30 Apr 20] Consider a contest where two contestants, i e (1,2), compete for a prize worth v (in utility …
20] Consider a contest where two contestants, i e (1,2), compete for a prize worth v (in utility terms). The probability of contestant i wining the compe tition is ei P(e1,e2) e where es is the effort exerted by contestant i. The losing contestant gets nothing. The (utility) cost of effort is c(e) ef. Thus, contestant i’s payoff is given by (a) (8) Find the symmetric Nash equilibrium effort level. (b) (4 Given an interpretation of r. Give an interpretation of what happens c) 18] Now, suppose r 2 and the contestants are restricted to putting i to the equilibrium effort level as r-0 one of two effort levels: high (e 3) or low (e1). Find all the Nas equilibria (including mixed strategy ones)
(e) [5) Find all the Pareto optimal allocations. (b) [5] Using the normali (e) [5] Carefully state the first welfare th (d) [5] Suppose the endowments had instead been е,- (18, 15) and ег- 1, find the Walrasian equilibrium. m and verify that it holds. zation, p2 eore (2,5). Find the Walrasian equilibrium. 4. [20) Answer the following. (a) [4] Explain the diference between a strategy that is a best response versus a strategy that is strictly dominant. (b) [6 Consider the following game: player 2 D E F G Al 3,7 | 7.3 | 1.2 | 4.3 player 1 B 8,9 8,5 2,8 5,2 C 0.10 7,0 1,9 2,2 Find the strictly dominant strategies solution and the iterated eliminati of strictly dominated strategies solution, if any (c) [10 Consider the following game: player 2 L C R T 10,4 1,2 1,0 player 1 M 6,4 2,0 3,0 B | 9,0 | 3,3 | 4,8 Find all the Nash equilibria (including mixed strategy ones).
Lalhot engage in any price discrimination. Uptimal pricing strategy. Calculate the firm’s Lerne lhdex. (b) [5] What is the deadweight loss (relative to the competitive market out come) associated with this pricing strategy, if any? (c) [5] Now, suppose price discri optimal third-degree p more inelastic at the optimal solution? mination is possible. Find the rice-discrimination strategy. Which (d) [5] W hat inform ation is required for the monopolist to be able to use third-degree price discrimination? Give a real-life example wh degree price discrimination is used. [20] Consider an Edgeworth box economy where preferences and endowment are given by (a) [4] Carefully state the theorem regarding the existence of a Walras (b) [6] Using the normalization p2 1, find the Walrasian equilibriurm. (c) [4] Carefully state the Walras’ Law and verify that it holds. d) [6] Can the allocation (5,23.4),(5,2.6)) be supported as an e equilibrium that was given in the lectures. librium with transfers? If yes, find the supporting prices (normalize price of the second good to one) and transfers. If no, explain.
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