Contributing to a public good. Each of n people chooses whether to contribute a

Question

Contributing to a public good. 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 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 and (iv) any outcome in which the good is not provided and she contributes. Formulate this situation as a strategic game and find its Nash equilibria.

Explanation / Answer

Case 1: If no one contributes

If player 2 contributes, good will not be provided.

If player 2 does not contribute, good will still not be provided.

It is better for player 2 to not to contribute in such scenario.

Case2 : If 2 persons have contributed

if player2 contributes, then good will be provided.

if player does not contribute, good will be provided

So it is better for player 2 to not to contribute in such scenario

Nash equilibrium is when no one contributes. Each player has an incentive to not to contribute expecting that the other will contribute.

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