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Calculations and mechanistic explanations for the probabilistic movement of objects at the highly relevant cm length scales has been lacking and overlooked due to the complexity of current techniques. Predicting the final-configuration…

We use ideas from distributed computing and game theory to study dynamic and decentralized environments in which computational nodes, or decision makers, interact strategically and with limited information. In such environments, which arise…

The theory of learning in games has extensively studied situations where agents respond dynamically to each other by optimizing a fixed utility function. However, in real situations, the strategic environment varies as a result of past…

This work establishes sufficient conditions for existence of saddle points in discrete Markov games. The result reveals the relation between dynamic games and static games using dynamic programming equations. This result enables us to prove…

We provide two methodologies in the area of computation theory to solve optimal strategies for board games such as Xi Gua Qi and Go. From experimental results, we find relevance to graph theory, matrix representation, and mathematical…

Game theory has been one of the most successful quantitative concepts to describe social interactions, their strategical aspects, and outcomes. Among the payoff matrix quantifying the result of a social interaction, the interaction…

Since the advent of computers, many tasks which required humans to spend a lot of time and energy have been trivialized by the computers' ability to perform repetitive tasks extremely quickly. Playing chess is one such task. It was one of…

We study games in which every action requires planning and preparation. Moreover, before players act, they can revise their plans based on partially revealing information that they receive on their adversary's preparations. In turn, we…

The game of chess is well-known and widely played all over the world. However, the rules for playing it are rather complex since there are different types of pieces and the ways they are allowed to move depend upon the type of the piece. In…

We use logistic regression to estimate the value of the pieces in standard chess and several chess variants, namely Chess 960, Atomic chess, Antichess, and Horde chess. We perform our regressions on several years of data from Lichess, the…

A version of the Schelling model on $\mathbb{Z}$ is defined, where two types of agents are allocated on the sites. An agent prefers to be surrounded by other agents of its own type, and may choose to move if this is not the case. It then…

We consider (random) strategic interactions in a large population consisting of a variety of players. A rational player chooses actions that maximize certain utility functions, while a behavioral player chooses actions based on preferences…

We study a stochastic game where one player tries to find a strategy such that the state process reaches a target of controlled-loss-type, no matter which action is chosen by the other player. We provide, in a general setup, a relaxed…

Patterns of wins and losses in pairwise contests, such as occur in sports and games, consumer research and paired comparison studies, and human and animal social hierarchies, are commonly analyzed using probabilistic models that allow one…

We study a class of stochastic dynamic games that exhibit strategic complementarities between players; formally, in the games we consider, the payoff of a player has increasing differences between her own state and the empirical…

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…

We study the quality of outcomes in repeated games when the population of players is dynamically changing and participants use learning algorithms to adapt to the changing environment. Game theory classically considers Nash equilibria of…

In many social dilemmas, individuals tend to generate a situation with low payoffs instead of a system optimum ("tragedy of the commons"). Is the routing of traffic a similar problem? In order to address this question, we present…

We perform a quantitative analysis of extensive chess databases and show that the frequencies of opening moves are distributed according to a power-law with an exponent that increases linearly with the game depth, whereas the pooled…

Passing during power plays in hockey is a crucial component to move one's team closer to scoring a goal. With the use of women's ice hockey event and tracking data from the elimination round games during the 2022 Winter Olympics, we…