A Graph Theoretical Model for the Total Balancedness of Combinatorial Games
نویسندگان
چکیده
In this paper we present a model for the study of the total balancedness of packing and covering games, concerning some aspects of graph theory. We give an alternative proof of van Velzen’s characterization of totally balanced covering games. We introduce new types of graph perfection, which allows us to give another approach to the open problem of characterizing totally balanced packing games.
منابع مشابه
Universally Balanced Combinatorial Optimization Games
This article surveys studies on universally balanced properties of cooperative games defined in a succinct form. In particular, we focus on combinatorial optimization games in which the values to coalitions are defined through linear optimization programs, possibly combinatorial, that is subject to integer constraints. In economic settings, the integer requirement reflects some forms of indivis...
متن کاملAn Efficient and Fair Solution for Communication Graph Games
We introduce an efficient solution for games with communication graph structures and show that it is characterized by efficiency, fairness and a new axiom called component balancedness. This latter axiom compares for every component in the communication graph the total payoff to the players of this component in the game itself to the total payoff of these players when applying the solution to t...
متن کاملDominating set games
In this paper we study cooperative cost games arising from domination problems on graphs. We introduce three games to model the cost allocation problem and we derive a necessary and sufficient condition for the balancedness of all three games. Furthermore we study concavity of these games.
متن کاملBalancedness of Integer Domination Games
In this paper, we consider cooperative games arising from integer domination problem on graphs. We introduce two games, {k}-domination game and its monotonic relaxed game, and focus on their cores. We first give characterizations of the cores and the relationship between them. Furthermore, a common necessary and sufficient condition for the balancedness of both games is obtained by making use o...
متن کاملCombinatorial Games on Graphs
The theory of combinatorial games is a rapidly developing subject of modern combinatorics. It is concerned with the study of certain twoplayer-games, ranging from popular games as Tic-Tac-Toe and Connect Four to merely abstract games defined in graph-theoretic terms. Besides being of interest on their own right, combinatorial games are strongly connected to other areas of combinatorics, such as...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012