Consider a voluntary contributions game played by 4 players. Each player starts off with $20. Players...

 

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Consider a voluntary contributions game played by 4 players. Each player starts off with $20. Players choose simultaneously how much to contribute. A player's contribution may be any amount from $0 up to $20. The marginal per-capita return (MPCR) is 0.4. a. (6 points) In period 1, three players contribute $10 and fourth player contributes $0. How much does each player earn? b. (6 points) Suppose that the group of four players plays the game for 10 rounds in an experiment. What would be the pattern of contributions over time? Would they decrease, increase, or stay the same over the course of 10 rounds? c. (6 points) Suppose that instead of 0.4, the MPCR was 0.8. How would behavior in experiments be different between the two treatments? What might account for a difference in behavior when the MPCR is changed? Fix the MPCR at 0.4. Suppose now that a second stage was added to the game where each player can observe what each other player contributed. Each player can then pay $1 to reduce any other player's payoff by $2, and can do this as many times as she would like within a period. d. (6 points) What is the subgame perfect equilibrium to this game? e. (6 points) How would you expect this change in the game to affect results in a 10 round experiment? Explain your answer. Consider a voluntary contributions game played by 4 players. Each player starts off with $20. Players choose simultaneously how much to contribute. A player's contribution may be any amount from $0 up to $20. The marginal per-capita return (MPCR) is 0.4. a. (6 points) In period 1, three players contribute $10 and fourth player contributes $0. How much does each player earn? b. (6 points) Suppose that the group of four players plays the game for 10 rounds in an experiment. What would be the pattern of contributions over time? Would they decrease, increase, or stay the same over the course of 10 rounds? c. (6 points) Suppose that instead of 0.4, the MPCR was 0.8. How would behavior in experiments be different between the two treatments? What might account for a difference in behavior when the MPCR is changed? Fix the MPCR at 0.4. Suppose now that a second stage was added to the game where each player can observe what each other player contributed. Each player can then pay $1 to reduce any other player's payoff by $2, and can do this as many times as she would like within a period. d. (6 points) What is the subgame perfect equilibrium to this game? e. (6 points) How would you expect this change in the game to affect results in a 10 round experiment? Explain your answer.

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a Earnings in Period 1 In this scenario three players contribute 10 each and the fourth player contributes 50 To calculate each players earnings well ... View the full answer