Quantum Game Theory — III

IHSIEN CHOU

This paper explores the quantum many-worlds interpretation (MWI) and its implications beyond fundamental physics, extending to decision theory, game theory, and economics. Starting from the foundational principles of MWI, we examine how observers interact with branching universes, analyze Newcomb’s paradox in both classical and quantum forms, and discuss applications in quantum game theory and quantum economics. By integrating quantum concepts like superposition, entanglement, and interference, we demonstrate how these ideas resolve classical paradoxes and offer novel frameworks for modeling complex systems. Mathematical formulations are presented using Unicode symbols for clarity. The many-worlds interpretation of quantum mechanics, proposed by Hugh Everett III in 1957, posits that the universe branches into multiple parallel realities during quantum measurements, avoiding the wave function collapse postulate. This framework has profound philosophical and practical implications, particularly in understanding decision-making under uncertainty. In this paper, we synthesize discussions on MWI, observer roles in branching, Newcomb’s paradox, its quantum variant, quantum game theory, and quantum economics. These topics form a coherent progression from quantum foundations to applied interdisciplinary fields, highlighting how quantum principles can reshape classical theories.

Indranil Ghosh

Indranil Ghosh

Katarzyna Bolonek-Lasoń

We outline the general construction of three-player games with incomplete information which fulfil the following conditions: (i) symmetry with respect to the permutations of players; (ii) the existence of an upper bound for total payoff resulting from Bell inequalities; (iii) the existence of both fair and unfair Nash equilibria saturating this bound. Conditions (i)–(iii) imply that we are dealing with conflicting interest games. An explicit example of such a game is given. A quantum counterpart of this game is considered. It is obtained by keeping the same utilities but replacing classical advisor by a quantum one. It is shown that the quantum game possesses only fair equilibria with strictly higher payoffs than in the classical case. This implies that quantum nonlocality can be used to resolve the conflict between the players.

Amine Marrakchi, Mikael DE LA SALLE

The aim of this note is to present a ``type III'' generalization of a distribution lemma of Connes. We then derive, following Vidick, consequences on infinite-dimensional quantum strategies for non-local games.

Taksu Cheon