Common Pool Resource Game.

Common Pool Resource Game on 2022-03-11 1:30 pm:

In this experiment there are 20 independent replications/rounds of the same one shot game.
You have 4 minutes to make your first round choice starting at 1:30 pm.
The second round starts at 1:35 pm, and you have 2 minutes to complete each subsequent round.
If you fall behind you will be removed from the experiment: please try to keep up!

Each round you are put into a new group of 3 people.
In each round your task is to choose how effort to put into fishing \(e_i\).
If the stock of fish \(f\) exceeds the total effort \(f>e_1+e_2+e_3\) then every unit of effort results in one fish caught.
However, the stock of fish is unknown: \(f\) equally likely to be any real number between 0 and 60: \(f∼U[0,60]\)
If the stock of fish is lower than the total effort \(f \leq e_1+e_2+e_3\) the resource is destroyed: all players catch zero fish.
The tradeoff: more effort more fish (if there are enough fish) vs. more effort lower probability there are enough fish.

The expected profit function for player 1 is:

\(E[\pi_1]=\left[\alpha e_1+\frac{1-\alpha}{3}(e_1+e_2+e_3)\right]\left(\frac{60-e_1-e_2-e_3}{60}\right)-\frac{e_1}{3}\)

Inside the first [square] brackets is the amount of fish you receive if there are enough fish.
Inside the second (round) brackets is the probability there are enough fish.
The last term is the cost of effort.

There are going to be 3 treatments that vary by the parameter \(\alpha\).
You will be told the value of \(\alpha\) for your treatment once you start the experiment.