Find a boundary condition

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Reference no: EM131449811

Question: The (present discounted) value of a public good is 1 for all players i = 1, I. Time is continuous, and the rate of interest is r. Each player, cost c of supplying the public good is distributed according to the cumulative distribution function P on [0,1]. Players' types are independent. The public good is supplied if at least one agent supplies it. The good is supplied at the first time at which at least one player chooses to contribute. Thus, the game is a kind of war of attrition. Look for a symmetric, pure-strategy equilibrium using the following outline:
(a) Argue formally or informally that the date at which a player with cost c supplies the public good, s(c), is increasing in c.
(b) Show that s(•) satisfies

Find a boundary condition. Infer that a player's waiting time to supply the good when there are I - 1 other players is I - 1 times his waiting time when there are two players. Show that each player's expected utility grows with I.
(Answers can be found in Bliss and Nalcbuff 1984)

Reference no: EM131449811

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