nash-equilibrium
Installation
SKILL.md
Nash Equilibrium
Overview
A Nash equilibrium is a stable point in multi-player interaction: a combination of strategies where no player can improve their payoff by unilaterally changing their own strategy, given others hold theirs fixed. Key properties: (1) best-response logic — the equilibrium is a fixed point of mutual best-responses; (2) equilibria can be Pareto-suboptimal (prisoner's dilemma); (3) multiple equilibria are common; (4) equilibrium does not predict the path to get there.
Composes with prisoners-dilemma, repeated-games-reputation, signaling-games, pricing-strategy, and batna-zopa.
When to Use
- Designing pricing in a competitive market with rational rivals
- Negotiating with a sophisticated counterparty; modeling regulatory or legislative outcomes
- Evaluating M&A or partnership decisions where multiple parties react strategically
- Designing auctions, marketplaces, or platform mechanisms
- Assessing an investment or capacity arms race where rivals match each other (e.g., AI capex spending, AI-native competition, matching AI adoption to keep position)
Not when: the situation is essentially solo; the counterparty is not rational; modeling cost exceeds the decision's value.