determine the pure strategy nash equilibrium
In order to determine the pure strategy Nash equilibrium, we need to analyze the strategies of all players and find a situation where no player can unilaterally deviate from their chosen strategy to increase their payoff.
To do this, we consider the strategies available to each player and the payoffs associated with each combination of strategies.
Let's take an example with two players, A and B, and two strategies available to each player, 1 and 2. The payoff matrix looks like this:
Player B
1 2
Player A
1 3,3 1,2
2 2,1 4,4
In this example, player A has two strategies: 1 and 2, and player B also has two strategies: 1 and 2. The payoffs associated with each combination of strategies are given in the matrix.
To determine the pure strategy Nash equilibrium, we need to find a situation where no player can unilaterally deviate from their chosen strategy to increase their payoff.
In this example, we can see that no player can increase their payoff by deviating from their chosen strategy. If player A chooses strategy 1, player B is already choosing strategy 1 to maximize their payoff. Similarly, if player A chooses strategy 2, player B is already choosing strategy 2 to maximize their payoff.
Therefore, the pure strategy Nash equilibrium in this game is for player A to choose strategy 1 and for player B to choose strategy 2.