In this lesson, we are going to learn about a game known as "Tragedy of the
Commons." The story if this game is that there are two fishermen that are fishing
a pond. They can either choose to fish or to over fish. Now if the both fish, they
get a pay off of three. And the reason is that fishing a normal amount is healthy
for the pond, and the pond can regenerate year after year. However, if they both
over fish, the ecosystem of the pond is harmed, and future crops, or future fish
production will be down. This will be bad for the fishermen, so they both earn a
reward of two. If one of the fishermen fishes, and the other one over fishes,
while the pond is still okay, but the person that over fished gets a much higher
pay off from the one who just fishes normally, because, in essence, he steals
all the other players fish. Now, if you've been paying attention, you'll
notice that this game is exactly the same as the prisoner's dilemma game, in which
two two, or over fish over fish is the unique pure strategy Nash equilibrium
What we're gonna see in this lesson, is how a regulator or government body can
improve the well fare, or improve the payoffs of the players in equilibrium by
subtracting payoffs. What do I mean by this? Well, let's do this through an
example. Suppose that there is a two... you can call it dollar, but I'll just call
it "two unit find" for over fishing.
Okay, so now this payoff matrix changes.
So when they both over fish, okay they get their payoff of two
but because they have pay the fine they each get payoffs of zero.
Similarly, when one person fishes and the other over fishes, the one that over
fishes, gets penalized too. Of course when they both fish regularly, nobody gets
fined. So we wanna see , can the regulator can the government body improve the
total utility of the players, by subtracting from some of the actions?
Well, to answer that question, all we have to ask now, is " Fish Fish" a Nash
equilibrium? So, let's look. Assuming player one plays fish, and player two
is playing fish, does player two have an incentive to over fish? Well, no he
doesn't, because if he over fishes, he gets two instead of three. Yes he caught
more fish, but he had to pay the two dollar fine to the regulator or the
government. Now consider player one. Assuming player two's strategy is fixed
at fish, does player one have an incentive to change his strategy from
fish, to over fish? Well, if he does that, he again gets two instead of three.
And since he prefers three over two, player one does not have an incentive
to over fish. Therefore, in the fishing game, in the tragedy of the commons,
what we see, is that a government regulator, or a regulating body can come
in and simply fine players for their actions, reducing their payoffs,
but the equilibrium outcome is an increase in payoffs for all players.