# Nash Equilibrium and Dominant Strategy

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Problem:A town has two repair shops, Blue and Red. Each shop must decide whether it will remain open on Sunday or be closed on that day. The payoffs, which are in dollars, are provided in the normal form below. This is a static, or one-shot, game.RedOpenClosed SundaySundayOpen Sunday8,0007,000Blue4,0007,000Closed Sunday10,00012,0003,0006,000Assuming the shops make their decisions simultaneously:(A)Which shop is the most profitable in the Nash equilibrium?First let’s find out the Nash Equilibrium using Best Response Functioni)BRblue(Open) = Openii)BRBlue(Closed) = Openiii)BRRED(Open) = Openiv)BRRED(Closed) = ClosedTherefore, the nash equilibrium in this case is (Open,Open) and RED Shop is the most profitable.(B)Does the shop you identified in part (A) have a dominant strategy? If so, what is it?Yes, Red shop has dominant strategy. As it can be seen in the first part no matter what strategy the RED shop follows (i.e. Open or Closed) the Blue will always choose Open strategy.(C)What should this shop do? Explain your answer.Considering the nash equilibrium and dominant strategy, we can say that the RED shop must Open its shop on Sunday as the Blue shop will be opened on Sunday in any case. To get the maximum payoff the RED must open its shop on Sunday to receive the highest payoff in this particular case i.e. 8000.(D) Is this an example of a prisoners’ dilemma.Yes, it is an example of prisoners’ dilemma.
Problem:Player 2LCRU879799Player 1M568967D8671088The payoffs are in dollars and the game is static. For parts (A) through (C) this is a simultaneous move game.(A) List the outcome from each player choosing his/her maximin strategy.(B) List any dominated strategies.(C) List the Nash equilibria (pure and mixed strategy).(D) List the sub-game perfect Nash equilibrium for the sequential game with player 1 moving first.(E) List the sub-game perfect Nash equilibrium for the sequential game with player 2 moving first.Problem:The data for this problem (Current dollar and real GDP) is available in BlackBoard in the Assignment tab. (A)Run an autoregression [AR(1)] on the annual GDP data using the current dollars.AR_Current_Dollar=arima(Time_Current_Dollars, order=c(1,0,0))AR_Current_Dollar(B)Run an autoregression [AR(1)] on the annual GDP data using the chained 2009 dollars.AR_Chained_Dollar=arima(Time_Chained_Dollars, order=c(1,0,0))AR_Chained_Dollar(C)Which of the autoregression models has a better fit? What information are you using to make your selection?Result of Current DollarCall:arima(x = Time_Chained_Dollars, order = c(1, 0, 0))Coefficients: ar1 intercept

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