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- In game theory, what is a subgame? What is a subgame-perfect Nash equilibrium? If possible, could you please provide an example? Thank you!A Nash equilibrium with a noncredible threat as a component is Multiple Choice a subgame perfect equilibrium. not a subgame perfect equilibrium. a sequential equilibrium. a somewhat subgame perfect equilibrium.TRUE OR FALSE: In urban economics, the Nash equilibrium outcome is typically greater than the Pareto efficient outcome. What principle in urban economics can explain this?
- Under what circumstances are the auctions likely to lead to an 'efficient" price for the item being sold?in every Nash equilibrium, the strategy of every player is a best response to the strategies chosen by the other players. (a) True. (b) False.There is a city, which looks like chopped isosceles triangle, as shown below. Citizens live uniformly distributed all over the city. Two ice-cream vendors, A and B, must independently set up stores in the city. Each citizen buys from the vendor closest to their location and when equidistant from both vendors they choose by coin toss. Each vendor’s aim is to maximize the expected number of customers. A choice of location by the two vendors is a Nash equilibrium if no vendor can do better by deviating unilaterally. Does this game have a Nash equilibrium? If so, describe it. If not, explain why not
- Jane and Sara are competing orange juice salespersons in Amherst. Their stands are next to each other on a street and consumers regard them as identical. The marginal cost of an orange juice is $1. The demand for orange juice every hour is Q = 20 − P where P is the lowest price between the two salespersons. If their prices are equal they split demand equally. a. If they set prices simultaneously (prices can be any real number), what is the Nash equilibrium price? b. If, against what we have assumed in class, orange juice salespersons have to charge prices in whole dollars ($1, $2, $3, etc), what are the Nash equilibrium prices? c. Assuming whole dollar pricing, if Jane sets her price before Sara, what price would she charge? Answer all 3 partsEvolutionary game theory provides a framework for understanding the emergence of preferences and behavior. Why are theoretical methodologies that employ the rational actor model an evolutionary stable strategy for economists?Consider a bargaining situation where the pie can be allocated only in three ways: The first player gets all the pie, the second player gets all the pie, the pie is split equally among the two players. Both players have constant and identical discount rates δ. For each of the three possible allocations of the pie, find out for which values of δ there is a a subgame perfect equilibrium such that this allocation can be offered and accepted in the first round of the game of alternating offers. (Note: the subgame perfect equilibria with a certain property that only applies to a part of the game, namely that a specific allocation is proposed and accepted in round 1 of the game.) The approach starts at some period ?+1 in the future (under the restriction that only these three divisions are possible). You make an assumption about what could be an equilibrium outcome in this period. This allows you to explain what are best replies of the player in period ? (again, under the restriction that…