Solving for dominant strategies and the Nash equilibrium Suppose Musashi and Rin

Question

Solving for dominant strategies and the Nash equilibrium Suppose Musashi and Rina are playing a game in which both must simultaneously choose the action left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Musashi chooses Right and Rina chooses Right, Musashi will receive a payoff of 3 and Rina will receive a payoff of 7. The only dominant strategy In this game is for to choose. The outcome reflecting the unique Nash equilibrium In this game is as follows: Musashi chooses and Rina chooses.

Explanation / Answer

(a) A dominant strategy is the strategy a player chooses irrespective of the strategy chosen by the other player.

When Rina chooses Left, Musahi chooses Right as this gives higher payoff (7 > 4).

When Rina chooses Right, Musahi chooses Left as this gives higher payoff (6 > 3).

When Musahi chooses Left, Rina chooses Right as this gives higher payoff (8 > 6).

When Musahi chooses Right, Rina chooses Right as this gives higher payoff (7 > 5).

So, the only dominant strategy is for Rina to choose Right.

(b) In a Nash equilibrium, the players decide their strategies keeping in mind the reaction of the other strategy.

Here, this is: Musahi chooses Left & Rina chooses Right (payoff: 6, 8).

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