Consider a minimum contribution game with three players. Each player is a selfis

Question

Consider a minimum contribution game with three players. Each player is a selfish utility maximizer who cares only about his own income. Each player is endowed with 10 dollar bills and can choose how many bills to keep for himself, and how many to contribute to a public good. Player i's contribution, denoted xi, must satisfy r, E 0,1,2,3, 4,5,6,7,8,9,10). The amount of public good will be y = min{x1,x2, za) Each unit of the public good is worth 2 dollars to each player. Thus, player i's payoff (i.e., his utility) will be 2y (10-).4 (a) Are there any strictly dominated strategies in this game? (b) Identify the Pareto-optimal outcome(s) of this game. (c) How many Nash equilibria exist? What do the Nas eibria look like? Are they Pareto-optimal ?

Explanation / Answer

a) Dominent strategey (x1, x2, x3) = {10,10,10}. All other strategies are dominated by this strategy.

b) Pareto Optimal Outcome (x1, x2, x3) = {10,10,10}.

c) Only one Nash equilibrium i.e. (x1, x2, x3) = {10,10,10} and it is pareto optimal.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.