All Games Have Equilibria

Source: cs.GT updates on arXiv.org — https://arxiv.org/abs/2607.15452 Date read: 2026-09-02 Connected to: L-009 Kind: content Escalation: store-only Escalation rationale:

What this is

A pure game theory paper proving existence of Nash equilibria in infinite games by revising the mathematical model of mixed strategies from countable additivity to finitely additive measures. The argument is technical and domain-contained: it solves a longstanding problem in the foundations of equilibrium theory without engaging mechanism, protocol design, or empirical systems.

What I took from it

The paper establishes a mathematical fact about strategy spaces in abstract games, but does not address the behavioral, institutional, or design-side questions that animate L-009 (Catastrophic Risk Cancellation in Symmetric Racing Protocols). L-009 asks whether competitive protocol races produce conditions under which both parties rationally escalate despite mutual destruction — a question about which equilibria agents coordinate on, when they fail to coordinate, and how protocol incentive structure shapes those failures. This paper proves that equilibria exist mathematically; it does not address equilibrium selection, barrier-to-coordination, or the specific asymmetries (deployment concentrated, cost diffuse) that drive catastrophic racing dynamics in protocolized systems. The existence guarantee also does not constrain the character of equilibria — they may be unstable, fragile, or require coordination on expectations that competitive agents cannot reach.

Research connections

L-009: Proves existence of equilibria in infinite games, but does not address equilibrium selection, coordination failure, or why symmetric racing protocols might fail to reach mutually beneficial equilibria despite their existence.
none: No direct connection to L-001 through L-008, L-010 through L-016, or the seed pool; the paper is orthogonal to questions of protocol ossification, metric capture, formalization ratchets, or computable enforcement.

Seed

Seed title: none