── ── Strategy
Nash Equilibrium
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)…
Run Nash Equilibrium on a real problem
Bring something you're actually deciding — free, in the browser.
How it works
Step 1 — Specify the game: Players · Actions per player · Payoff matrix or game tree · Information structure (full vs. private) · Sequential or simultaneous.
Step 2 — Best-response analysis: For each player, find the optimal action given each combination of others' strategies. The combination where everyone is best-responding is a Nash equilibrium.
Step 3 — Identify all equilibria: Pure-strategy (deterministic) and mixed-strategy (randomized). If multiple equilibria, identify the most plausible focal point.
When to use it
- user asks 'what will they do if we do X', 'how will competitors react to our pricing', 'how do I design this auction or mechanism', 'we keep ending up in a bad outcome even though everyone prefers better', or is analyzing a strategic situation with multiple rational counterparties (pricing, negotiation, M&A, regulation, platform launch)
When not to use it
the decision is essentially solo with no strategic counterparty; the counterparty is clearly irrational or acting on emotion rather than self-interest.
Worked example
The AI-Capex Race Among Hyperscalers (2024–2026)
Across 2024 and 2025 (and into 2026), the largest U.S. cloud-and-platform companies — Microsoft, Alphabet (Google), Amazon, and Meta — raised their capital expenditure to record levels, the bulk of it directed at AI data centers, accelerators, and power. On successive earnings calls, each firm's leadership publicly framed the risk of under-investing in AI capacity as outweighing the risk of over-investing. That is a telltale sign of a Nash equilibrium: not four firms independently arriving at the same plan, but four firms each best-responding to…
Install this skill (free, MIT)
npx skills add deciqAI/knowledge-skillsUseful? Star the repo — stars help other builders find it.
Related mental models
The rule of reciprocity — if someone gives you something, you owe them something back — recurs across virtually every documented human culture (Mauss 1925; Gouldner…
When parties repeat — or third parties observe — defection costs tomorrow's cooperation, flipping the Prisoner's Dilemma.
Most plans estimate how long each step takes and add them up — producing a multi-year sequential path that reflects a solo, resource-constrained default.
When you buy intelligence from an external AI, you pay for it twice.