quality:corruption
Computing Nash equilibria

If a player A has a dominant strategy s A {\displaystyle s_{A}} then there exists a Nash equilibrium in which A plays s A {\displaystyle s_{A}}. In the case of two players A and B, there exists a Nash equilibrium in which A plays s A {\displaystyle s_{A}} and B plays a best response to s A {\displaystyle s_{A}}. If s A {\displaystyle s_{A}} is a strictly dominant strategy, A plays s A {\displaystyle s_{A}} in all Nash equilibria. If both A and B have strictly dominant strategies, there exists a unique Nash equilibrium in which each plays their strictly dominant strategy.

In games with mixed-strategy Nash equilibria, the probability of a player choosing any particular (so pure) strategy can be computed by assigning a variable to each strategy that represents a fixed probability for choosing that strategy. In order for a player to be willing to randomize, their expected payoff for each (pure) strategy should be the same. In addition, the sum of the probabilities for each strategy of a particular player should be 1. This creates a system of equations from which the probabilities of choosing each strategy can be derived.