Two players can jointly provide a public good which has a total cost of 5. Each player has private information which determines how valuable player i finds the public good. In particular, each player has two types, where vi = 1 with probability 0.5 and vi = 4 with probability 0.5. These types are drawn independently. The timing of the game is as follows: (1) nature draws type vi (equal to 1 or 4 with equal probability for each player); (2) each player (privately) observes vi and simultaneously decides whether to contribute bi ≥ 0; and (3) the good is provided if and only if b1 + b2 ≥ 5; finally payoffs are realised. The payoff of each player i is equal to vi - bi if the good is provided, and player i’s payoff is -bi if it is not provided. (a) Draw the game in extensive form (be careful in correctly characterising information sets) (b) Find the Nash equilibria of the game
Two players can jointly provide a public good which has a total cost of 5. Each player has private information which determines how valuable player i finds the public good. In particular, each player has two types, where vi = 1 with probability 0.5 and vi = 4 with probability 0.5. These types are drawn independently.
The timing of the game is as follows: (1) nature draws type vi (equal to 1 or 4 with equal probability for each player); (2) each player (privately) observes vi and simultaneously decides whether to contribute bi ≥ 0; and (3) the good is provided if and only if b1 + b2 ≥ 5; finally payoffs are realised.
The payoff of each player i is equal to vi - bi if the good is provided, and player i’s payoff is -bi if it is not provided.
(a) Draw the game in extensive form (be careful in correctly characterising information sets)
(b) Find the Nash equilibria of the game
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