Three players live in a town, and each can choose to contribute to fund a streetlamp. The value of having the streetlamp is 3 for each player, and the value of not having it is 0. The mayor asks each player to contribute either 1 or nothing. If at least two players contribute then the lamp will be erected. If one player or no players contribute then the lamp will not be erected, in which case any person who contributed will not get his money back. Required:
Write down the normal form of this game.

The Nash equilibrium of the game is ( 1, 1 )

Explanation:

Given data:

Number of players = 3

The value of having the streetlamp = 3 for each player

value of not having the street lamp = 0

If at least 2 players contribute ; Lamp will be erected

If 1 or no player contribute then the lamp will not be erected

The normal form of this game can be written as

attached below is a detailed solution

The best response function from both conditions ( s= i , s = i ) shows that

The Nash equilibrium of the game is ( 1, 1 )