VI. Game Theory Assume the following payoff matrix for Delta and American airlin
ID: 1128918 • Letter: V
Question
VI. Game Theory Assume the following payoff matrix for Delta and American airlines, where the numbers represent the protits (+) or losses () per passenger over their NY-LA routes Detta Delta Full-Price Discount American $150 $100 Full-Price $100 $50 $40 $60 Discount $140 $70 Does either Delta or American have a dominant strategy? Explain. What is the Nash equilibrium and outcome from the above game? Explain. Would it make a difference to the outcome if Delta and American must repeat this game manyExplanation / Answer
Dominant strategy is a strategy for a player i.e. best response to all strategy profile of other player.
American has the dominant strategy of choosing Discount because it gives higher payoff as compared to Full price and irrespective of the decision of Delta.
Delta does not have any dominant strategy because its payoff depends on the decision of American.
Nash equilibrium is a strategy profile such that for each player given strategy, it is best response. Nash equilibrium is a set of strategies such that each player is doing their best given the strategy of other player.
If American chooses Discount then best response of Delta is to choose Discount because of higher payoff.
If Delta chooses Discount then best response of American is to choose Discount.
So, (Discount, Discount) is the Nash Equilibrium.
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