There is a collection of 5 NGOs operating in the health sector of a country. Eac

Question

There is a collection of 5 NGOs operating in the health sector of a country. Each NGO can choose either to invest in a large-scale and collaborative project with other NGOs, or invest in an independent, small-scale, project where the NGO does not have to collaborate with other NGOs. A small-scale project is always successful and gives the NGO a payoff of S. For the large-scale project to succeed, at least 3 NGOs have to invest in it. If the large-scale project is successful, the value that it generates is L, which is evenly divided between the collaborating NGOs. Assume that L/5 > S > 0. If the large-scale project fails, each collaborating NGO gets 0.

a) Describe the normal form of this game

b) Find the BR function for an NGO.

c) Find all NE (in pure strategies).

Explanation / Answer

a) The game has 5 players deciding one of the two choices/strategy sets: Investment in large scale or investment in small scale.

b) Small project is always successful so that it gives a payoff of S. A large scale investment project is successful only when m NGOs are collaborated so that the payoff is L/5 which is greater than S. But if it fails, it gives a zero payoff. The same decision is to be faced by all the NGOs so that the game is symmetric.

If all the 5 - 1 NGOs are chosing large investment, then the best reply function for a given NGO is to invest in large scale project. Similarly, If all the 5 - 1 NGOs are chosing small investment, then the best reply function for a given NGO is to invest in small scale project.

c)

NE in pure strategies is that all the NGOs are investing in small scale project.

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