相关论文: The topology of simple games

The relationship between topology and dynamics of complex systems has motivated continuing interest from the scientific community. In the present work, we address this interesting topic from the perspective of simple games, involving two…

We use simplicial complexes to model simple games as well as weighted voting games where certain coalitions are considered impossible. Topological characterizations of various ideas from simple games are provided, as are the expressions for…

We use the topology of simplicial complexes to model political structures following [1]. Simplicial complexes are a natural tool to encode interactions in the structures since a simplex can be used to represent a subset of compatible…

We present an algebraic framework for the analysis of combinatorial games. This framework embraces the classical theory of partizan games as well as a number of misere games, comply-constrain games, and card games that have been studied…

Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…

We present a unified approach, based on dominating families in binary relations, for the study of topological properties defined in terms of selection principles and the games associated to them.

Combinatorial Game Theory is a branch of mathematics and theoretical computer science that studies sequential 2-player games with perfect information. Normal play is the convention where a player who cannot move loses. Here, we generalize…

We analyze the computational complexity of the problem of deciding whether, for a given simple game, there exists the possibility of rearranging the participants in a set of $j$ given losing coalitions into a set of $j$ winning coalitions.…

In this manuscript, we define and study probabilistic values for cooperative games on simplicial complexes. Inspired by the work of Weber "Probabilistic values for games", we establish the new theory step by step, following the classical…

We will describe a combinatorial game that models the problem of resolution of singularities of algebraic varieties over a field of characteristic zero. By giving a winning strategy for this game, we give another proof of the existence of…

Placement games are a subclass of combinatorial games which are played on graphs. We will demonstrate that one can construct simplicial complexes corresponding to a placement game, and this game could be considered as a game played on these…

A solution concept on a class of transferable utility coalitional games is a multifunction satisfying given criteria of economic rationality. Every solution associates a set of payoff allocations with a coalitional game. This general…

We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…

Consider a situation with $n$ agents or players where some of the players form a coalition with a certain collective objective. Simple games are used to model systems that can decide whether coalitions are successful (winning) or not…

Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of ``yea''…

The class of algorithmically computable simple games (i) includes the class of games that have finite carriers and (ii) is included in the class of games that have finite winning coalitions. This paper characterizes computable games,…

With increasing game size, a problem of computational complexity arises. This is especially true in real world problems such as in social systems, where there is a significant population of players involved in the game, and the complexity…

Classify simple games into sixteen "types" in terms of the four conventional axioms: monotonicity, properness, strongness, and nonweakness. Further classify them into sixty-four classes in terms of finiteness (existence of a finite carrier)…

A combinatorial simplex algorithm is an instance of the simplex method in which the pivoting depends on combinatorial data only. We show that any algorithm of this kind admits a tropical analogue which can be used to solve mean payoff…

In a vintage paper concerning Parsimonious games, a subset of constant sum homogeneous weighted majority games, Isbell introduced a twin relationship based on transposition properties of the incidence matrices upon minimal winning…