\"34\" and RAD are Maymester 13 fashionistas, and want to wear their tank tops t
ID: 1216330 • Letter: #
Question
"34" and RAD are Maymester 13 fashionistas, and want to wear their tank tops to class. But being the only one wearing a tank top makes them uncomfortable. Their strategies are thus (tt, s), mnemonic for "tank top" and "sleeves," and their payoffs are tt s tt (3, 3) (1, 2) s (2, 1) (2, 2). Determine the Nash equilibrium (if any) for this game. Your answer should have the form: "The Nash equilibrium (equilibrium) is the pair (a, b), (or, "there is no Nash equilibrium in pure strategies." Explain your reasoning. Lauren and Julia, two other Maymester 13 fashionistas, like to wear their favorite tank tops-which are identical- on co-curricular activities. But they really hate it when they both are wearing the same top. Their strategies are thus (tt, s), mnemonic for "tank top" and "sleeves," and their payoffs are tt s tt (1, 1) (3, 2) s (2, 3) (2, 2). Determine the Nash equilibrium (if any) for this game, and explain your reasoning. "34" and RAD are "team followback" members of twitter, and can communicate before class. So are Lauren and Julia. Does this suggest anything about the Nash equilibrium (if there are any) of the games in (1) and (2)?Explanation / Answer
Problems stated in part 1 and part 2 are on game theory. First consider problem (1). Two players are "34" and RAD.
They have two strategies tt and s. The payoff table is-
In Nash equilibrium, each player tries to maximze his payoff subject to a given strategy of opponent. Here 34 will go for tt if RAD has selected tt. Similarly he will go for s if RAD has adopted s. Put * against 3 of cell (tt,tt) and 2 of cell (s,s).
Suppose 34 has selected tt. Then RAD will go for tt. If he has adopted s then also RAD will adopt s. Put # sign against 3 in cell(tt,tt) and against 2 in cell (s,s).
Thus both cell (tt,tt) and (s,s) are Nash equilibrium.
In Nash equilibrium there is no comunication among 36 and RAD. So they may stay at s,s strategy although tt,tt is best for them. If they can communicate among them, then this two Nash equilibrium situation can be discussed. In that case, both will decide to adopt tt to get maximum advantages. Thus equilbrium solution will be reached where both will enjoy maximum payoff 3. No one will have any incentive to shift from this poinbt.
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Now consider problem 2. Here two players are Lauren and Julia. Their payoff table is-
Consider Nash equilibrium again.If Julia has adopted tt then Lauren will go for s.to get highest payoff 2. If he has adopted s then Lauren will take tt to get maximum payoff 3. Put * sign against these payoff in the table.
Now suppose Lauren has adopted tt, then Julia will adopt s to get maximum pay off 2. In case of strategy s by Lauren, Julia will go for tt to get maximum payoff. Thus two Nash equilibriums are strategies (tt,s) and (s,tt).
Note that these solutions are not atable. In one solution, Laurel is better off and in another strategy Julia will be better off. So each of them will always try to deviate to get maximum advantage.
This instable situation can be solved if two of them communicate. Then both will decide for a new combination (s,s) where payoff is (2,2). Although they have payoff less than highest pay off 3, yet it is better than lowest payoff 1. Further it will bring stability. So final solution will be (s,s)=(2,2)
RAD tt s "34" tt (3*,3#) (1,2) s (2,1) (2*,2#)Related Questions
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