We have briefly touched upon the topic of Pareto efficiency in one of the earlier posts. Let’s understand the term a bit deeper. Start with the definition: An outcome is Pareto efficient if there is no other outcome that makes at least one person better off without leaving anyone worse off. Any move away from the efficient position will harm someone, or it is not efficient if I can make someone better off and not hurt somebody else.
Two chocolate lovers
Andy and Becky love chocolate. There were ten chocolates, and Andy got four and Becky six. Are they in a Pareto equilibirum? Test the situation by taking one chocolate away from Andy or Becky. Will it make someone unhappy? Since the answer is yes, They are in Pareto efficient state.
Prisoner’s dilemma
Time to revisit the Prisoner’s dilemma. The payoff matrix is of the following form.
| Prisoner B | |||
| Cooperate | Betray | ||
| Prisoner A | Cooperate | (3, 3) | (1, 4) |
| Betray | (4, 1) | (2, 2) |
Let’s look at each of the four outcomes. Remember, we already know that (betray, betray) is the Nash equilibrium or the rationally expected outcome.
- Cooperate-Cooperate (3, 3): Try to move in any direction; one of them will be worse off. For example, move to the right: player B gets richer (3 to 4), whereas A becomes poorer (3 to 1). Therefore, the state is Pareto efficient.
- Cooperate-Betray (1, 4): Try to go to any other quadrant; B falls short. So their current state is Pareto efficient.
- Betray-Cooperate (4, 1): This time, player A gets the stick. The existing condition is Pareto efficient.
- Betray-Betray (2,2): Move to the Cooperate-Cooperate quadrant, and both players will be better off (3 and 3), suggesting their state is not Pareto efficient.
In summary
The only outcome in the prisoner’s dilemma that is not Pareto efficient is the one that is the rational choice or the Nash equilibrium.
