Related papers: Optimal sequence for Parrondo games
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 is widely observed in populations of decision-making agents. Using our recent convergence results for asynchronous imitation dynamics on networks, we consider how such networks can be efficiently driven to a desired equilibrium…
We describe the probability theory behind a casino game, blackjack, and the procedure to compute the optimal strategy for a deck of arbitrary cards and player's expected win given that he follows the optimal strategy. The exact blackjack…
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…
Many poker systems, whether created with heuristics or machine learning, rely on the probability of winning as a key input. However calculating the precise probability using combinatorics is an intractable problem, so instead we approximate…
The optimal value computation for turned-based stochastic games with reachability objectives, also known as simple stochastic games, is one of the few problems in $NP \cap coNP$ which are not known to be in $P$. However, there are some…
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…
In this paper we present a novel approach to optimise tactical and strategic decision making in football (soccer). We model the game of football as a multi-stage game which is made up from a Bayesian game to model the pre-match decisions…
Infinite-duration games with disturbances extend the classical framework of infinite-duration games, which captures the reactive synthesis problem, with a discrete measure of resilience against non-antagonistic external influence. This…
We consider a repeated sequential game between a learner, who plays first, and an opponent who responds to the chosen action. We seek to design strategies for the learner to successfully interact with the opponent. While most previous…
This paper investigates a class of multi-player discrete games where each player aims to maximize its own utility function. Each player does not know the other players' action sets, their deployed actions or the structures of its own or the…
We study a setting in which two players play a (possibly approximate) Nash equilibrium of a bimatrix game, while a learner observes only their actions and has no knowledge of the equilibrium or the underlying game. A natural question is…
Inspired by the flashing ratchet, Parrondo's game presents an apparently paradoxical situation. Parrondo's game consists of two individual games, game A and game B. Game A is a slightly losing coin-tossing game. Game B has two coins, with…
We introduce a method of analyzing entanglement enhanced quantum games on regular lattices of agents. Our method is valid for setups with periodic and non-periodic boundary conditions. To demonstrate our approach we study two different…
I consider a family of games with corresponding payoff matrices, parametrized by the parameter The informal question of interest is: what game is the best? Instead of attempting to suggest a more or less arbitrary definition of the best…
Optimal designs are usually model-dependent and likely to be sub-optimal if the postulated model is not correctly specified. In practice, it is common that a researcher has a list of candidate models at hand and a design has to be found…
We conducted an experiment where participants played a perfect-information game against a computer, which was programmed to deviate often from its backward induction strategy right at the beginning of the game. Participants knew that in…
We consider zero sum stochastic games. For every discount factor $\lambda$, a time normalization allows to represent the game as being played on the interval [0, 1]. We introduce the trajectories of cumulated expected payoff and of…
Game balancing is an important part of the (computer) game design process, in which designers adapt a game prototype so that the resulting gameplay is as entertaining as possible. In industry, the evaluation of a game is often based on…
We give a new proof of the sufficiency of Landau's conditions for a non-decreasing sequence of integers to be the score sequence of a tournament. The proof involves jumping down a total order on sequences satisfying Landau's conditions and…