Related papers: Set Equality in Combinatorial Game Theory
We are studying the Gately point, an established solution concept for cooperative games. We point out that there are superadditive games for which the Gately point is not unique, i.e. in general the concept is rather set-valued than an…
The computation of a solution concept of a cooperative game usually employs values of all coalitions. However, in some applications, the values of some of the coalitions might be unknown due to high costs associated with their determination…
We study a combinatorial game derived from a problem in the German National Mathematics Competition. In this game, two players take turns removing numbers from a finite set of natural numbers, aiming to satisfy a certain divisibility…
We develop a generic computational model that can be used effectively for establishing the existence of winning strategies for concrete finite combinatorial games. Our modelling is (equational) logic-based involving advanced techniques from…
The coherence of an individual quantum state can be meaningfully discussed only when referring to a preferred basis. This arbitrariness can however be lifted when considering sets of quantum states. Here we introduce the concept of set…
Egalitarian considerations play a central role in many areas of social choice theory. Applications of egalitarian principles range from ensuring everyone gets an equal share of a cake when deciding how to divide it, to guaranteeing balance…
We propose a novel algorithm for the solution of mean-payoff games that merges together two seemingly unrelated concepts introduced in the context of parity games, small progress measures and quasi dominions. We show that the integration of…
A systematic theory is introduced that describes stochastic effects in game theory. In a biological context, such effects are relevant for the evolution of finite populations with frequency-dependent selection. They are characterized by…
In 1901, Bouton proved that a winning strategy of the game of Nim is given by the bitwise XOR, called the nim-sum. But, why does such a weird binary operation work? Led by this question, this paper introduces a categorical reinterpretation…
We generalize the notion of convexity and average-convexity to the notion of weighted average-convexity. We show several results on the relation between weighted average-convexity and cooperative games. First, we prove that if a game is…
The core of a cooperative game on a set of players $N$ is one of the most popular concept of solution. When cooperation is restricted (feasible coalitions form a subcollection $\cF$ of $2^N$), the core may become unbounded, which makes it…
This article introduces differential hybrid games, which combine differential games with hybrid games. In both kinds of games, two players interact with continuous dynamics. The difference is that hybrid games also provide all the features…
In this paper, we introduce a framework of new mathematical representation of Game Theory, including static classical game and static quantum game. The idea is to find a set of base vectors in every single-player strategy space and to…
We introduce the category of optiongraphs and option-preserving maps as a model to study impartial combinatorial games. Outcomes, remoteness, and extended nim-values are preserved under option-preserving maps. We show that the four…
We present a definition for the sum of a sequence of combinatorial games. This sum coincides with the classical sum in the case of a converging sequence of real numbers and with the infinitary natural sum in the case of a sequence of…
The basic Monty Hall problem is explored to introduce into the fundamental concepts of the game theory and to give a complete Bayesian and a (noncooperative) game-theoretic analysis of the situation. Simple combinatorial arguments are used…
Matching games naturally generalize assignment games, a well-known class of cooperative games. Interest in matching games has grown recently due to some breakthrough results and new applications. This state-of-the-art survey provides an…
Mathematical reasoning with algebraic and graphical representations is essential for success in physics courses. Many problems require students to fluently move between algebraic and graphical representations. We developed a freely…
We propose an alternative to the tree representation of extensive form games. Games in product form represent information with $\sigma$-fields over a product set, and do not require an explicit description of the play temporality, as…
Correlated equilibria -- and their generalization $\Phi$-equilibria -- are a fundamental object of study in game theory, offering a more tractable alternative to Nash equilibria in multi-player settings. While computational aspects of…