Dominating 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 su cient condition for the balancedness of all three games.Furthermore we study concavity of these games.game theory;cost allocation;cooperative games

Socially Structured Games and their Applications

In this paper we generalize the concept of a non-transferable utility game by introducing the concept of a socially structured game.A socially structured game is given by a set of players, a possibly empty collection of internal organizations on any subset of players, for any internal organization a set of attainable payo.s and a function on the collection of all internal organizations measuring the power of every player within the internal organization.Any socially structured game induces a non-transferable utility game.In the derived nontransferable utility game, all information concerning the dependence of attainable payo.s on the internal organization gets lost.We show this information to be useful for studying non-emptiness and re.nements of the core. For a socially structured game we generalize the concept of p-balancedness to social stability and show that a socially stable game has a non-empty socially stable core.In order to derive this result, we formulate a new intersection theorem that generalizes the KKM-Shapley intersection theorem.The socially stable core is a subset of the core of the game.We give an example of a socially structured game that satis.es social stability, whose induced non-transferable utility game therefore has a non-empty core, but does not satisfy p-balanced for any choice of p.The usefulness of the new concept is illustrated by some applications and examples.In particular we de.ne a socially structured game, whose unique element of the socially stable core corresponds to the Cournot-Nash equilibrium of a Cournot duopoly.This places the paper in the Nash research program, looking for a unifying approach to cooperative and non-cooperative behavior in which each theory helps to justify and clarify the other.game theory

The core of bicapacities and bipolar games

Bicooperative games generalize classical cooperative games in the sense that a player is allowed to play in favor or against some aim, besides non participation. Bicapacities are monotonic bicooperative games, they are useful in decision making where underlying scales are of bipolar nature, i.e., they distinguish between good/satisfactory values and bad/unsatisfactory ones. We propose here a more general framework to represent such situations, called bipolar game. We study the problem of finding the core of such games, i.e., theset of additive dominating games.fuzzy measure, bicapacity, cooperative game, bipolar scale,core

Monotonicity of Social Optima With Respect to Participation Constraints.

In this paper we consider solutions which select from the core. For games with side payments with at least four players, it is well-known that no core-selection satifies monotonicity for all coalitions; for the particular class of core-selections found by maximizing a social welfare function over the core, we investigate whether such solutions are monotone for a given coalition. It is shown that if this is the case then the solution actually maximizes aggregate coalition payoff on the core. Furthermore, the social welfare function to be maximized exhibits larger marginal social welfare with respect to the payoff of any member of the coalition. The results may be used to show that there are no monotonic core selection rules of this type in the context of games without side payments.coalitional games; monotonicity; core; social welfare

The Coalition Structure Core is Accessible

For each outcome (i.e.~a payoff vector augmented with a coalition structure) of a TU-game with a non-empty coalition structure core there exists a finite sequence of successively dominating outcomes that terminates in the coalition structure core. In order to obtain this result a restrictive dominance relation - which we label outsider independent - is employed.Coalition structure, core-extension, non-emptiness, dominance

The Core Can Be Accessed in a Bounded Number of Steps

This paper strengthens the result of Sengupta and Sengupta (1996). We show that for the class of games with nonempty cores the core can be reached in a bounded number of proposals and counterproposals. Our result is more general than this: the boundedness holds for any two imputations with an indirect dominance relation between them.dynamic cooperative game, indirect dominance, core.

Domination problems in social networks

The thesis focuses on domination problems in social networks. Domination problems are one of the classical types of problems in computer science. Domination problems are fundamental and widely studied problems in algorithms and complexity theory. They have been extensively studied and adopted in many real-life applications. In general, a set D of vertices of a simple (no loops or multiple edges), undirected graph G = (V,E) is called dominating if each vertex in V −D is adjacent to some vertex in D. The computational problem of computing a dominating set of minimum size is known as “the dominating set problem”. The dominating set problem is NP-hard in general graphs. A social network - the graph of relationships and interactions within a group of individuals - plays a fundamental role as a medium for the spread of information, ideas, and influence among its members. In a social network, people, who have problems such as drinking, smoking and drug use related issues, can have both positive and negative impact on each other and a person can take and move among different roles since they are affected by their peers. As an example, positive impacts of intervention and education programs on a properly selected set of initial individuals can diffuse widely into society via various social contacts: face to face, phone calls, email, social networks and so on. Exploiting the relationships and influences among individuals in social networks might offer considerable benefit to both the economy and society. In order to deal with social problems, the positive influence dominating set (PIDS) is a typical one to help people to alleviate these social problems. However, existing PIDS algorithms are usually greedy and finding approximation solutions that are inefficient for the growing social networks. By now these proposed algorithms can deal with social problems only in undirected social networks with uniform weight value. To overcome the shortcomings of the existing PIDS model, a novel domination model namely weight positive influence dominating set (WPIDS) is presented. A main contribution of the thesis is that the proposed WPIDS model can be applied in weighted directed social networks. It considers the direction and degree of users’ influence in social networks in which the PIDS model does not. The experimental results have revealed that the WPIDS model is more effective than the PIDS model. At the same time, thanks to the publication of Dijkstra’s pioneering paper, a lot of self-stabilizing algorithms for computing minimal dominating sets have been proposed, such as the self-stabilizing algorithms for minimal single dominating sets and minimal k-dominating sets (MKDS). However, for the MKDS problem, so far there is no self-stabilizing algorithm that works in arbitrary graphs. The proposed algorithms for the MKDS either work for tree graphs or find a minimal 2-dominating set. So, in the thesis, for the MKDS problem, two self-stabilizing algorithms are presented that can operate on general graphs. For the weighted dominating set (WDS) problem, most of the proposed algorithms find approximation solutions to a WDS. For the non-uniform WDS problem, there is no self-stabilizing algorithm for the WDS. In the thesis, self-stabilizing algorithms for the minimal weighted dominating set (MWDS) and minimal positive influence dominating set (MPIDS) are presented when operating in any general network. The worst case convergence time of the two algorithms from any arbitrary initial state are also proved. Finally, in order to reduce cost in an education/intervention programme arising from the PIDS problem, two cooperative cost games about PIDS problem are constructed

The Core can be accessed in a Bounded Number of Steps

We prove the existence of an upper bound for the number of blockings required to get from one imputation to another provided that accessibility holds. The bound depends only on the number of players in the TU game considered. For the class of games with non-empty cores this means that the core can be reached via a bounded sequence of blockings. Primitive recursive algorithms are provided to locate accessibility paths.