Cooperative quantum Parrondo's games

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 figure

Exotic smoothness on spacetime new developments

I discuss recent development in investigation of physical consequences of exotic differential structures on manifolds. I show, following T. Asselmayer, that corrections to the curvature after the change of differential structure produce a source like term in the Einstein equations. Then I give examples of topologically trivial spaces on which exotic differential structures act as a source of gravitational force even in the absence of matter

Spacetime structure and unification of fundamental interactions

I discuss the problem to what extent fundamental interactions determine the structure of spacetime. I show that when we are using only topological methods the spacetime should be modelled on an H-compact space. Demanding the existence of a differential structure substantially narrows the choice of possible models but the differential structure may not be unique. I also show by using the noncommutative geometry construction of the standard model that fundamental interactions determine the spacetime in the class of H-compact spaces. Fermions are essential for the process of determining the spacetime structure

Do transitive preferences always result in indifferent divisions?

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 figure

A mechanism of compactification

To explain why our Universe is four-dimensional is one of the main goals of contemporary theoretical physics. Of course, one may answer that the Universe is four-dimensional because only four-dimensional universes allow human beings to exist. But then the question may be reformulated in an obvious way. In the Kaluza-Klein approach [1] the space-time is higher-dimensional and symmetries in the additional dimensions are the sources of gauge interactions[…

Enhancing pseudo-telepathy in the Magic Square game

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 figure

Dynamical symmetry breaking in superstring scenario

The possibility of dynamical symmetry breaking in the field theory limit of superstring theories is discussed. The proposed scenario should lead to a natural solution to the hierarchy problem