Recall that in our common pool resource game, groups of n (typically 3) players share a resource where

the size, f(fish), is not known. Each group member j attempts to catch c_j units of fish.

Decisions are made independently and anonymously. If (c₁ + c₂ + c₃ < f), there is enough fish and each

group member receives profit equal to their attempted catch; Otherwise the resource is destroyed and all

group members get nothing. For all group sizes the number of fish is a random variable drawn from a

uniform distribution over support [0, 20n]. Expected profits for individual j are equal to their attempted

catch c_j times the probability that there are enough sh P(c₁+ c₂ + c₃ < f)

E[profit_j ] = c_jP(c₁ + c₂ + c₃ < f) = c_j*(20n - c₁ - c₂ - c₃)/20n

(a) What is the equilibrium prediction for catch size for a group of size 3?

(b)what is the socially optimal total catch size?

(c)partition the data by variable "rematching" and calculate the average "choice" (catch size)