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Small Progress Measures is one of the classical parity game solving algorithms. For games with n vertices, m edges and d different priorities, the original algorithm computes the winning regions and a winning strategy for one of the players…
Evolutionary game theory is a powerful mathematical framework to study how intelligent individuals adjust their strategies in collective interactions. It has been widely believed that it is impossible to unilaterally control players'…
We will try to tackle both the theoretical and practical aspects of a very important problem in chess programming as stated in the title of this article - the issue of draw detection by move repetition. The standard approach that has so far…
In several standard models of dynamic programming (gambling houses, MDPs, POMDPs), we prove the existence of a very robust notion of value for the infinitely repeated problem, namely the pathwise uniform value. This solves two open…
We investigate pruning in search trees of so-called quantified integer linear programs (QIPs). QIPs consist of a set of linear inequalities and a minimax objective function, where some variables are existentially and others are universally…
Minimax-based search algorithms with alpha-beta pruning and transposition tables are a central component of classical game-playing engines and remain widely used in practice. Despite their widespread use, these algorithms are subtle, highly…
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…
The landmark achievements of AlphaGo Zero have created great research interest into self-play in reinforcement learning. In self-play, Monte Carlo Tree Search is used to train a deep neural network, that is then used in tree searches.…
This book summarizes ongoing research introducing probability space isomorphic mappings into the strategy spaces of game theory. This approach is motivated by discrepancies between probability theory and game theory when applied to the same…
Monte-Carlo Tree Search (MCTS) is a family of sampling-based search algorithms widely used for online planning in sequential decision-making domains and at the heart of many recent advances in artificial intelligence. Understanding the…
Tackling simulation optimization problems with non-convex objective functions remains a fundamental challenge in operations research. In this paper, we propose a class of random search algorithms, called Regular Tree Search, which…
Evolutionary game theory classically investigates which behavioral patterns are evolutionarily successful in a single game. More recently, a number of contributions have studied the evolution of preferences instead: which subjective…
Game-theoretic probability uses the structure of gambles to define a concept like probability, but which is more flexible and robust. We show that results in game-theoretic probability can be thought of as minimax theorems for specific…
Recent advances in bandit tools and techniques for sequential learning are steadily enabling new applications and are promising the resolution of a range of challenging related problems. We study the game tree search problem, where the goal…
Strategic-form min-max game theory examines the existence, multiplicity, selection of equilibria, and the worst-case computational complexity under perfect rationality. However, in many applications, games are drawn from an ensemble, and…
This paper proposes a new mechanism for pruning a search game-tree in computer chess. The algorithm stores and then reuses chains or sequences of moves, built up from previous searches. These move sequences have a built-in forward-pruning…
In decision problems, often, utilities and probabilities are hard to determine. In such cases, one can resort to so-called choice functions. They provide a means to determine which options in a particular set are optimal, and allow…
We consider how an agent should update her uncertainty when it is represented by a set P of probability distributions and the agent observes that a random variable X takes on value x, given that the agent makes decisions using the minimax…
In this paper, we analyse a misere tree searching game, where players take turns to guess vertices in a tree with a secret `poisoned' vertex. After each turn, the guessed vertex is removed from the tree and the game continues on the…
This paper introduces a novel algorithm for two-player deterministic games with perfect information, which we call PROBS (Predict Results of Beam Search). Unlike existing methods that predominantly rely on Monte Carlo Tree Search (MCTS) for…