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Nash Equilibrium

Activate when: 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 e... Skill: Nash Equilibrium Owner: deciqai Summary: Activate when: 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 e... Tags: latest:1.0.5 Version history: v1.0.5 | 2026-07-16T18:08:07.042Z | user Description tail link + agents machine-readable metadata line (deciqai.com/s/nash-equilibrium.json) v1.0.4 | 2026-07-09T11:19:05.292Z

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Downloads

1.1k

Updated

Oct 11, 2026

Version

1.0.5

Source

CLAWHUB

About

What it does, and when to use it.

Capability contract not published. No trust telemetry is available yet. 1.1K downloads reported by the source. Last updated 10/11/2026.

Avoid when

Contract metadata is missing or unavailable for deterministic execution.

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Public facts

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Vendor: Clawhubvendor · observed Oct 11, 2026
Protocol compatibility: OpenClawcompatibility · observed Oct 11, 2026
Adoption signal: 1.1K downloadsadoption · observed Oct 11, 2026
Latest release: 1.0.5release · observed Jul 16, 2026
Handshake status: UNKNOWNsecurity

Install and run

Setup complexity: low.

clawhub skill install s17a4mqcnk515kvaca5ze55d0x88pfpx:nash-equilibrium

Setup complexity is classified as HIGH. You must provision dedicated cloud infrastructure or an isolated VM. Do not run this directly on your local workstation.
Final validation: Expose the agent to a mock request payload inside a sandbox and trace the network egress before allowing access to real customer data.

Contract: missing

curl -s "https://www.xpersona.co/api/v1/agents/clawhub-deciqai-nash-equilibrium/snapshot"

Documentation

CLAWHUB

143,352 characters of source documentation, loaded on request.

Extracted files

5 files captured from the source.

SKILL.md

---
name: nash-equilibrium
description: "Activate when: 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). Do NOT activate when: the decision is essentially solo with no strategic counterparty; the counterparty is clearly irrational or acting on emotion rather than self-interest. More: deciqai.com/c/nash-equilibrium"
---

# 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.

## Coaching Novices (Adaptive Front Door)

- **Engine mode:** user has a concrete case → run The Process directly.
- **Coach mode:** user is unfamiliar → guide step by step.

In Coach mode, respond one step at a time. Each [WAIT] is a hard stop — output only that step's question, then stop.

1. One-line what-it-is: find the point in a multi-player situation where no one has incentive to deviate from their strategy.
2. Check fit: no rational counterparty? Nash adds less value than other frameworks.
3. Elicit their real case: who are the players, what can each do, what does each gain or lose?
> **[WAIT — do not advance until user responds]**
4. Run The Process one step at a time with their input.
> **[WAIT — do not advance until user responds]**
5. Close by naming the equilibrium and recommended action; if equilibrium is bad, name a redesign option.
> **[WAIT — do not advance until user responds]**

## The Process

**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, fin

_meta.json

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  "ownerId": "kn754b8sk22s8c6gjxt02bftbn88q7ye",
  "slug": "nash-equilibrium",
  "version": "1.0.5",
  "publishedAt": 1784225287042
}

references/sources.md

# Sources — nash-equilibrium

> *Primary sources for the [nash-equilibrium](../SKILL.md) skill.*

- Nash, J. F. (1950). "Equilibrium Points in N-Person Games." *Proceedings of the National Academy of Sciences*, 36(1), 48-49. The foundational two-page proof.
- Nash, J. F. (1951). "Non-Cooperative Games." *Annals of Mathematics*, 54(2), 286-295. The extended treatment.
- von Neumann, J. & Morgenstern, O. (1944). *Theory of Games and Economic Behavior.* Princeton University Press. The precursor; covers zero-sum games.
- Cournot, A. A. (1838). *Recherches sur les principes mathématiques de la théorie des richesses.* Paris: Hachette. The duopoly precursor.
- Milgrom, P. (2004). *Putting Auction Theory to Work.* Cambridge University Press. ISBN 978-0521536729. The FCC auction case study.
- Camerer, C. F. (2003). *Behavioral Game Theory: Experiments in Strategic Interaction.* Princeton University Press. ISBN 978-0691090399. Empirical deviations from Nash predictions.
- Palacios-Huerta, I. (2003). "Professionals Play Minimax." *Review of Economic Studies*, 70(2), 395-415. Field test of mixed-strategy equilibrium on professional penalty kicks.
- Roth, A. E. (2002). "The Economist as Engineer." *Econometrica*, 70(4), 1341-1378. Mechanism-design applications.
- Schelling, T. C. (1960). *The Strategy of Conflict.* Harvard University Press. ISBN 978-0674840317. Strategic applications to security.
- Tirole, J. (1988). *The Theory of Industrial Organization.* MIT Press. ISBN 978-0262200714. Industrial-organization applications.
- Microsoft, Alphabet, Amazon, and Meta (2024–2026). Quarterly earnings calls and investor disclosures on AI-related capital expenditure guidance. Contemporary example of investment competition sustaining a high-capex equilibrium among rational rivals.
- Investor commentary and reporting on the hyperscaler AI-capex build-out (2024–2026), e.g., quarterly earnings coverage in the financial press. Documents the "risk of under-investing exceeds risk of over-investing" framing that signals best-response spending.

examples/ai-capex-race-among-hyperscalers-2024-2026.md

# Method in Action: The AI-Capex Race Among Hyperscalers (2024–2026)

> *Example for the [nash-equilibrium](../SKILL.md) skill.*

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 what the others are doing. This example runs the case through the skill's six-step Process.

**Step 1 — Specify the game.** *Players:* the major hyperscalers (Microsoft, Alphabet, Amazon, Meta), plus adjacent capacity buyers. *Actions per player:* along a spectrum from "spend aggressively on AI compute" to "hold capex flat and harvest cash." *Payoffs:* market position in AI-driven cloud and consumer products, which depends on relative capacity, not just absolute spend. *Information:* largely public — capex guidance is disclosed on quarterly earnings calls, so each player observes rivals' commitments with a short lag. *Timing:* effectively simultaneous and repeated, quarter after quarter, since all players revise guidance on a similar cadence.

**Step 2 — Best-response analysis.** Consider any single firm's choice given the others are spending heavily. If it also spends, it holds its position and shares in whatever AI demand materializes. If it unilaterally pulls back, it frees cash and lifts near-term margins — but it risks ceding compute capacity, model quality, and enterprise-cloud share to rivals who kept building, in a market where capacity is a binding constraint and lead times for chips and power are long. Given rivals spending, the best response is to keep spending. The same logic holds for each player. The mutual-best-response fixed point is "everyone spends heavily."

**Step 3 — Identify all equilibria.** The high-capex profile is a pure-strategy Nash equilibrium: no firm can improve its position by unilaterally cutting while the others build. A low-capex "everyone restrains" profile would be more profitable collectively in the short run, but it is *not* an equilibrium — from it, any single firm gains by defecting and out-building the restrained rivals to capture position, so it unravels. This is the structural signature of a prisoner's-dilemma-type game: the cooperative outcome is not self-enforcing. The most plausible focal point is therefore the high-spend equilibrium, which is what the public capex trajectory through this period reflects.

**Step 4 — Evaluate quality.** The equilibrium is not Pareto-optimal for the firms as a group: collectively they would earn higher near-term free cash flow spending less, if all could credibly commit to restraint. The game st

examples/nash-1950-51-and-the-fcc-auctions-1994.md

# Method in Action: Nash 1950-51 and the FCC Auctions 1994

> *Example for the [nash-equilibrium](../SKILL.md) skill.*

**John Forbes Nash Jr.** (1928-2015) wrote his doctoral dissertation at Princeton in 1950, at age 21. The thesis was 28 pages. From it came the 1950 PNAS paper (two pages) and the 1951 *Annals of Mathematics* paper (10 pages). For these two papers — establishing the equilibrium concept that bears his name — Nash received the 1994 Nobel Memorial Prize in Economic Sciences (shared with Reinhard Selten and John Harsanyi for the broader development of non-cooperative game theory).

The theorem's mathematical proof used the Kakutani fixed-point theorem (Nash 1951). The proof's essence: in the space of mixed strategies, the best-response correspondence is upper-hemicontinuous and the strategy space is compact and convex; therefore by Kakutani, there exists a fixed point — i.e., a strategy combination where every player is best-responding. That fixed point is the equilibrium.

What made Nash's contribution revolutionary was not the equilibrium concept itself (which had been informally articulated by Cournot in 1838 for the duopoly case) but the *generality* — the proof that *every* finite n-person game has at least one equilibrium. Before Nash, game theory could analyze only special cases. After Nash, game theory could analyze any finite strategic interaction. This is why Nash's two short papers are considered among the most important in 20th-century mathematics and economics.

The framework took decades to translate into operational policy. The breakthrough moment was the **1994 FCC spectrum auction**.

The U.S. Federal Communications Commission had historically allocated radio spectrum via "comparative hearings" (essentially bureaucratic beauty contests) and lotteries. Both methods had clear flaws: hearings were corruptible and slow; lotteries gave spectrum to entities who promptly resold it for windfall profits to actual operators. By the early 1990s, the value of spectrum was understood to be enormous and growing (especially for cellular telephony), and pressure was rising for a better mechanism.

Paul Milgrom and Robert Wilson at Stanford were retained as consultants to design the new auction. Their core insight: spectrum auctions are complex strategic games with multiple bidders who hold private valuations for combinations of licenses. The auction rules must be designed so that bidders' Nash-equilibrium strategies — what each bidder rationally does given what every other bidder rationally does — produce efficient allocations (the spectrum ends up with the operators who value it most) and reasonable revenue.

Milgrom and Wilson designed the **simultaneous multiple-round (SMR) auction**: licenses are auctioned simultaneously, in multiple rounds with rising bids, until no bidder is willing to raise any bid. This rule produces a Nash equilibrium in which bidders coordinate on combinations of licenses they want, while preventing bidde

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