Related papers: Cumulative Games: Who is the current player?
In Combinatorial Game Theory, the fundamental relation of game equivalence, denoted by $=$, is introduced early on and overrides the notion of set equality. We explore what happens if set equality is given its due before game equivalence is…
In this paper, we introduce a notion of generalized potential games that is inspired by a newly developed theory on generalized gradient flows. More precisely, a game is called generalized potential if the simultaneous gradient of the loss…
In Combinatorial Game Theory, short game forms are defined recursively over all the positions the two players are allowed to move to. A form is decomposable if it can be expressed as a disjunctive sum of two forms with smaller birthday. If…
The theory of combinatorial game (like board games) and the theory of social games (where one looks for Nash equilibria) are normally considered as two separate theories. Here we shall see what comes out of combining the ideas. The central…
The extensive-form game has been studied considerably in recent years. It can represent games with multiple decision points and incomplete information, and hence it is helpful in formulating games with uncertain inputs, such as poker. We…
Game theory is the mathematical framework for analyzing strategic interactions in conflict and competition situations. In recent years quantum game theory has earned the attention of physicists, and has emerged as a branch of quantum…
A combinatorial game is a two-player game without hidden information or chance elements. The disjunctive sum $G + H$ of games $G$ and $H$ is the game in which $G$ and $H$ are played in parallel, and a player makes a move on exactly one of…
Hybrid games are models which combine discrete, continuous, and adversarial dynamics. Game logic enables proving (classical) existence of winning strategies. We introduce constructive differential game logic (CdGL) for hybrid games, where…
We apply the generalized conditional gradient algorithm to potential mean field games and we show its well-posedeness. It turns out that this method can be interpreted as a learning method called fictitious play. More precisely, each step…
Game theory is a powerful analytical tool for modeling decision makers strategies, behaviors and interactions. Act and decisions of a decision maker can benefit or negatively impact other decision makers interests. Game theory has been…
Data mining and knowledge discovery are two important growing research fields in the last two decades due to the abundance of data collected from various sources. The exponentially growing volumes of generated data urge the development of…
Two-player quantitative zero-sum games provide a natural framework to synthesize controllers with performance guarantees for reactive systems within an uncontrollable environment. Classical settings include mean-payoff games, where the…
Two-player zero-sum games are a well-established model for synthesising controllers that optimise some performance criterion. In such games one player represents the controller, while the other describes the (adversarial) environment, and…
In this paper, we propose a Quantum variation of combinatorial games, generalizing the Quantum Tic-Tac-Toe proposed by Allan Goff. A combinatorial game is a two-player game with no chance and no hidden information, such as Go or Chess. In…
Poset games have been the object of mathematical study for over a century, but little has been written on the computational complexity of determining important properties of these games. In this introduction we develop the fundamentals of…
Game theory is an established branch of mathematics that offers a rich set of mathematical tools for multi-person strategic decision making that can be used to model the interactions of decision makers in security problems who compete for…
We introduce a simple extensive-form algorithm for finding equilibria of two-player, zero-sum games. The algorithm is realization equivalent to a generalized form of Fictitious Play. We compare its performance to that of a similar…
The known results regarding two-player zero-sum games are naturally generalized in complex space and are presented through a complete compact theory. The payoff function is defined by the real part of the payoff function in the real case,…
Game Theory (GT) has been used with significant success to formulate, and either design or optimize, the operation of many representative communications and networking scenarios. The games in these scenarios involve, as usual, diverse…
Cumulative Games were introduced by Larsson, Meir, and Zick (2020) to bridge some conceptual and technical gaps between Combinatorial Game Theory (CGT) and Economic Game Theory. The partizan ruleset {\sc Robin Hood} is an instance of a…