4 players (Alex, Boris, Cato, David) are on the reality show. The prize is 4 gold coins. Each coin cannot be divided into perts, so player can only win some integer number of coins. In the first stage Alex offer some sharing of 4 coins to players (for ex., 3 21 0). If strictly more than a half of players (accounting for the proposer) vote for this sharing then game ends and cach player takes the number of coins as in the offer. If a half of players or more vote against the sharing then Alex leave the island with O coins and then Boris offers a sharing of 4 coins across the rest 3 players and so on. If only David will survive, he will gain all 4 coins. Note0: player's payoff is equal to the number of coins he gets Notel: if some player in some vote is indifferent about the vote, he will vote against a sharing. Note2: each player is indifferent between leaving the island with 0 and staying on the island with an approved offer of 0 coins for him.

4 players (Alex, Boris, Cato, David) are on the reality show. The prize is 4 gold coins. Each coin cannot be divided into perts, so player can only win some integer number of coins. In the first stage Alex offer some sharing of 4 coins to players (for ex., 3 21 0). If strictly more than a half of players (accounting for the proposer) vote for this sharing then game ends and cach player takes the number of coins as in the offer. If a half of players or more vote against the sharing then Alex leave the island with O coins and then Boris offers a sharing of 4 coins across the rest 3 players and so on. If only David will survive, he will gain all 4 coins. Note0: player's payoff is equal to the number of coins he gets Notel: if some player in some vote is indifferent about the vote, he will vote against a sharing. Note2: each player is indifferent between leaving the island with 0 and staying on the island with an approved offer of 0 coins for him.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.9P

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Question

1. Draw tree of the game clearly, handwritten is preferable.

4 players (Alax, Boris, Cate, David) are on the reality show. The
prize is 4 gold coins. Each coin cannot be divided into perts, so
player can only win some integer number of coins.
In the first stage Alex offer some sharing of 4 coins to players (for
ex., 3 21 0). If strictly more than a half of players (accounting
for the proposcr) vote for this sharing then game ends and cach
player takes the number of coins as in the offer. If a half of players
or more vote against the sharing then Alex leave the island with
O coins and then Boris offers a sharing of 4 coins across the rest
3 players and so on. If only David will survive, he will gain all 4
coins.
CX.,
Note0: player's payoff is equal to the number of coins he gets
Notel: if some player in some vote is indifferent about the vote,
he will vote against a sharing.
Note2: each player is indifferent between leaving the island with
O and staying on the island with an approved offer of 0 coins for
him.

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