Introduction
John von Neumann and Oskar Morgenstern’s game theory is an attempt to reconstruct the hidden constitution of economic actions. Instead of simplified models of "lone maximizers," the authors propose a mathematics of decision and conflict, viewing the economic system as a dense network of interactions. This article analyzes how concepts such as expected utility, imputation, and the minimax rule allow us to understand the modern market—from wage negotiations to the dominance of AI algorithms. You will learn why traditional economics fails when faced with a small number of players and how mathematics unmasks the power structures hidden beneath the cloak of the free market.
Neumann and Morgenstern: The Mathematization of Market Strategy
Von Neumann and Morgenstern shifted the foundations of economics by replacing differential calculus with set theory and combinatorics. In their framework, utility is not a measure of psychological satisfaction, but a numerical scale derived from dynamic lotteries. Although behavioral economics shows that humans are not entirely rational (e.g., they excessively discount the future), game theory provides tools to correct intuitive errors. An example is the Monty Hall paradox in corporate settings: managers often cling to flawed strategies due to sunk costs, ignoring the calculus of probability. Meanwhile, the minimax rule teaches a form of pessimistic rationality—maximizing profit in the most hostile scenario—which serves as the foundation for modern stress tests and stop-loss policies.
Coalitions and Power Mechanisms
In game theory, coalitions (labor unions, cartels) are treated as an inherent element of the system rather than a market pathology. The key is imputation—a mathematical scheme for dividing surplus that must guarantee individual rationality and coalition efficiency. The dominance relation shows that power is not linear; the cyclical nature of alliances (A dominates B, B dominates C, C dominates A) precisely reflects political realities. These models vary regionally: from clan-based Arab rentier states to the American capital market and the EU's multi-level game. Game theory thus becomes a tool for unmasking dominance structures, showing how powerful interest groups impose distributions of goods that favor themselves.
AI Algorithms and the Digital Aristocracy
The modern economy is in a state of disrupted equilibrium, where a digital aristocracy is emerging. Tech giants do not just participate in the game; they design its rules through algorithms. Artificial intelligence automates decisions using a generalized minimax approach, which raises the risk of algorithmic price fixing. The analysis of small numbers (digital oligopolies and duopolies) demonstrates that traditional pricing models are useless against the strategic anticipation of machines. In this context, the utility function must be supplemented with ethical and communicative dimensions to prevent the reduction of humans to silent parameters within the profit systems of major corporations controlling data flow.
Summary
Game theory reminds us that behind every mathematical function lie real conflicts and human values. In a world dominated by algorithms and rising inequality, understanding the mathematics of strategy becomes a vital component of civilizational literacy. The challenge remains to create institutions capable of renegotiating the rules of a game where humans sit on one side of the table and non-human intelligences on the other. Will we succeed in transforming the economy into an arena for fair dialogue, or will we remain pawns in a match whose rules are written by the few? Ultimately, the calculus of propositions must meet the calculus of conscience.
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