POLS2130 · Week 2

Pareto Efficiency & Nash Equilibrium

Evaluate Pareto efficiency, check the Nash equilibrium, and explore when civil society is preferred to the state of nature.

Key Concepts

Pareto Efficiency

An outcome where no one can be made better off without making someone else worse off.

Pareto Improvement

A move to a new outcome that makes at least one player better off and no one worse off.

Pareto Dominated

An outcome is Pareto dominated if a Pareto improvement from it exists — someone could gain and no one would lose.

The Big Question

Is the Nash equilibrium always Pareto efficient? Not necessarily. The Prisoner's Dilemma is the classic counter-example.

Choose a scenario

Individual A's payoffs

A steals, B refrains:4
Both refrain:3
Both steal:2
A refrains, B steals:1

Individual B's payoffs

B steals, A refrains:4
Both refrain:3
Both steal:2
A steals, B refrains:1
Nash Equilibrium
Pareto Efficient
Inefficient NE
Individual B
RefrainSteal
Individual ARefrain
Steal

Source
Clark, W. R., Golder, M., & Golder, S. N. (2013). Principles of Comparative Politics (2nd ed.). CQ Press. Chapter 4: The Origins of the Modern State (Civil Society and the Social Contract; The Predatory View of the State), pp. 109–117.

Choosing between the State of Nature and Civil Society

The sovereign imposes a punishment (p) on anyone who steals, making cooperation rational. But the predatory view warns: this sovereign also charges a tax (t) and holds a monopoly on violence. Civil society is only preferred when punishment is high enough to enforce cooperation and the tax is low enough that citizens are still better off than in the state of nature.

Punishment (p):2
Tax (t):0.5
State of Nature
B
RefrainSteal
ARefrain
Steal
Civil Society
B
RefrainSteal
ARefrain
Steal

Source
Clark, W. R., Golder, M., & Golder, S. N. (2013). Principles of Comparative Politics (2nd ed.). CQ Press. Chapter 4: The Origins of the Modern State (Civil Society and the Social Contract; The Predatory View of the State), pp. 109–117.

Quiz: Test Your Understanding