Related papers: Using Elementary Techniques to Characterize the Re…
The numbers game is a one-player game played on a finite simple graph with certain "amplitudes" assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at…
We find various series that involves the central binomial coefficients $\binom{2n}{n}$, harmonic numbers and Fibonacci Numbers.\\ Contrary to the traditional hypergeometric function $_pF_q$ approach, our method utilizes a straightforward…
We revisit the golden sieve, a self-referential deletion process on increasing sequences of positive integers introduced by the author in 2002. Applied to the natural numbers, the sieve produces the Wythoff pair as a Beatty partition. For…
The Grundy number of an impartial game G is the size of the unique Nim heap equal to G. We introduce a new variant of Nim, Restricted Nim, which restricts the number of stones a player may remove from a heap in terms of the size of the…
Quantum mechanics dramatically differs from classical physics, allowing for a wide range of genuinely quantum phenomena. The goal of quantum information is to understand information processing from a quantum perspective. In this mindset, it…
We investigate the consequences of allowing players to adopt strategies which take advantage of quantum randomization devices. In games of full information, the resulting equilibria are always correlated equilibria, but not all correlated…
The Fibonacci sequence (FS) possesses exceptional mathematical properties that have captivated mathematicians, scientists, and artists across centuries. Its intriguing nature lies in its profound connection to the golden ratio, as well as…
Many-body dynamical models in which Boltzmann statistics can be derived directly from the underlying dynamical laws without invoking the fundamental postulates of statistical mechanics are scarce. Interestingly, one such model is found in…
The game of nim, with its simple rules, its elegant solution and its historical importance is the quintessence of a combinatorial game, which is why it led to so many generalizations and modifications. We present a modification with a new…
The golden ratio and Fibonacci numbers are found to occur in various aspects of nature. We discuss the occurrence of this ratio in an interesting physical problem concerning center of masses in two dimensions. The result is shown to be…
The semijoin algebra is the variant of the relational algebra obtained by replacing the join operator by the semijoin operator. We discuss some interesting connections between the semijoin algebra and the guarded fragment of first-order…
We analyse the role of degree of entanglement for Vaidman's game in a setting where the players share a set of partially entangled three-qubit states. Our results show that the entangled states combined with quantum strategies may not be…
The game in which acts of participants don't have an adequate description in terms of Boolean logic and classical theory of probabilities is considered. The model of the game interaction is constructed on the basis of a non-distributive…
Quantum game theory offers a lot of interesting questions, and it is relevant to use the quantum information theory to resolve or improve games with lack of information : how to use the power of quantum entanglement to show the superiority…
In this paper a hierarchical extension of the Minority Game is defined and studied. Numerical simulations show a special type of emergent global behavior between separated parts of the hierarchical structure, connected only through a…
We analyse the typical structure of games in terms of the connectivity properties of their best-response graphs. Our central result shows that, among games that are `generic' (without indifferences) and that have a pure Nash equilibrium,…
We study a quantum game played by two players with restricted multiple strategies. It is found that in this restricted quantum game Nash equilibrium does not always exist when the initial state is entangled. At the same time, we find that…
This note explains why a large class of fair, or reversible "money games", i.e., stochastic models of wealth redistribution among agents, lead to steady states described by canonical and microcanonical distributions. The games considered…
A generalized model of games is proposed, in which cooperative games and non-cooperative games are special cases. Some games that are neither cooperative nor non-cooperative can be expressed and analyzed. The model is based on relationships…
We study the influence of Unruh effect on quantum non-zero sum games. In particular, we investigate the quantum Prisoners' Dilemma both for entangled and unentangled initial states and show that the acceleration of the noninertial frames…