POLS2130 · Week 2

Normal-Form Games & Nash Equilibrium

Build a 2×2 payoff matrix, identify players, strategies, and strategy profiles — then find the Nash equilibrium step by step using best replies.

Key Concepts

Players

The decision-makers. Here: Individual A (row) and Individual B (column).

Strategies

Actions available to each player: Refrain or Steal.

Strategy Profile

An ordered pair — one strategy per player, e.g. (Steal, Refrain).

Payoffs

The utility each player receives for a given strategy profile. A's payoff is listed first.

Best Reply

The strategy giving the highest payoff given the other player's choice. Marked with ★A or ★B.

Nash Equilibrium

A profile where both players are playing a best reply. No one wants to deviate.

Build the Game

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
Individual B
RefrainSteal
Individual A Refrain
Steal
Solve step by step:

Source
Hindmoor, A., & Taylor, B. (2015). Rational Choice (2nd ed.). Palgrave Macmillan. Chapter 2: James M. Buchanan and Constitutional Political Economy, pp. 20–47.

Quiz: Test Your Understanding