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Exercise 1.6. There are three players. Each player is given an unmarked envelope and asked to put in it either nothing or $3 of his own money or $6 of his own money. A referee collects the envelopes, opens them, gathers all the money and then doubles the amount (using his own money) and divides the total into three equal parts which he then distributes to the players. For example, if Players 1 and 2 put nothing and Player 3 puts $6, then the referee adds another $6 so that the total becomes $12, divides this sum into three equal parts and gives $4 to each player. Each player is selfish and greedy, in the sense that he ranks the outcomes exclusively in terms of his net change in wealth (what he gets form the referee minus what he contributed). (a) Represent this game by means of a set of tables. (Do not treat the referee as a player.) (b) For each player and each pair of strategies determine if one of the two dominates the other and specify if it is weak or strict dominance. (c) Is there a strict dominant-strategy equilibrium?

Exercise 1.6. There are three players. Each player is given an unmarked envelope and asked to put in it either nothing or $3 of his own money or $6 of his own money. A referee collects the envelopes, opens them, gathers all the money and then doubles the amount (using his own money) and divides the total into three equal parts which he then distributes to the players. For example, if Players 1 and 2 put nothing and Player 3 puts $6, then the referee adds another $6 so that the total becomes $12, divides this sum into three equal parts and gives $4 to each player. Each player is selfish and greedy, in the sense that he ranks the outcomes exclusively in terms of his net change in wealth (what he gets form the referee minus what he contributed). (a) Represent this game by means of a set of tables. (Do not treat the referee as a player.) (b) For each player and each pair of strategies determine if one of the two dominates the other and specify if it is weak or strict dominance. (c) Is there a strict dominant-strategy equilibrium?

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Exercise 1.6. There are three players. Each player is given an unmarked envelope and asked to put in it either nothing or $3 of his own money or $6 of his own money. A referee collects the envelopes, opens them, gathers all the money and then doubles the amount (using his own money) and divides the total into three equal parts which he then distributes to the players. For example, if Players 1 and 2 put nothing and Player 3 puts $6, then the referee adds another $6 so that the total becomes $12, divides this sum into three equal parts and gives $4 to each player. Each player is selfish and greedy, in the sense that he ranks the outcomes exclusively in terms of his net change in wealth (what he gets form the referee minus what he contributed). (a) Represent this game by means of a set of tables. (Do not treat the referee as a player.) (b) For each player and each pair of strategies determine if one of the two dominates the other and specify if it is weak or strict dominance. (c) Is there a strict dominant-strategy equilibrium?
Transcribed Image Text:Exercise 1.6. There are three players. Each player is given an unmarked envelope and asked to put in it either nothing or $3 of his own money or $6 of his own money. A referee collects the envelopes, opens them, gathers all the money and then doubles the amount (using his own money) and divides the total into three equal parts which he then distributes to the players. For example, if Players 1 and 2 put nothing and Player 3 puts $6, then the referee adds another $6 so that the total becomes $12, divides this sum into three equal parts and gives $4 to each player. Each player is selfish and greedy, in the sense that he ranks the outcomes exclusively in terms of his net change in wealth (what he gets form the referee minus what he contributed). (a) Represent this game by means of a set of tables. (Do not treat the referee as a player.) (b) For each player and each pair of strategies determine if one of the two dominates the other and specify if it is weak or strict dominance. (c) Is there a strict dominant-strategy equilibrium?
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