Related papers: Quantum Solution to the Extended Newcomb's Paradox
Using the representation introduced in \cite{frame}, an artificial game in quantum strategy space is proposed and studied. Although it has well-known classical correspondence, which has classical mixture strategy Nash Equilibrium states,…
In this paper, we propose two new methods for solving Set Constraint Problems, as well as a potential polynomial solution for NP-Complete problems using quantum computation. While current methods of solving Set Constraint Problems focus on…
We present a new framework for creating a quantum version of a classical game, based on Fine's theorem. This theorem shows that for a given set of marginals, a system of Bell's inequalities constitutes both necessary and sufficient…
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…
It is often argued that bottom-up causation under a physicalist, reductionist worldview precludes free will in the libertarian sense. On the one hand, the paradigm of classical mechanics makes determinism inescapable, while on the other,…
We develop a general game-theoretic framework for reasoning about strategic agents performing possibly costly computation. In this framework, many traditional game-theoretic results (such as the existence of a Nash equilibrium) no longer…
Nash equilibrium serves as a fundamental mathematical tool in economics and game theory. However, it classically assumes knowledge of player utilities, whereas economics generally regards preferences as more fundamental. To leverage…
In this letter, we point to three widely accepted challenges that the quantum theory, quantum information, and quantum foundations communities are currently facing: indeterminism, the semantics of conditional probabilities, and the spooky…
Physics has long lived with a schizophrenia that desires determinism for measured systems while demanding that experimenters decide what to measure on a whim. Intriguingly, such a free will assumption for experimenters has thwarted many…
We propose the use of a quantum algorithm to deal with the problem of searching with errors in the framework of two-person games. Specifically, we present a solution to the Ulam's problem that polynomially reduces its query complexity and…
The well known refinement of the Nash Equilibrium (NE) called an Evolutionarily Stable Strategy (ESS) is investigated in the quantum Prisoner's Dilemma (PD) game that is played using an Einstein-Podolsky-Rosen type setting. Earlier results…
The quantum decision theory is examined in its simplest form of two-condition two-choice setting. A set of inequalities to be satisfied by any quantum conditional probability describing the decision process is derived. Experimental data…
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…
In a society of multiple individuals, if everybody is only interested in maximizing his own payoff, will there exist any equilibrium for the society? John Nash proved more than 50 years ago that an equilibrium always exists such that nobody…
We introduce Q-Nash, a quantum annealing algorithm for the NP-complete problem of Fnding pure Nash equilibria in graphical games. The algorithm consists of two phases. The first phase determines all combinations of best response strategies…
In 1953, Kuhn showed that every sequential game has a Nash equilibrium by showing that a procedure, named ``backward induction'' in game theory, yields a Nash equilibrium. It actually yields Nash equilibria that define a proper subclass of…
Combining quantum computers with classical compute power has become a standard means for developing algorithms that are eventually supposed to beat any purely classical alternatives. While in-principle advantages for solution quality or…
The choice of a unique Nash equilibrium (NE) is crucial in theoretical classical and quantum games. The Eiswer-Wilkens-Lewenstein quantization scheme solves the prisoner's dilemma only for high entanglement. At medium entanglement, there…
Artificial intelligence (AI) is understood to affect the content of people's decisions. Here, using a behavioral implementation of the classic Newcomb's paradox in 1,305 participants, we show that AI can also change how people decide. In…
While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…