Related papers: A simpler winning strategy for Sim

A valuation for a player in a game in extensive form is an assignment of numeric values to the players moves. The valuation reflects the desirability moves. We assume a myopic player, who chooses a move with the highest valuation.…

We introduce a 2-player game played on an infinite grid, initially empty, where each player in turn chooses a vertex and colours it. The first player aims to create some pattern from a target set, while the second player aims to prevent it.…

Priced timed games are two-player zero-sum games played on priced timed automata (whose locations and transitions are labeled by weights modeling the costs of spending time in a state and executing an action, respectively). The goals of the…

We investigate a two player game called the $K^4$-building game: two players alternately claim edges of an infinite complete graph. Each player's aim is to claim all six edges on some vertex set of size four for themself. The first player…

We present a Spades bidding algorithm that is superior to recreational human players and to publicly available bots. Like in Bridge, the game of Spades is composed of two independent phases, \textit{bidding} and \textit{playing}. This paper…

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…

We study a combinatorial game derived from a problem in the German National Mathematics Competition. In this game, two players take turns removing numbers from a finite set of natural numbers, aiming to satisfy a certain divisibility…

We characterize the initial positions from which the first player has a winning strategy in a certain two-player game. This provides a generalization of Hall's theorem. Vizing's edge coloring theorem follows from a special case.

Holding on to one's strategy is natural and common if the later warrants success and satisfaction. This goes against widespread simulation practices of evolutionary games, where players frequently consider changing their strategy even…

In many combinatorial games, one can prove that the first player wins under best play using a simple but non-constructive argument called strategy-stealing. This work is about the complexity behind these proofs: how hard is it to actually…

This document presents the rules of a tactical two-player board game which is inspired by spin glasses. The aim is, while placing bonds and spins, to achieve a majority of the spins facing the chosen direction of each player. The game has…

We consider games played on finite graphs, whose goal is to obtain a trace belonging to a given set of winning traces. We focus on those states from which Player 1 cannot force a win. We explore and compare several criteria for establishing…

The multiplication game is a two-person game in which each player chooses a positive integer without knowledge of the other player's number. The two numbers are then multiplied together and the first digit of the product determines the…

We revisit the game in which each of several players chooses a pattern and then a coin is flipped repeatedly until one of these patterns is generated. In particular, we demonstrate how to compute the probability of any one player winning…

This paper consider the possibility of using some quantum tools in decision making strategies. In particular, we consider here a dynamical open quantum system helping two players, $\G_1$ and $\G_2$, to take their decisions in a specific…

Playing two-player games using reinforcement learning and self-play can be challenging due to the complexity of two-player environments and the possible instability in the training process. We propose that a reinforcement learning algorithm…

We consider an extension of strategic normal form games with a phase of negotiations before the actual play of the game, where players can make binding offers for transfer of utilities to other players after the play of the game, in order…

Let A be a finite subset of $\nat$. Then NIM(A;n) is the following 2-player game: initially there are $n$ stones on the board and the players alternate removing $a\in A$ stones. The first player who cannot move loses. This game has been…

We introduce and study an evolutionary complementarity game where in each round a player of population 1 is paired with a member of population 2. The game is symmetric, and each player tries to obtain an advantageous deal, but when one of…

Recent work in reinforcement learning demonstrated that learning solely through self-play is not only possible, but could also result in novel strategies that humans never would have thought of. However, optimization methods cast as a game…