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Game theory is playing more and more important roles in understanding complex systems and in investigating intelligent machines with various uncertainties. As a starting point, we consider the classical two-player zero-sum linear-quadratic…
We introduce a new virtual environment for simulating a card game known as "Big 2". This is a four-player game of imperfect information with a relatively complicated action space (being allowed to play 1,2,3,4 or 5 card combinations from an…
In robot games on Z, two players add integers to a counter. Each player has a finite set from which he picks the integer to add, and the objective of the first player is to let the counter reach 0. We present an exponential-time algorithm…
This paper aims to solve two fundamental problems on finite or infinite horizon dynamic games with perfect or almost perfect information. Under some mild conditions, we prove (1) the existence of subgame-perfect equilibria in general…
We prove the existence and computability of optimal strategies in weighted limit games, zero-sum infinite-duration games with a B\"uchi-style winning condition requiring to produce infinitely many play prefixes that satisfy a given regular…
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…
We prove the existence and computability of optimal strategies in weighted limit games, zero-sum infinite-duration games with a B\"uchi-style winning condition requiring to produce infinitely many play prefixes that satisfy a given regular…
We consider linear problems in the worst case setting. That is, given a linear operator and a pool of admissible linear measurements, we want to approximate the values of the operator uniformly on a convex and balanced set by means of…
This short paper describes an ongoing research project that requires the automated self-play learning and evaluation of a large number of board games in digital form. We describe the approach we are taking to determine relevant features,…
We study two-player concurrent stochastic games on finite graphs, with B\"uchi and co-B\"uchi objectives. The goal of the first player is to maximize the probability of satisfying the given objective. Following Martin's determinacy theorem…
Energy parity games are infinite two-player turn-based games played on weighted graphs. The objective of the game combines a (qualitative) parity condition with the (quantitative) requirement that the sum of the weights (i.e., the level of…
Quantum technologies, i.e., technologies benefiting from the features of quantum physics such as objective randomness, superposition, and entanglement, have enabled an entirely different way of distributing and processing information. The…
Infinite-state games are a commonly used model for the synthesis of reactive systems with unbounded data domains. Symbolic methods for solving such games need to be able to construct intricate arguments to establish the existence of winning…
Poker is in the family of imperfect information games unlike other games such as chess, connect four, etc which are perfect information game instead. While many perfect information games have been solved, no non-trivial imperfect…
The objective of this book is to give a comprehensive presentation of the research field concerned with infinite duration games on graphs. Historically, these game models appeared in the study of automata and logic, and they later became…
This paper has two central aims: first, to provide simple conditions under which the generalized games in choice form and, consequently, the abstract economies, admit equilibrium; second, to study the solvability of several types of systems…
We study Stackelberg equilibria in finitely repeated games, where the leader commits to a strategy that picks actions in each round and can be adaptive to the history of play (i.e. they commit to an algorithm). In particular, we study…
We introduce the notion of universal graphs as a tool for constructing algorithms solving games of infinite duration such as parity games and mean payoff games. In the first part we develop the theory of universal graphs, with two goals:…
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…
The article presents research on the use of Monte-Carlo Tree Search (MCTS) methods to create an artificial player for the popular card game "The Lord of the Rings". The game is characterized by complicated rules, multi-stage round…