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The present authors have put forward a quantum game theory based model of market prices movements. By using Fisher information, we present a construction of an equation of Schr\"{o}dinger type for probability distributions for relationship between demand and supply. Various analogies between quantum physics and market phenomena can be found., Comment: 15 pages, 6 figures

This paper focuses on two problems. The first is related to the consistency checks of the complete correlation coefficients between two groups of variables obtained in Phys. Lett. B 749, 262 (2015). The first group collects parameters that describe properties of nuclear matter referring to the transport model involved. The second one is a group of observables adopted in the heavy ion collision experiments. The second problem concerns the method of determining the values of pure correlations between some variables in heavy ion collision. The application of this method for the analysis of the correlations of the isospin sensitive variables is pointed out., Comment: 4 pages 2 figures

Quality of approximations is an important issue in modelling nuclear matter. It is shown that the Pad{\' e} approximation provides a useful tool for describing the symmetry energy in highly asymmetric systems. The focus is on the symmetry energy constraints. Some implications of the obtained results for astrophysics are also discussed., Comment: 25 pages, 9 figures

The aim of the paper is to study the Bertrand duopoly example in the quantum domain. We use two ways to write the game in terms of quantum theory. The first one adapts the Li-Du-Massar scheme for the Cournot duopoly. The second one is a simplified model that exploits a two qubit entangled state. In both cases we focus on finding Nash equilibria in the resulting games.

This paper presents a continuous variable generalization of the Aoki-Yoshikawa sectoral productivity model. Information theoretical methods from the Frieden-Soffer extreme physical information statistical estimation methodology were used to construct exact solutions. Both approaches coincide in first order approximation. The approach proposed here can be successfully applied in other fields of research., Comment: 24 pages, 1 figure

We consider properties of the measurement intensity $\rho$ of a random variable for which the probability density function represented by the corresponding Wigner function attains negative values on a part of the domain. We consider a simple economic interpretation of this problem. This model is used to present the applicability of the method to the analysis of the negative probability on markets where there are anomalies in the law of supply and demand (e.g. Giffen's goods). It turns out that the new conditions to optimize the intensity $\rho$ require a new strategy. We propose a strategy (so-called $\grave{a}$ rebours strategy) based on the fixed point method and explore its effectiveness., Comment: 11 pages, 4 figures

The transitivity of preferences is one of the basic assumptions used in the theory of games and decisions. It is often equated with rationality of choice and is considered useful in building rankings. Intransitive preferences are considered paradoxical and undesirable. This problem is discussed by many social and natural sciences. The paper discusses a simple model of sequential game in which two players in each iteration of the game choose one of the two elements. They make their decisions in different contexts defined by the rules of the game. It appears that the optimal strategy of one of the players can only be intransitive! (the so-called \textsl{relevant intransitive strategies}.) On the other hand, the optimal strategy for the second player can be either transitive or intransitive. A quantum model of the game using pure one-qubit strategies is considered. In this model, an increase in importance of intransitive strategies is observed -- there is a certain course of the game where intransitive strategies are the only optimal strategies for both players. The study of decision-making models using quantum information theory tools may shed some new light on the understanding of mechanisms that drive the formation of types of preferences., Comment: 16 pages, 5 figures

We introduce a method of analyzing entanglement enhanced quantum games on regular lattices of agents. Our method is valid for setups with periodic and non-periodic boundary conditions. To demonstrate our approach we study two different types games, namely the prisoner's dilemma game and a cooperative Parrondo's game. In both cases we obtain results showing, that entanglement is a crucial resource necessary for the agents to achieve positive capital gain., Comment: 7 pages, 6 figures

We study the possibility of reversing an action of a quantum channel. Our principal objective is to find a specific channel that reverses as accurately as possible an action of a given quantum channel. To achieve this goal we use semidefinite programming. We show the benefits of our method using the quantum pseudo-telepathy Magic Square game with noise. Our strategy is to move the pseudo-telepathy region to higher noise values. We show that it is possible to reverse the action of a noise channel using semidefinite programming., Comment: 7 pages, 3 figures

Coordination and cooperation are among the most important issues of game theory. Recently, the attention turned to game theory on graphs and social networks. Encouraged by interesting results obtained in quantum evolutionary game analysis, we study cooperative Parrondo's games in a quantum setup. The game is modeled using multidimensional quantum random walks with biased coins. We use the GHZ and W entangled states as the initial state of the coins. Our analysis shows than an apparent paradox in cooperative quantum games and some interesting phenomena can be observed., Comment: 13 pages, 10 figures

The problem of possible astrophysical consequences of the existence of exotic differential structures on manifolds is discussed. It is argued that corrections to the curvature of the form of a source like terms should be expected in the Einstein equations if they are written in the "wrong" differential structure. Examples of topologically trivial spaces on which exotic differential structures act as a source of gravitational force even in the absence of matter are given. Propagation of light in the presence of such phenomena is also discussed. A brief review of exotic smoothness is added for completeness., Comment: Talk given at XXXIII International Conference of Theoretical Physics: "Matter to the Deepest: Recent Developments in Physics of Fundamental Interactions"

We investigate activities that have different periods of duration. We define the profit intensity as a measure of this economic category. The profit intensity in a repeated trading has a unique property of attaining its maximum at a fixed point regardless of the shape of demand curves for a wide class of probability distributions of random reverse transaction (ie closing of the position). This type of market games is often considered in the research aiming at finding an algorithm that maximizes profit of a trader who negotiates prices with the Rest of the World (a collective opponent) that posses a definite and objective supply profile. Such idealization neglects the sometimes important influence of an individual trader on the demand/supply profile of the Rest of the World and in extreme cases questions the very idea of demand/supply profile. Therefore we put forward a trading model in which the demand/supply profile of the Rest of the World induces the (rational) trader to (subjectively) presume that he/she lacks (almost) all knowledge concerning the market but his/hers average frequency of trade. This point of view introduces maximum entropy principles into the model and broadens the range of economics phenomena that can be perceived as a sort of thermodynamical system. As a consequence, the profit intensity has a fixed point:the profit in tensity reaches its maximum when the probability of transaction is given by the Golden Ratio rule $\frac{\sqrt{5}-1}{2}$., Comment: Presented at the SIGMAPHI 08 Conference

Financial markets investors are involved in many games -- they must interact with other agents to achieve their goals. Among them are those directly connected with their activity on markets but one cannot neglect other aspects that influence human decisions and their performance as investors. Distinguishing all subgames is usually beyond hope and resource consuming. In this paper we study how investors facing many different games, gather information and form their decision despite being unaware of the complete structure of the game. To this end we apply reinforcement learning methods to the Information Theory Model of Markets (ITMM). Following Mengel, we can try to distinguish a class $\Gamma$ of games and possible actions (strategies) $a^{i}_{m_{i}}$ for $i-$th agent. Any agent divides the whole class of games into analogy subclasses she/he thinks are analogous and therefore adopts the same strategy for a given subclass. The criteria for partitioning are based on profit and costs analysis. The analogy classes and strategies are updated at various stages through the process of learning. This line of research can be continued in various directions., Comment: Talk given at the conference APFA6 (July 2007, Lisbone); 7 pages

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, 2006

We reason about possible future development of quantum game theory and its impact on information processing and the emerging information society. Two of the authors have recently proposed a quantum description of financial market in terms of quantum game theory. These "new games" cannot by themselves create extraordinary profits or multiplication of goods, but they may cause the dynamism of transaction which would result in more effective markets and capital flow into hands of the most efficient traders. We focus upon the problem of universality of measurement in quantum market games. Quantum-like approach to market description proves to be an important theoretical tool for investigation of computability problems in economics or game theory even if never implemented in real markets., Comment: 13 pages; References to significant previous results by other authors are inserted and made more explicit in section 4. References are updated

Attention to the very physical aspects of information characterizes the current research in quantum computation, quantum cryptography and quantum communication. In most of the cases quantum description of the system provides advantages over the classical approach. Game theory, the study of decision making in conflict situation has already been extended to the quantum domain. We would like to review the latest development in quantum game theory that is relevant to information processing. We will begin by illustrating the general idea of a quantum game and methods of gaining an advantage over "classical opponent". Then we review the most important game theoretical aspects of quantum information processing. On grounds of the discussed material, we reason about possible future development of quantum game theory and its impact on information processing and the emerging information society. The idea of quantum artificial intelligence is explained., Comment: Some obvious errors are corrected. References to significant previous results by other authors are inserted and made more explicit in section 4

On grounds of the discussed material, we reason about possible future development of quantum game theory and its impact on information processing and the emerging information society. The idea of quantum artificial intelligence is explained., Comment: 17 pages, 11 figures; pure LaTeX

We discuss some aspects of Astumian suggestions that combination of biased games (Parrondo's paradox) can explain performance of molecular motors. Unfortunately the model is flawed by explicit asymmetry overlooked by the author. In addition, we show that taking into consideration stakes allows to remove the paradoxical behaviour of Parrondo games.

Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The authors have recently proposed a quantum description of financial market in terms of quantum game theory. The paper contain an analysis of such markets that shows that there would be advantage in using quantum computers and quantum strategies., Comment: 20 pages, pure LaTeX

We use various results concerning isometry groups of Riemannian and pseudo-Riemannian manifolds to prove that there are spaces on which differential structure can act as a source of gravitational force (Brans conjecture). The result is important for the analysis of the possible physical meaning of differential calculus. Possible astrophysical consequences are discussed.

We discuss the problem of determining the spacetime structure. We show that when we are using only topological methods the spacetime can be modelled as an R- or Q-compact space although the R-compact spaces seem to be more appropriate. Demanding the existence of a differential structure substantially narrows the choice of possible models. The determination of the differential structure may be difficult if it is not unique. By using the noncommutative geometry construction of the standard model we show that fundamental interactions determine the spacetime in the class of R-compact spaces. Fermions are essential for the process of determining the spacetime structure., Comment: 28 pages, LaTeX: no special macros required

Short introduction to exotic differential structures on manifolds is given. The possible physical context of this mathematical curiosity is discussed. The topic is very interesting although speculative., Comment: 8 pages, pure LaTeX, Lecture given at the conference Particle Physics and Astrophysics in the Standard Model and Beyond, Bystra (Poland), September 1995

Recent development in noncommutative geometry generalization of gauge theory is reviewed. The mathematical apparatus is reduced to minimum in order to allow the non-mathematically oriented physicists to follow the development in the interesting field of research. (Lectures presented at the Silesian School of Theoretical Physics: Standard Model and Beyond'93, Szczyrk (Poland), September 1993.), Comment: 16 pages, LaTeX file, BI-TP 93/64

The proposed by Bastianelli and van Nieuwenhuizen new method of calculations of trace anomalies is applied in the conformal gauge field case. The result is then reproduced by the heat equation method. An error in previous calculation is corrected. It is pointed out that the introducing gauge symmetries into a given system by a field-enlarging transformation can result in unexpected quantum effects even for trivial configurations., Comment: 9 pages, LaTeX file, BI-TP 93/34

It is argued that the noncommutative geometry construction of the standard model predicts a nonlinear symmetry breaking mechanism rather than the orthodox Higgs mechanism. Such models have experimentally verifiable consequences., Comment: 12 pages, LaTeX file, BI-TP 93/26

A field-enlarging transformation in the chiral electrodynamics is performed. This introduces an additional gauge symmetry to the model that is unitary and anomaly-free and allows for comparison of different models discussed in the literature. The problem of superfluous degrees of freedom and their influence on quantization is discussed. Several "mysteries" are explained from this point of view., Comment: 14 pages, LaTeX-file, BI-TP 93/07