Strategic Superposition and Replicator Dynamics: Quantum Collapses in Decision Processes

Area of Science:

• Game Theory
• Quantum Mechanics
• Decision Science

Background:

• Classical evolutionary game theory assumes actors have predefined strategies, failing to account for real-world decision-making complexities like interference and framing effects.
• Human and organizational choices often exhibit behaviors not explained by classical probability, indicating a need for a more nuanced theoretical framework.

Purpose of the Study:

• To propose a novel framework for evolutionary game theory using quantum mechanics to model undecided economic actors.
• To demonstrate how quantum principles can explain strategy selection and market dynamics beyond classical limitations.

Main Methods:

• Modeling economic actors as strategic superpositions in a Hilbert space before interaction.
• Utilizing a density operator to describe populations, with interactions causing state collapse via Born-rule probabilities.
• Developing a strategic master equation incorporating coherent deliberation, decoherence, and replicator selection.

Main Results:

• A square-root representation unifies quantum normalization and evolutionary selection.
• The classical replicator equation is recovered as a strong-decoherence limit with an error bound.
• Quantum interference leads to basis-dependent strategy realization, unachievable with classical mixtures.

Conclusions:

• The proposed quantum framework offers a more comprehensive model for evolutionary dynamics, encompassing classical game theory as a limiting case.
• This approach formalizes constitutive self-opacity and links bounded rationality to quantum interference.
• It provides a new perspective on understanding complex decision-making in economic and social systems.