Related papers: Variations on Keeler's Theorem

We study the evolution of behavior under reinforcement learning in a Prisoner's Dilemma where agents interact in a regular network and can learn about whether they play one-shot or repeatedly by incurring a cost of deliberation. With…

We study quantum heat exchange in a multi-state impurity coupled to two thermal reservoirs. Allowing for strong system-bath interactions, we show that a steady-state heat exchange fluctuation theorem holds, though the dynamical processes…

The iterated prisoner's dilemma is a game that produces many counter-intuitive and complex behaviors in a social environment, based on very simple basic rules. It illustrates that cooperation can be a good thing even in a competitive world,…

A quantum simulator is a well controlled quantum system that can simulate the behavior of another quantum system which may require exponentially large classical computing resources to understand otherwise. In the 1980s, Feynman proposed the…

We consider a quantum many-body system made of $N$ interacting $S{=}1/2$ spins on a lattice, and develop a formalism which allows to extract, out of conventional magnetic observables, the quantum probabilities for any selected spin pair to…

Exchangeability is a fundamental concept in probability theory and statistics. It allows to model situations where the order of observations does not matter. The classical de Finetti's theorem provides a representation of infinitely…

Cooperative behavior, where one individual incurs a cost to help another, is a wide spread phenomenon. Here we study direct reciprocity in the context of the alternating Prisoner's Dilemma. We consider all strategies that can be implemented…

There is a sudden surge to model human behavior due to its vast and diverse applications which includes modeling public policies, economic behavior and consumer behavior. Most of the human behavior itself can be modeled into a choice…

In quantum many-body problems, one of the main difficulties comes from the description of non-negligible interactions which require, at least in principle, an exponential amount of information. Recently, in the context of spin glasses and…

We present a discussion of the extended Wigner's friend thought experiment proposed by Frauchiger and Renner in [1]. We show by using various arguments, including textbook quantum mechanics and the ontological approach of Contexts, Systems,…

Universal quantum simulation may provide insights into those many-body systems that cannot be described classically, and that cannot be efficiently simulated with current technology. The Trotter formula, which decomposes a desired unitary…

We theoretically study the effect of a third person enforcement on a one-shot prisoner's dilemma game played by two persons, with whom the third person plays repeated prisoner's dilemma games. We find that the possibility of the third…

A game in which one player makes unitary transformations of a simple system, and another seeks to confound the resulting state by a randomly chosen action is analyzed carefully. It is shown that the second player can reduce any system to a…

Wigner's friend experiment and its modern extensions display the ambiguity of the quantum mechanical description regarding the assignment of quantum states. While the friend applies the state-update rule to the system upon observing an…

We show that quantum game theory offers solution to the famous Newcomb's paradox (free will problem). Divine foreknowledge is not necessary for successful completion of the game because quantum theory offers a way to discern human…

This paper investigates how natural language communication with an AI agent affects human cooperative behaviour in indefinitely repeated Prisoner's Dilemma games. We conduct a laboratory experiment (n = 126) with two between-subjects…

What happens when an infinite number of players play a quantum game? In this tutorial, we will answer this question by looking at the emergence of cooperation, in the presence of noise, in a one-shot quantum Prisoner's dilemma (QuPD). We…

We show that any permutation of ${1,2,...,N}$ can be written as the product of two involutions. As a consequence, any permutation of the elements of an array can be performed in-place in parallel in time O(1). In the case where the…

Due to the no-cloning theorem, the unknown quantum state can only be cloned approximately or exactly with some probability. There are two types of cloners: universal and state-dependent cloner. The optimal universal cloner has been found…

In a game of permutation wordle, a player attempts to guess a secret permutation in the fewest number of guesses possible. Previously, Samuel Kutin and Lawren Smithline (arXiv:2408.00903) introduced this game and proposed a strategy called…