Related papers: Assessing Game Balance with AlphaZero: Exploring A…

Learning from repeated play in a fixed two-player zero-sum game is a classic problem in game theory and online learning. We consider a variant of this problem where the game payoff matrix changes over time, possibly in an adversarial…

Decision-making agents with planning capabilities have achieved huge success in the challenging domain like Chess, Shogi, and Go. In an effort to generalize the planning ability to the more general tasks where the environment dynamics are…

Crazyhouse is a chess variant that incorporates all of the classical chess rules, but allows users to drop pieces captured from the opponent as a normal move. Until 2018, all competitive computer engines for this board game made use of an…

We study the problem of repeated play in a zero-sum game in which the payoff matrix may change, in a possibly adversarial fashion, on each round; we call these Online Matrix Games. Finding the Nash Equilibrium (NE) of a two player zero-sum…

The emergence of complex structures in the systems governed by a simple set of rules is among the most fascinating aspects of Nature. The particularly powerful and versatile model suitable for investigating this phenomenon is provided by…

From the standpoint of game theory, dominoes is a game that has not received much attention (specially the variety known as draw). It is usually thought that this game is already solved, given general results in game theory. However, the…

We study an independent best-response dynamics on network games in which the nodes (players) decide to revise their strategies independently with some probability. We provide several bounds on the convergence time to an equilibrium as a…

Nash equilibrium is often heralded as a guiding principle for rational decision-making in strategic interactions. However, it is well-known that Nash equilibrium sometimes fails as a reliable predictor of outcomes, with two of the most…

Powerful artificial intelligence systems are often used in settings where they must interact with agents that are computationally much weaker, for example when they work alongside humans or operate in complex environments where some tasks…

Randomized mechanisms can have good normative properties compared to their deterministic counterparts. However, randomized mechanisms are problematic in several ways such as in their verifiability. We propose here to derandomize such…

This paper investigates Nash equilibria in pure strategies for quantum approach to the Prisoner's Dilemma. The quantization process involves extending the classical game by introducing two additional unitary strategies. We consider five…

Classical game theory is a powerful framework to analyze the strategic interactions among rational players. However, in many real-life scenarios, players choose actions based on their inherent natural tendencies rather than deliberate…

Balancing an ever growing strategic game of high complexity, such as Hearthstone is a complex task. The target of making strategies diverse and customizable results in a delicate intricate system. Tuning over 2000 cards to generate the…

Hex and Counter Wargames are adversarial two-player simulations of real military conflicts requiring complex strategic decision-making. Unlike classical board games, these games feature intricate terrain/unit interactions, unit stacking,…

AlphaZero learns to play go, chess and shogi at a superhuman level through self play given only the rules of the game. This raises the question of whether a similar thing could be done for mathematics -- a MathZero. MathZero would require a…

We analyze the performance of the best-response dynamic across all normal-form games using a random games approach. The playing sequence -- the order in which players update their actions -- is essentially irrelevant in determining whether…

Blotto Games are a popular model of multi-dimensional strategic resource allocation. Two players allocate resources in different battlefields in an auction setting. While competition with equal budgets is well understood, little is known…

This work presents a novel policy iteration algorithm to tackle nonzero-sum stochastic impulse games arising naturally in many applications. Despite the obvious impact of solving such problems, there are no suitable numerical methods…

The recently released AlphaZero algorithm achieves superhuman performance in the games of chess, shogi and Go, which raises two open questions. Firstly, as there is a finite number of possibilities in the game, is there a quantifiable…

Zero-sum games such as chess and poker are, abstractly, functions that evaluate pairs of agents, for example labeling them `winner' and `loser'. If the game is approximately transitive, then self-play generates sequences of agents of…