(b) Consider the following game. 2 L M H L 4,4 2,4 1,5 1 M 4,2 3,3 0,2 H 5,1 2,0 0,0 Suppose the game above is played twice. The players do not discount the future (i.e. the discount factor for each player is 8 = 1). Describe a subgame-perfect equilibrium of this twice- repeated game in which players play (L, L) in period 1. Consider an auction for a single object with N> 1 symmetric, risk-neutral bidders whose private valuations v¡, i € {1,...,N}, are independent draws from a given distribution F on the in- terval [0, 1]. Prove that in a sealed-bid second-price auction (i.e. Vickrey auction), bidding true value is a weakly dominant strat- egy for any bidder.

(b) Consider the following game. 2 L M H L 4,4 2,4 1,5 1 M 4,2 3,3 0,2 H 5,1 2,0 0,0 Suppose the game above is played twice. The players do not discount the future (i.e. the discount factor for each player is 8 = 1). Describe a subgame-perfect equilibrium of this twice- repeated game in which players play (L, L) in period 1. Consider an auction for a single object with N> 1 symmetric, risk-neutral bidders whose private valuations v¡, i € {1,...,N}, are independent draws from a given distribution F on the in- terval [0, 1]. Prove that in a sealed-bid second-price auction (i.e. Vickrey auction), bidding true value is a weakly dominant strat- egy for any bidder.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

(b) Consider the following game.
2
L
M H
L
4,4
2,4 1,5
1 M 4,2 3,3 0,2
H 5,1 2,0 0,0
Suppose the game above is played twice. The players do not
discount the future (i.e. the discount factor for each player is
8 = 1). Describe a subgame-perfect equilibrium of this twice-
repeated game in which players play (L, L) in period 1.
Consider an auction for a single object with N> 1 symmetric,
risk-neutral bidders whose private valuations vi, i = {1,..., N},
are independent draws from a given distribution F on the in-
terval [0, 1]. Prove that in a sealed-bid second-price auction (i.e.
Vickrey auction), bidding true value is a weakly dominant strat-
egy for any bidder.

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