Related papers: Best play in Dots and Boxes endgames

Von Neumann's Min-Max Theorem guarantees that each player of a zero-sum matrix game has an optimal mixed strategy. This paper gives an elementary proof that each player has a near-optimal mixed strategy that chooses uniformly at random from…

Consider concurrent, infinite duration, two-player win/lose games played on graphs. If the winning condition satisfies some simple requirement, the existence of Player 1 winning (finite-memory) strategies is equivalent to the existence of…

In this paper, we consider $\mathcal{L}\mathcal{R}$-ending partisan rulesets as a branch of combinatorial game theory. In these rulesets, the sets of options of both players are the same. However, there are two kinds of terminal positions.…

This paper investigates repeated win-lose coordination games (WLC-games). We analyse which protocols are optimal for these games covering both the worst case and average case scenarios, i,e., optimizing the guaranteed and expected…

In an all-pay auction, only one bidder wins but all bidders must pay the auctioneer. All-pay bidding games arise from attaching a similar bidding structure to traditional combinatorial games to determine which player moves next. In contrast…

In games with a large number of players where players may have overlapping objectives, the analysis of stable outcomes typically depends on player types. A special case is when a large part of the player population consists of imitation…

We consider extensive games with perfect information with well-founded game trees and study the problems of existence and of characterization of the sets of subgame perfect equilibria in these games. We also provide such characterizations…

Parity games are abstract infinite-round games that take an important role in formal verification. In the basic setting, these games are two-player, turn-based, and played under perfect information on directed graphs, whose nodes are…

The convergence of online learning algorithms in games under self-play is a fundamental question in game theory and machine learning. Among various notions of convergence, last-iterate convergence is particularly desirable, as it reflects…

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 study (a:a) Maker-Breaker games played on the edge set of the complete graph on n vertices. In the following four games - perfect matching game, Hamilton cycle game, star factor game and path factor game, our goal is to determine the…

We show the existence and effective computability of optimal winning strategies for request-response games in case the quality of a play is measured by the limit superior of the mean accumulated waiting times between requests and their…

We consider two-player stochastic games played on a finite graph for infinitely many rounds. Stochastic games generalize both Markov decision processes (MDP) by adding an adversary player, and two-player deterministic games by adding…

Players are arranged on a regular lattice and coded with a specific strategy for a pre-defined game. Each player sums their payoffs from playing the game with each of their neighbors, and then adopts the strategy of the most successful…

Taking the absolute value of consecutive differences of a cyclicly ordered list of integers constitutes a simple dynamical system. For lists of lenght a power of two the process will terminate in all zeros, but examples with arbitarily long…

Game theory has emerged as a powerful framework for modeling a large range of multi-agent scenarios. Many algorithmic solutions require discrete, finite games with payoffs that have a closed-form specification. In contrast, many real-world…

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 study strategic games on weighted directed graphs, in which the payoff of a player is defined as the sum of the weights on the edges from players who chose the same strategy, augmented by a fixed non-negative integer bonus for picking a…

We define a class of zero-sum games with combinatorial structure, where the best response problem of one player is to maximize a submodular function. For example, this class includes security games played on networks, as well as the problem…

This paper revisits the problem of predicting box locations in object detection architectures. Typically, each box proposal or box query aims to directly maximize the intersection-over-union score with the ground truth, followed by a…