All games that have a dominant-strategy equilibrium _____ have a Nash equilibrium;all games with a Nash equilibrium _____ have a dominant-strategy equilibrium.
A)may not;must
B)must;must
C)may not;may not
D)must;may not

Question

Quizplus · Accepted Answer

A dominant strategy equilibrium exists when each player has a dominant strategy, meaning there is a single best move regardless of the other player's choices. In games with dominant strategy equilibrium, players will always choose their dominant strategy, and this will result in a Nash equilibrium, which is a situation in which no player can improve their payoff by unilaterally changing their strategy. However, not all games have a dominant strategy equilibrium, and in these cases, a Nash equilibrium may still exist. Therefore, all games with a Nash equilibrium do not necessarily have a dominant strategy equilibrium. However, if a game has a dominant strategy equilibrium, then it must also have a Nash equilibrium.

All Games That Have a Dominant-Strategy Equilibrium _____ Have a Nash