Related papers: Matroid isomorphism games
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…
We introduce a quantum cloning game in which $k$ separate collaborative parties receive a classical input, determining which of them has to share a maximally entangled state with an additional party (referee). We provide the optimal winning…
An example of the macroscopic game of two partners consisting of two classical games played simultaneously with special dependence of strategies is considered. The average profit of each partner is equal to the average profit obtained in…
How coperation between self-interested individuals evolve is a crucial problem, both in biology and in social sciences, that is far from being well understood. Evolutionary game theory is a useful approach to this issue. The simplest model…
Effect of replacing the classical game object with a quantum object is analyzed. We find this replacement requires a throughout reformation of the framework of Game Theory. If we use density matrix to represent strategy state of players,…
In the standard approach to quantum games, players' moves are local unitary transformations on an entangled state that is subsequently measured. Players' payoffs are then obtained as expected values of the entries in the payoff matrix of…
The graph isomorphism problem is theoretically interesting and also has many practical applications. The best known classical algorithms for graph isomorphism all run in time super-polynomial in the size of the graph in the worst case. An…
We introduce a notion of strategies based on averaging for nonlocal games in quantum information theory. These so-called statistical strategies come in a commuting type and a more specific spatial type, which are respectively special cases…
In this paper, by using permutation matrices as a representation of symmetric group $S_N$ and Fourier matrix, we investigate quantum roulette with an arbitrary $N$-state. This strategy, which we introduce, is general method that allows us…
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 introduce classical and quantum no-signalling bicorrelations and characterise the different types thereof in terms of states on operator system tensor products, exhibiting connections with bistochastic operator matrices and with…
It has recently been shown that infinite matroids can be axiomatized in a way that is very similar to finite matroids and permits duality. This was previously thought impossible, since finitary infinite matroids must have non-finitary…
We prove that an imitation game has a perfect quantum approximate strategy if and only if there exists a bi-tracial state on the minimal tensor product of two universal C${^*}$-algebras, which induces the perfect correlation. Moreover, we…
In this work we propose and develop modified quantum games (zero and non-zero sum) in which payoffs and strategies are entangled. For the games studied, Nash and Pareto equilibriums are always obtained indicating that there are some…
We associate to each synchronous game an algebra whose representations determine if the game has a perfect deterministic strategy, perfect quantum strategy or one of several other perfect strategies. when applied to the graph coloring game,…
Let $G$ be a simple finite graph, and let $\mathcal U_G$ be the related quantum graph. We study the game algebra $C(\mathrm{Qut}(\mathcal U_G))$ of quantum automorphism of $\mathcal U_G$. Moreover, we prove that for any graph $G$ with…
We investigate the quantization of non-zero sum games. For the particular case of the Prisoners' Dilemma we show that this game ceases to pose a dilemma if quantum strategies are allowed for. We also construct a particular quantum strategy…
Rough set theory is a useful tool to deal with uncertain, granular and incomplete knowledge in information systems. And it is based on equivalence relations or partitions. Matroid theory is a structure that generalizes linear independence…
This paper studies sequential quantum games under the assumption that the moves of the players are drawn from groups and not just plain sets. The extra group structure makes possible to easily derive some very general results characterizing…
Classical game theory is a powerful tool focusing on optimized resource distribution, allocation and sharing in classical wired and wireless networks. As quantum networks are emerging as a means of providing true connectivity between…