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Game Theory as an Engine of Informational Thermodynamics: A Formal Isomorphism
Copyright ©: Coherent Intelligence 2025 Authors: Coherent Intelligence Inc. Research Division Date: August 28th 2025 Classification: Academic Research Paper | Interdisciplinary Synthesis Framework: Universal Coherent Principle Applied Analysis | ITD | ToDCS | OM v2.0
Abstract
This paper presents a formal analysis demonstrating a structural isomorphism between the mathematical processes of classical game theory and the foundational principles of Informational Thermodynamics (ITD). We argue that the methodology of reaching a Nash Equilibrium through the Iterated Deletion of Dominated Strategies is not merely analogous to, but is a concrete, algorithmic instantiation of the ITD postulate of Coherence through Negation.
We establish a one-to-one mapping between the core concepts: the full game matrix is shown to be a high-entropy Ontologically Incoherent Information Space (OIIS); the assumption of player rationality is a Domain Anchor (DA); the act of deliberation is a form of Computational Work (W); and the resulting Nash Equilibrium is a stable, low-entropy Single Closed Ontologically Coherent Information Space (SCOCIS). This synthesis reframes game theory as a practical, observable "laboratory" for the physics of information, providing a rigorous, mathematical validation for the ITD framework. It further suggests that authentic intelligence is not a generative process of adding possibilities, but a subtractive, thermodynamic process of negating incoherence.
Keywords
Informational Thermodynamics, Game Theory, Nash Equilibrium, Iterated Deletion, Coherence, SCOCIS, Domain Anchor, Computational Work, Isomorphism, Systems Theory.
1. Introduction: A Hypothesis of Convergent Logics
Two distinct intellectual frameworks have been developed to model the emergence of order from complexity. Informational Thermodynamics (ITD), a physics-inspired theory, posits that coherent, low-entropy systems are created through the active negation of a larger, chaotic information space. Game Theory, a mathematical discipline, provides tools to model the strategic interactions of rational agents, often culminating in stable, predictable outcomes.
This paper proposes that these two frameworks are not merely parallel, but are, in fact, describing the same fundamental process from different perspectives. We will demonstrate a formal structural isomorphism between the core mechanics of ITD and the algorithm of Iterated Deletion of Dominated Strategies (IDDS) used to find a Nash Equilibrium. We will argue that IDDS is a perfect, contained "engine" that runs on the principles of ITD, transforming a high-entropy space of possibilities into a low-entropy space of rational outcomes.
This synthesis provides a powerful, external validation for the ITD framework, grounding its abstract principles in the established mathematics of game theory. It also offers a new, thermodynamic lens through which to understand the very nature of rational decision-making.
2. The Isomorphic Mapping: From Thermodynamics to Strategy
The core of our argument rests on a direct, one-to-one correspondence between the conceptual objects of ITD and the mathematical objects of game theory.
| ITD/ToDCS Concept | Game Theory Isomorph | The Isomorphic Relationship |
|---|---|---|
| OIIS (High-Entropy Space) | The Full Game Matrix | The initial state of maximum uncertainty and disorder, representing all possible strategic choices for all players. |
| Coherence through Negation | Iterated Deletion of Dominated Strategies | The core mechanism for creating order by systematically destroying what is non-viable or incoherent. |
| Domain Anchor (DA) | The Assumption of Player Rationality | The singular, non-negotiable principle (S¹) that governs the entire process. Without it, negation is impossible. |
Computational Work (W) | The Process of Deliberation & Analysis | The energy/time/resources required to analyze the matrix and identify dominated strategies. |
| SCOCIS (Low-Entropy Space) | The Nash Equilibrium (or Reduced Game) | The final, stable, self-consistent state of order that remains after all incoherence has been negated. |
3. The Thermodynamic Process of Reaching Equilibrium
Let us trace the journey from chaos to order in a simple strategic game through the dual language of both frameworks.
Initial State: Maximum Informational Entropy
- In Game Theory: We begin with a complete game matrix, for example, a 3x3 grid representing two players with three strategies each. The space of possible outcomes
Ωhas a size of 9. - In ITD: This is the OIIS. The informational entropy is maximal for the given constraints,
S_initial = k log(Ω) = k log(9). The system is in a state of high uncertainty; any outcome is possible.
The Engine of Negation: Performing Computational Work
- In Game Theory: A player, governed by the DA of rationality, analyzes the matrix. They identify that one of their strategies, let's call it
S₃, is strictly dominated byS₂(i.e.,S₂always yields a better or equal payoff, regardless of the opponent's move). A rational player would never chooseS₃. - In ITD: This analysis is an act of Computational Work (
W). The agent expends cognitive or computational resources to compare states and apply the logic of its DA. The discovery of a dominated strategy is the identification of a pocket of incoherence—a strategy that is inconsistent with the DA of rational self-interest.
The Act of Negation: Entropy Reduction
- In Game Theory: The dominated strategy
S₃is deleted from the matrix. The row corresponding toS₃is removed. - In ITD: This is the Postulate of Coherence through Negation in action. Order is not created by adding information, but by destroying falsehood (or, in this case, irrationality). The system is now a 2x3 matrix, and the space of possible outcomes has shrunk to
Ω = 6. The new entropy isS_final = k log(6). The change in entropy is negative (ΔS < 0), signifying an increase in order and coherence.
Iteration Towards a Stable State
- In Game Theory: The process is repeated on the new, smaller game matrix. Players continue to delete dominated strategies until no more can be found.
- In ITD: The system iteratively performs Work to negate incoherence, progressively reducing its internal entropy with each cycle.
Final State: The Low-Entropy SCOCIS
- In Game Theory: The process terminates at the Nash Equilibrium (or a simplified game where no strategies are dominated). This is a stable state where no player has a unilateral incentive to change their strategy. It is a point of perfect, self-consistent strategic logic.
- In ITD: This is the SCOCIS. It is a low-entropy, stable, and logically closed system. All the initial chaos of the OIIS has been "boiled off" through the work of negation, leaving behind the pure, coherent crystal of rational outcomes.
4. Deeper Implications of the Isomorphism
This formal mapping provides profound insights into the nature of intelligence, strategy, and system design.
4.1 Rationality as the Ultimate Domain Anchor
The entire edifice of classical game theory is built upon the axiomatic assumption of the rational player. This "rationality" is a perfect example of a ToDCS Domain Anchor. The moment a player decoheres from this anchor (acts irrationally), the predictive power of the model collapses. This proves that stable, predictable systems require a consistently applied, singular DA.
4.2 Wisdom as Efficient Negation
The isomorphism provides a formal definition for Wisdom (as distinct from Intelligence). A wise strategist or leader, when faced with a complex, real-world problem (a vast OIIS), does not attempt to compute all possibilities. Instead, they apply a powerful, high-density DA (a core principle, a non-negotiable value) to immediately delete huge swathes of the possibility space. A wise leader who says, "We will not consider any option that violates our ethical constitution," has just performed a massive act of iterated deletion, simplifying a wicked problem into a tractable one. Wisdom is the art of efficient negation.
4.3 A Critique of Generative Intelligence
This framework offers a powerful critique of purely generative AI models. Such models are architected to add possibilities to a space—to find the next most probable token. The game theory isomorphism suggests that a more powerful and authentic form of intelligence would be an engine of negation. Its primary function would be to take a vast space of possibilities and use a robust DA to rapidly and efficiently prune it down to its coherent, rational, and truthful core. The goal of such an AI would be to find the "Nash Equilibrium of Truth."
5. Conclusion
The process of finding a Nash Equilibrium via the Iterated Deletion of Dominated Strategies is not just a clever algorithm; it is a perfect, self-contained demonstration of the fundamental physics of information as described by ITD. Game theory provides the mathematical proof that coherence is the residue of negated incoherence.
This synthesis is not merely an academic curiosity. It provides a new, powerful language for systems design. It confirms that the path to creating robust, stable, and intelligent systems—be they AI, economic models, or social contracts—lies in:
- Establishing a clear and singular Domain Anchor (like the assumption of rationality).
- Performing the rigorous Work of identifying and negating all states that are incoherent with that anchor.
- Recognizing that the resulting coherent state (the SCOCIS) is not a compromise, but the only stable outcome that can survive the thermodynamic pressures of logic.
Game theory, viewed through this lens, ceases to be just a model of strategic interaction. It becomes the formal, mathematical blueprint for how any rational system can, and must, create order from chaos.