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Respond to the question: Aggregative game?

10/29/2018 05:35 AM by Sarella; Aggregative game
Each of n citizens may voluntarily contribute to a public good a sum c_i, with i =1,2,..., n. For m<n citizens, a sponsor would double the individual contribution (i.e. contribute as much as each of the sponsored citizen has done). The quality of the public good, G, is then given by the sum of all contributions, including both those of the citizens and of the sponsor. The payoff to any citizen i, be he/she sponsored or not is:

u_i = G^(1/2) - c_i

Describe this contribution problem as a game and find the Nash equilibrium of the game. [Manage messages]