Related papers: The Game of Pure Strategy is solved!

We will describe a combinatorial game that models the problem of resolution of singularities of algebraic varieties over a field of characteristic zero. By giving a winning strategy for this game, we give another proof of the existence of…

This paper discusses the problem of efficiently solving parity games where player Odd has to obey an additional 'strong transition fairness constraint' on its vertices -- given that a player Odd vertex $v$ is visited infinitely often, a…

While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the properties that optimal solutions need to have, and devised a…

While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the constraints that optimal solutions need to satisfy, and…

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…

We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). We introduce these basic ideas in the context of a simple example, closely…

Games have a long history as benchmarks for progress in artificial intelligence. Approaches using search and learning produced strong performance across many perfect information games, and approaches using game-theoretic reasoning and…

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…

We study pure-strategy Nash equilibria in multi-player concurrent deterministic games, for a variety of preference relations. We provide a novel construction, called the suspect game, which transforms a multi-player concurrent game into a…

This paper studies the equilibrium properties of the ``obvious strategy profile'' in large finite-player games. Each player in such a strategy profile simply adopts a randomized strategy as she would have used in a symmetric equilibrium of…

Previous works suggested the use of Branch and Bound techniques for finding the optimal allocation in (multi-unit) combinatorial auctions. They remarked that Linear Programming could provide a good upper-bound to the optimal allocation, but…

In classical game theory, optimal strategies are determined for games with complete information; this requires knowledge of the opponent's goals. We analyze games when a player is mistaken about their opponents goals. For definitiveness, we…

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…

Something is definitely wrong. If the game has a linear winning strategy, then it is tractable. What's going on? Well, we describe a two-person game which has a definite winner, that is, a player who can force a win in a finite number of…

We show that the higher-order matching problem is decidable using a game-theoretic argument.

Consider a very simple class of (finite) games: after an initial move by nature, each player makes one move. Moreover, the players have common interests: at each node, all the players get the same payoff. We show that the problem of…

Parity games are infinite two-player games played on directed graphs. Parity game solvers are used in the domain of formal verification. This paper defines parametrized parity games and introduces an operation, Justify, that determines a…

We characterize winning strategies in various infinite games involving filters on the natural numbers in terms of combinatorics or structural properties of the given filter. These generalize several ultrafilter games of Galvin.

We present efficient algorithms for computing optimal or approximately optimal strategies in a zero-sum game for which Player I has n pure strategies and Player II has an arbitrary number of pure strategies. We assume that for any given…

We revisit classic algorithmic search and optimization problems from the perspective of competition. Rather than a single optimizer minimizing expected cost, we consider a zero-sum game in which an optimization problem is presented to two…