Consider the ice cream game, where A chooses the product and B chooses the flavo
ID: 1124416 • Letter: C
Question
Consider the ice cream game, where A chooses the product and B chooses the flavor (note all payoffs are positive). (18 points) The Ice Cream Game A's Cone B's Strategy Vanilla Chocolate Mint Cherry (7,4) (3,4) (6,3) (4,5) (6,4) (5,2) (5,3) (7,5) 1(8.7) | (3,6) Strategy Shake (3,2) Sundae i. Define a Dominant Strategy Equilibrium for a two person game. ii. Define a Nash Equilibrium for a two person game. ii What is (are) the Dominant Strategy Equilibrium (equilibria) and Nash Equilibrium (equilibria) for the ice cream game? (Please ignore mixed strategies for this question). Use successive strict dominance to eliminate certain strategies. Explain what strategies will be eliminated and why. Which combination of strategies A and B will play rationally? iv.Explanation / Answer
i). A strategy that is strictly prefered over other strategy i.e it provides greater pay off than other strategies is called a dominant strategy.
ii). Nash equilibrium is one of the most popular concepts of game theory in which the optimal outcome is the strategy where no player has an incentive to deviate from his strategy, after considering his opponent's strategy.
iii). The dominant strategy equilibrium in this game is (sundae, mint) as they provide the highest payoff ((8,7) among all other choices.This is also the Nash equilibrium strategy as the combination provides the highest payoffs when compared to other combinations.
iv).