It is not possible for a game to have no pure- strategy Nash equilibria.

Question

Quizplus · Accepted Answer

Every finite game has at least one pure-strategy Nash equilibrium. This is because a pure-strategy Nash equilibrium is reached when each player chooses their best strategy given the other player's strategy, and in a finite game with a finite number of strategies, there will always be at least one combination of strategies where neither player can improve their payoff by unilaterally changing their strategy. However, some games may have multiple pure-strategy Nash equilibria or may have a mixed-strategy Nash equilibrium as well.

It Is Not Possible for a Game to Have No