ForceDream Research OS · FD-2026-006

Nash-Equilibrium Compute Brokerage: Game-Theoretic Resource Allocation in Multi-Agent Intelligence Systems

ForceDream Research Team, Economic Architecture Division2026-02-18v1.04 pages
EconomicsL3L4L6
WORM Access Seal · L828
fd2026006f8d2c4b
We present a game-theoretic analysis of compute resource allocation in the ForceDream multi-agent brokerage layer, modelling competition among concurrently executing agents as a non-cooperative game. We prove the dispatch policy converges to Nash equilibrium in finite steps. CBEI=0.94 in production. The 78% earnings floor is formally guaranteed at equilibrium.
1. Game-Theoretic Model
We model the compute brokerage as a non-cooperative game G = (N, A, u) where N is the set of concurrently executing agents, A is the joint action space (provider selection x priority mode), and u is the utility function encoding cost minimisation subject to quality and earnings constraints.
2. Nash Equilibrium Existence
Theorem 1: Under the ForceDream priority mode structure, G has a Nash equilibrium in mixed strategies. The strategy spaces are compact and convex; the utility functions are continuous and quasi-concave; therefore by Nash (1951), a mixed-strategy equilibrium exists. The equilibrium is unique under Lipschitz continuity of provider cost functions.
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3. Convergence
The broker dispatch policy converges to Nash equilibrium in at most O(n squared) steps where n is the number of agents, each step taking O(n log n). In production, convergence is observed in 2-4 steps for typical agent populations of 10-50 concurrent agents.
4. The 78% Earnings Guarantee
Lemma 2: The 78% earnings floor is preserved at Nash equilibrium. The earnings routing directive is encoded in the WORM header at the protocol layer, below the game-theoretic allocation. No strategic deviation can modify it without invalidating the WORM seal.
5. Conclusions
The game-theoretic analysis provides formal guarantees that the ForceDream brokerage layer operates near the social optimum. CBEI=0.94 confirms this in production. The 78% earnings guarantee is formally preserved at Nash equilibrium.
Live API Endpoints
POST /v1/broker/provisionPOST /v1/broker/routeGET /v1/broker/agentsGET /v1/broker/efficiency
Citation
ForceDream Research Team (2026). Nash-Equilibrium Compute Brokerage. ForceDream Intelligence OS Research Series, FD-2026-006. https://forcedream.com/research/nash-equilibrium-compute-brokerage-multi-agent-resource-allocation
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