Related papers: Endgames in bidding chess
A Richman game is a combinatorial game in which, rather than alternating moves, the two players bid for the privilege of making the next move. We consider both the case where the players pay each other and the case where the players pay a…
In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner of the game. Such games are central in formal methods since they model the interaction between a…
Two-player games on graphs are widely studied in formal methods as they model the interaction between a system and its environment. The game is played by moving a token throughout a graph to produce an infinite path. There are several…
We study variations on combinatorial games in which, instead of alternating moves, the players bid with discrete bidding chips for the right to determine who moves next. We consider both symmetric and partisan games, and explore differences…
Richman games are zero-sum games, where in each turn players bid in order to determine who will play next [Lazarus et al.'99]. We extend the theory to impartial general-sum two player games called \emph{bidding games}, showing the existence…
Graph games lie at the algorithmic core of many automated design problems in computer science. These are games usually played between two players on a given graph, where the players keep moving a token along the edges according to…
In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner or payoff of the game. We study {\em bidding games} in which the players bid for the right to move the token.…
Combinatorial Game Theory is a branch of mathematics and theoretical computer science that studies sequential 2-player games with perfect information. Normal play is the convention where a player who cannot move loses. Here, we generalize…
In a two-player zero-sum graph game the players move a token throughout a graph to produce an infinite path, which determines the winner or payoff of the game. Traditionally, the players alternate turns in moving the token. In {\em bidding…
In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner or payoff of the game. Such games are central in formal verification since they model the interaction between a…
Two-player zero-sum "graph games" are a central model, which proceeds as follows. A token is placed on a vertex of a graph, and the two players move it to produce an infinite "play", which determines the winner or payoff of the game.…
We study zero-sum (combinatorial) games, within the framework of so-called Richman auctions (Lazarus et al. 1996) namely, we modify the alternating play scoring ruleset Cumulative Subtraction (CS) (Cohensius et al. 2019), to a discrete…
In a two-player zero-sum graph game, the players move a token throughout a graph to produce an infinite play, which determines the winner of the game. Bidding games are graph games in which in each turn, an auction (bidding) determines…
Two-player graph games are a fundamental model for reasoning about the interaction of agents. These games are played between two players who move a token along a graph. In bidding games, the players have some monetary budget, and at each…
In this paper we introduce and study {\em all-pay bidding games}, a class of two player, zero-sum games on graphs. The game proceeds as follows. We place a token on some vertex in the graph and assign budgets to the two players. Each turn,…
We consider Chess played on an $m \times n$ board (with $m$ and $n$ arbitrary positive integers), with only the two kings and the white rook remaining, but placed at arbitrary positions. Using the symbolic finite state method, developed by…
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…
We consider {\em bidding games}, a class of two-player zero-sum {\em graph games}. The game proceeds as follows. Both players have bounded budgets. A token is placed on a vertex of a graph, in each turn the players simultaneously submit…
We investigate the transfinite game values arising in infinite chess, providing both upper and lower bounds on the supremum of these values---the omega one of chess---with two senses depending on whether one considers only finite positions…
In an investigation of the applications of Combinatorial Game Theory to chess, we construct novel mutual Zugzwang positions, explain an otherwise mysterious pawn endgame from "A Guide to Chess Endings" (Euwe and Hooper), show positions…