Related papers: Late comment on Astumian's paradox

General Markov chains in an arbitrary phase space are considered in the framework of the operator treatment. Markov operators continue from the space of countably additive measures to the space of finitely additive measures. Cycles of…

We derive an adiabatic theorem for Markov chains using well known facts about mixing and relaxation times. We discuss the results in the context of the recent developments in adiabatic quantum computation.

We prove that in a general zero-sum repeated game where the first player is more informed than the second player and controls the evolution of information on the state, the uniform value exists. This result extends previous results on…

Partially Observable Markov Games (POMGs) provide a general framework for modeling multi-agent sequential decision-making under asymmetric information. A common approach is to reformulate a POMG as a fully observable Markov game over belief…

We review the Markov theoretic description of 1D aperiodic crystals, describing the stacking-faulted crystal polytype as a special case of an aperiodic crystal. Under this description we generalise the centrosymmetric unit cell underlying a…

We study security threats to Markov games due to information asymmetry and misinformation. We consider an attacker player who can spread misinformation about its reward function to influence the robust victim player's behavior. Given a…

This is an introduction into John Conway's beautiful Combinatorial Game Theory, providing precise statements and detailed proofs for the fundamental parts of his theory. (1) Combinatorial game theory, (2) the GROUP of games, (3) the FIELD…

We consider a simple but important class of metastable discrete time Markov chains, which we call perturbed Markov chains. Basically, we assume that the transition matrices depend on a parameter $\varepsilon$, and converge as $\varepsilon$.…

We study the stochastic dynamics of evolutionary games, and focus on the so-called `stochastic slowdown' effect, previously observed in (Altrock et. al, 2010) for simple evolutionary dynamics. Slowdown here refers to the fact that a…

This paper has a two-folded purpose. First, we attempt to outline the development of the turnpike theorems in the the last several decades. Second, we study turnpike theorems in finite-horizon two-person zero-sum Markov games on a general…

Parrondo's paradox indicates a paradoxical situation in which a winning expectation may occur in sequences of losing games. There are many versions of the original Parrondo's games in the literature, but the games are played by two players…

Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…

Imitation dynamics for population games are studied and their asymptotic properties analyzed. In the considered class of imitation dynamics - that encompass the replicator equation as well as other models previously considered in…

It is well-known that in finite strategic games true common belief (or common knowledge) of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies. We…

A quantum logic gate of particular interest to both electrical engineers and game theorists is the quantum multiplexer. This shared interest is due to the facts that an arbitrary quantum logic gate may be expressed, up to arbitrary…

Questions are posed regarding the influence that the column sums of the transition probabilities of a stochastic matrix (with row sums all one) have on the stationary distribution, the mean first passage times and the Kemeny constant of the…

The paper [Ras15a] introduced distribution-valued games. This game-theoretic model uses probability distributions as payoffs for games in order to express uncertainty about the payoffs. The player's preferences for different payoffs are…

We consider a zero-sum stochastic game for continuous-time Markov chain with countable state space and unbounded transition and pay-off rates. The additional feature of the game is that the controllers together with taking actions are also…

We survey information-theoretic approaches to the reduction of Markov chains. Our survey is structured in two parts: The first part considers Markov chain coarse graining, which focuses on projecting the Markov chain to a process on a…

An interaction system has a finite set of agents that interact pairwise, depending on the current state of the system. Symmetric decomposition of the matrix of interaction coefficients yields the representation of states by self-adjoint…