Jan Sładkowski

An Invitation to Quantum Game Theory

Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper presents the history, basic ideas, and recent development in quantum game theory. In this context, a new application of the Ising chain model is proposed.

Quantum market games

We propose a quantum-like description of markets and economics. The approach has roots in the recently developed quantum game theory.

Quantum bargaining games

We continue the analysis of quantum-like description of markets and economics. The approach has roots in the recently developed quantum game theory and quantum computing. The present paper is devoted to quantum bargaining games which are a special class of quantum market games without institutionalized clearinghouses.

Trading by Quantum Rules: Quantum Anthropic Principle

This is a short review of the background and recent development in quantum game theory and its possible application in economics and finance. The intersection of science and society is discussed and Quantum Anthropic Principle is put forward. The review is addressed to nonspecialists.

Interference of quantum market strategies

Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper is devoted to the analysis of interference of quantum strategies in quantum market games.

Quantum Auctions: Facts and Myths

Quantum game theory, whatever opinions may be held due to its abstract physical formalism, have already found various applications even outside the orthodox physics domain. In this paper we introduce the concept of a quantum auction, its advantages and drawbacks. Then we describe the models that have already been put forward. A general model involves Wigner formalism and infinite dimensional Hilbert spaces — we envisage that the implementation might not be an easy task. But a restricted model advocated by the Hewlett–Packard group (Hogg et al.) seems to be much easier to implement. We focus on problems related to combinatorial auctions and technical assumptions that are made. Powerful quantum algorithms for finding solutions would extend the range of possible applications. Quantum strategies, being qubits, can be teleported but are immune from cloning — therefore extreme privacy of the agent’s activity could in principle be guaranteed. Then we point out some key problems that have to be solved before commercial use would be possible. With present technology, optical networks, single photon sources and detectors seems to be sufficient for an experimental realization in the near future.

Quantum English auctions

We continue the analysis of quantum-like description of markets and economics. The approach has roots in the recently developed quantum game theory and quantum computing. The present paper is devoted to quantum English auction which we consider as a special class of quantum market games. The approach allows to calculate profit intensities for various possible strategies.

Quantum diffusion of prices and profits

We discuss the time evolution of quotations of stocks and commodities and show that corrections to the orthodox Bachelier model inspired by quantum mechanical time evolution of particles may be important. Our analysis shows that traders tactics can interfere as waves do and traders strategies can be reproduced from the corresponding Wigner functions. The proposed interpretation of the chaotic movement of market prices imply that the Bachelier behaviour follows from short-time interference of tactics adopted (paths followed) by the rest of the world considered as a single trader and the Ornstein–Uhlenbeck corrections to the Bachelier model should qualitatively matter only for large time scales. The famous smithonian invisible hand is interpreted as a short-time tactics of whole the market considered as a single opponent. We also propose a solution to the currency preference paradox.

Giffen paradoxes in quantum market games

Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper presents the history and basic ideas of quantum game theory. Description of Giffen paradoxes in this new formalism is discussed.

Quantum Prisoner’s Dilemma game on hypergraph networks

We study the possible advantages of adopting quantum strategies in multi-player evolutionary games. We base our study on the three-player Prisoner’s Dilemma (PD) game. In order to model the simultaneous interaction between three agents we use hypergraphs and hypergraph networks. In particular, we study two types of networks: a random network and a SF-like network. The obtained results show that in the case of a three-player game on a hypergraph network, quantum strategies are not necessarily stochastically stable strategies. In some cases, the defection strategy can be as good as a quantum one.