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.Comment: 12 pages (2 figs), LaTe

Geometry of Financial Markets -- Towards Information Theory Model of Markets

Most of parameters used to describe states and dynamics of financial market depend on proportions of the appropriate variables rather than on their actual values. Therefore, projective geometry seems to be the correct language to describe the theater of financial activities. We suppose that the object of interest of agents, called here baskets, form a vector space over the reals. A portfolio is defined as an equivalence class of baskets containing assets in the same proportions. Therefore portfolios form a projective space. Cross ratios, being invariants of projective maps, form key structures in the proposed model. Quotation with respect to an asset X (i.e. in units of X) are given by linear maps. Among various types of metrics that have financial interpretation, the min-max metrics on the space of quotations can be introduced. This metrics has an interesting interpretation in terms of rates of return. It can be generalized so that to incorporate a new numerical parameter (called temperature) that describes agent's lack of knowledge about the state of the market. In a dual way, a metrics on the space of market quotation is defined. In addition, one can define an interesting metric structure on the space of portfolios/quotation that is invariant with respect to hyperbolic (Lorentz) symmetries of the space of portfolios. The introduced formalism opens new interesting and possibly fruitful fields of research.Comment: Talk given at the APFA5 Conference, Torino, 200

Geometry of Financial Markets - Towards Information Theory Model of Markets

Most of parameters used to describe states and dynamics of financial market depend on proportions of the appropriate variables rather than on their actual values. Therefore, projective geometry seems to be the correct language to describe the theater of financial activities. We suppose that the object of interest of agents, called here baskets, form a vector space over the reals. A portfolio is defined as an equivalence class of baskets containing assets in the same proportions. Therefore portfolios form a projective space. Cross ratios, being invariants of projective maps, form key structures in the proposed model. Quotation with respect to an asset X (i.e. in units of X) are given by linear maps. Among various types of metrics that have financial interpretation, the min-max metrics on the space of quotations can be introduced. This metrics has an interesting interpretation in terms of rates of return. It can be generalized so that to incorporate a new numerical parameter (called temperature) that describes agent's lack of knowledge about the state of the market. In a dual way, a metrics on the space of market quotation is defined. In addition, one can define an interesting metric structure on the space of portfolios/quotation that is invariant with respect to hyperbolic (Lorentz) symmetries of the space of portfolios. The introduced formalism opens new interesting and possibly fruitful fields of research.

Quantum-Like Approach to Financial Risk: Quantum Anthropic Principle

We continue the analysis of quantum-like description of market phenomena and economics. We show that it is possible to define a risk inclination operator acting in some Hilbert space that has a lot of common with quantum description of the harmonic oscillator. The approach has roots in the recently developed quantum game theory and quantum computing. A quantum anthropic principle is formulated. (final version published in Acta Phys.Pol.B,32(2001)3873-3879)

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.