1) Consider a collective action game where each of the 100 members of a community can contribute to the production of a public good

1) Consider a collective action game where each of the 100 members of a community can
contribute to the production of a public good. The benefit from the public good, which all
individuals in the community receive, is equal to 3n where n is the number of community
members who contribute to the project. Individuals who contribute pay a cost of 13.
Individuals who do not contribute do not pay this cost of 13, but do suffer a cost in
terms of feeling guilty. This "guilt" cost is equal to .025n^2.
(a) Describe the equilibrium (equilibria) of this game. For each equilibrium, is it stable
or not?
(b) Draw a graph in the style of Figures 11.6-11.8 that represents this game.
(c) How many members of the community contribute in the socially optimal outcome
of this game?