Answer the following

QUEsTtoN 1 There are two customer service workers; workert' (i E {1, 2}} chooses an effort level 2 s, E [man] to exert in helping a customer. The cost of effort is e.{e.} = iii5L for worker I and J \"1032) =% for worker 2. The customer's satisfaction level equals the total effort that the workers exert. up to a maximum satisfaction level of ll}+ that is, it is equal to min{sI +e1,l[t} . Each worker's payoff is the difference between the customer's satisfaction level and hist'her own effort cost. Consider rst the game G in which the two workers choose their efforts simultaneously. {:1 Write down each worker's payoff mctioo in G. {It} Describe each worker's best response [or reaction} function in f}. {c} Draw the two best response functions in the same diagram and find all the pure-strategy Nash equilibria of G. Now consider sequential versions of the interaction In game 1;. rst Player 1 {= worker I} selects an effort level1 then Player 2 (= worker 2) after observing Player 1"'s choice chooses her own effort level. {:1} Completely describe all the pure-strategy subgame perfect equilibria of f}. In game 1;, the sequence of events starts with those in F2 1 but after Player 2 moves1 Player 1 observes Player 2's choice and decides whether to exert some additional effort d'. E [than] . so that his own total effort is s. +'l. {e} {2.1} What is a pure strategy for Player 1 in 11'? {e1} What is a pure strategy for Player 2'? [You are free to state your answers in words. rather than in mathematical notation; but1 in either case+ your answers should be explicit and complete.] {e3} Give an example of a pure strategy for Player 1 and a pure strategy for Player 11in the special case where each effort level must be chosen from the set {3,4}1 that is. when 2.32.5, E314}. {1'} Completely describe all pure strategy subgame perfect equilibria of i"; when are: E [1110] {instead of {0.53)} and a". E [If]1 if] s.] {instead of [[t,ao}}. QUESTION 2 Consider a simultaneous two-player second-price auction concerning a single indivisible good. The game-frame is as follows: S, = S, = B where B= (P,, P2,..., Pm) is a finite subset of [0,co) with Px , (2, p'); for every p and p', (1, p) >, (1, p') if and only if p (2, p') if and only if p (2, p') if and only if p > p'; (2, P,) -, (1,v,); and everything that follows from the above by transitivity. In what follows assume that m > 3, v, V E B, p,