Each of n people chooses whether to contribute a fixed amount toward the provision of a public good. The good is provided if and only if at least k people contribute, where 2 ≤ k ≤ n; if it is not provided, contributions are not refunded. Each person ranks outcomes from best to worst as follows: (i) any outcome in which the good is provided and she does not contribute,
(ii) any outcome in which the good is provided and she contributes,
(iii) any outcome in which the good is not provided and she does not contribute,
(iv) any outcome in which the good is not provided and she contributes.
1. Formulate this situation as a strategic game and find its Nash equilibria.
2. Is there a Nash equilibrium in which more than k people contribute? One in which k people contribute? One in which fewer than k people contribute?
3. Provide a definition of a Pareto optimal strategy profile. Which pure strategy equi libria of this game are Pareto optimal? Briefly explain.