Question

the following payoff matrix is for two players, each with two strategies: what is player 2's dominant strategy in this game? always cooperate always cheat cooperate when player 1 cooperates and cheat when player 1 cheats player 2 does not have a dominant strategy.

Answer 1

Player 2 does not have a dominant strategy in this game.

What is dominant?
To be dominant is to exercise power. One male wolf in a pack engages in combat with the others, prevails, and rises to the position of leader. Dominus, which means "lord or master" in Latin, is where the word dominant originates. This is one of many names for God that you may be familiar with if you attended a Latin mass as a child. If you treat others as though you are their master, you are dominant. The word dominant can also be used to describe something frequent as well as typical. For instance, making calls was the primary function of cell phones when they first became available. Some people hardly ever make calls on their cell phones because they can do so much more now.

A dominant strategy is one that provides the best outcome regardless of what strategies the other player chooses. In this game, if Player 1 cooperates, then Player 2's best strategy is to also cooperate. However, if Player 1 cheats, then Player 2's best strategy is to cheat. Therefore, Player 2 does not have a dominant strategy because the best strategy depends on what Player 1 does.

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