A Nash equilibrium is a set of strategies where no player can improve their payoff by changing strategy alone, given everyone else keeps their strategy unchanged.
Model Logic
For players (i = 1,\dots,n) with strategies (s_i), a profile (s^*) is Nash if:
[ u_i(s_i^, s_{-i}^) \ge u_i(s_i, s_{-i}^*) \quad \text{for all } s_i ]
Each strategy is a best response to the others.
Why It Matters In Economics
Nash equilibrium is the baseline concept for pricing rivalry, auction bidding, entry deterrence, bargaining, and policy games. It captures strategic interdependence, which is central in oligopoly and regulation.
Practical Caveats
- Multiple equilibria are common.
- Some equilibria are inefficient.
- Equilibrium selection can depend on institutions, expectations, or repeated interaction.
So Nash equilibrium is a powerful organizing tool, but not always a unique prediction.