The Prisoner's Dilemma is a classic example of game theory that demonstrates why two rational individuals might not cooperate, even if it appears that it is in their best interest to do so. Here’s an in-depth look at the Prisoner's Dilemma and what it can teach us:
Scenario
Two individuals, A and B, are
arrested for a crime. The police do not have enough evidence to convict them of
the principal charge but can convict them of a lesser charge. The prisoners are
separated and cannot communicate with each other. The police offer each
prisoner a deal:
- If A betrays B (defects) and B remains
silent (cooperates), A will be set free, and B will get a 10-year sentence
(and vice versa).
- If both A and B betray each other, they
will each get a 5-year sentence.
- If both A and B remain silent, they will
each get a 1-year sentence on the lesser charge.
Payoff Matrix
The following payoff matrix can
represent the situation:
|
B Cooperates |
B Defects |
|
|
A Cooperates |
(-1, -1) |
(-10, 0) |
|
A Defects |
(0, -10) |
(-5, -5) |
There are many versions of the
current scenario, but all have the same results (link to
another scenario).
The predicted outcome of the game (Nash
Equilibrium) is when both prisoners choose to defect, resulting in a (-5,
-5) outcome. Namely, five years in prison. This is a stable state where neither
prisoner can improve their situation by changing their strategy unilaterally.
On the other hand, the (Pareto)
optimal outcome is when both prisoners cooperate (-1, -1), which is better for
both compared to the (-5, -5) outcome. However, reaching this outcome is
challenging due to the lack of trust and inability to communicate.
The dilemma highlights the importance of trust
in cooperative scenarios. If prisoners could trust each other, they would both
remain silent, achieving a better outcome. In real-world situations, building
trust is essential for cooperation.
It is important to notice that if an
equivalent interaction to the Prisoner's Dilemma repeats, the players might
cooperate.
Merrill Flood and Melvin Dresher first raised the prisoner dilemma issue in the 1950s (for example, one of the articles in the field (link)). Since then, many works studied this issue in many variations. The main question is, what can a simple person study from it?
In a sense, a large proportion of
social interactions can be thought of in terms of the Prisoner's Dilemma, which
pits our self‐ish interests against the motivation to cooperate with and help
others. A simple rule of the Prisoner's Dilemma is this: When we play against
someone else in an iterated manner, expecting to have further interactions with
that same person, we tend to be nicer than when we are playing against someone
in a one-off capacity.
Interacting with strangers, which is
now commonplace in some of the human experience, can be seen as a form of Prisoner's
Dilemma. In modern conditions, we constantly find ourselves in situations where
social interactions are between strangers who have no expectations of
interacting with one another again. Perhaps this simple insight can help us
create environments more conducive to helping, cooperation, and love.
The moral of the Prisoner’s Dilemma
is that self-interest can sometimes lead to an optimal outcome beyond
everyone's reach. And in that case, everybody loses.
The
pictures in this post were taken from Unsplash.
