Related papers: Recycling Parrondo games
We address the problems in applying cycle expansions to bound chaotic systems, caused by e.g. intermittency and incompleteness of the symbolic dynamics. We discuss zeta functions associated with weighted evolution operators and in…
In the 60's Shapley provided an example of a two player fictitious game with periodic behaviour. In this game, player $A$ aims to copy $B$'s behaviour and player $B$ aims to play one ahead of player $A$. In this paper we generalize…
We introduce a new solution concept, called periodicity, for selecting optimal strategies in strategic form games. This periodicity solution concept yields new insight into non-trivial games. In mixed strategy strategic form games, periodic…
Iterated admissibility is a well-known and important concept in classical game theory, e.g. to determine rational behaviors in multi-player matrix games. As recently shown by Berwanger, this concept can be soundly extended to infinite games…
The Parrondo game, devised by Parrondo, means that winning strategy is constructed a combination of losing strategy. This situation is called the Parrondo paradox. The Parrondo game based on quantum walk and the search algorithm via quantum…
We prove the undecidability of determining whether a Turing machine yields an eventually periodic trajectory. From this, we deduce the undecidability of orbit finiteness in the polynomial dynamical system on infinite tuples of integers.
The inequality in capital or resource distribution is among the important phenomena observed in populations. The sources of inequality and methods for controlling it are of practical interest. To study this phenomenon, we introduce a model…
We consider the general model of zero-sum repeated games (or stochastic games with signals), and assume that one of the players is fully informed and controls the transitions of the state variable. We prove the existence of the uniform…
Subtraction games is a class of impartial combinatorial games, They with finite subtraction sets are known to have periodic nim-sequences. So people try to find the regular of the games. But for specific of Sprague-Grundy Theory, it is too…
Ladder tournaments are widely used to rank individuals in real-world organizations and games. Their mathematical properties however are still poorly understood. We formalize the ranking rule generated by a ladder tournament, and we show…
Repeated games have a long tradition in the behavioral sciences and evolutionary biology. Recently, strategies were discovered that permit an unprecedented level of control over repeated interactions by enabling a player to unilaterally…
Using a group-theoretic approach, a method for determining the equivalence classes (also called orbits) of the set of rules of one-dimensional cellular automata induced by the symmetry operations of reflection and permutation and their…
Parrondo's paradox occurs in sequences of games in which a winning expectation may be obtained by playing the games in a random order, even though each game in the sequence may be lost when played individually. Several variations of…
We study the large-time behavior of a class of periodically driven macroscopic systems. We find, for a certain range of the parameters of either the system or the driving fields, the time-averaged asymptotic behavior effectively is that of…
We study the problem of characterizing optimal learning algorithms for playing repeated games against an adversary with unknown payoffs. In this problem, the first player (called the learner) commits to a learning algorithm against a second…
The existing periodic orbit theory of spectral correlations for classically chaotic systems relies on the Riemann-Siegel-like representation of the spectral determinants which is still largely hypothetical. We suggest a simpler derivation…
We study parity games in which one of the two players controls only a small number $k$ of nodes and the other player controls the $n-k$ other nodes of the game. Our main result is a fixed-parameter algorithm that solves bipartite parity…
We investigate the quantum recurrence phenomena in periodically driven systems. We calculate the classical period and the quantum recurrence time and develop their interdependence. We further predict the behavior of the recurrence phenomena…
Periodic orbits are important objects of discrete dynamical systems, but finding them is not always easy. We present a self-contained introductory account, aimed at non-experts, to prove their existence and study their stability using the…
How humans make decisions in non-cooperative strategic interactions is a challenging question. For the fundamental model system of Rock-Paper-Scissors (RPS) game, classic game theory of infinite rationality predicts the Nash equilibrium…