Solving for dominant strategies and the Nash equilibrium :Suppose Rajiv and Simone 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 Rajiv chooses Right and Simone (in bold) chooses Right, Rajiv will receive a payoff of 4 and Simone will receive a payoff of 6. (Simone) left (Simone) right(Rajiv) left 2,3 2,4(Rajiv) right 3,7 4,6The only dominant strategy in this game is for __Simone/Rajiv__ to choose __Right/Left__ .The outcome reflecting the unique Nash equilibrium in this game is as follows: Rajiv chooses __Right/Left__ and Simone chooses __Right/Left__ .

Answer :

a) Dominant strategy is for Rajiv to choose Right.

b) Rajiv chooses Right and Simone chooses Left ( payoffs 6,7)

Explanation :

As per the data given in the question,

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

When Simone chooses left, Rajiv chooses right as this give higher payoff(3>2)

When Simone chooses right, Rajiv chooses left as this give higher payoff(4>2)

When Rajiv chooses left, Simone chooses right as this give higher payoff(4>3)

When Rajiv chooses right, Simone chooses left as this give higher payoff(7>6)

So only dominant strategy is for Rajiv to choose Right

b) In a Nash equilibrium, the players decide their strategies taking in consideration other strategy.

Hence, Rajiv chooses Right and Simone chooses Left, (payoff: 6,7)

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