147 research outputs found
Complexity of Determining Nonemptiness of the Core
Coalition formation is a key problem in automated negotiation among
self-interested agents, and other multiagent applications. A coalition of
agents can sometimes accomplish things that the individual agents cannot, or
can do things more efficiently. However, motivating the agents to abide to a
solution requires careful analysis: only some of the solutions are stable in
the sense that no group of agents is motivated to break off and form a new
coalition. This constraint has been studied extensively in cooperative game
theory. However, the computational questions around this constraint have
received less attention. When it comes to coalition formation among software
agents (that represent real-world parties), these questions become increasingly
explicit.
In this paper we define a concise general representation for games in
characteristic form that relies on superadditivity, and show that it allows for
efficient checking of whether a given outcome is in the core. We then show that
determining whether the core is nonempty is -complete both with
and without transferable utility. We demonstrate that what makes the problem
hard in both cases is determining the collaborative possibilities (the set of
outcomes possible for the grand coalition), by showing that if these are given,
the problem becomes tractable in both cases. However, we then demonstrate that
for a hybrid version of the problem, where utility transfer is possible only
within the grand coalition, the problem remains -complete even
when the collaborative possibilities are given
Coalitional Games for Transmitter Cooperation in MIMO Multiple Access Channels
Cooperation between nodes sharing a wireless channel is becoming increasingly
necessary to achieve performance goals in a wireless network. The problem of
determining the feasibility and stability of cooperation between rational nodes
in a wireless network is of great importance in understanding cooperative
behavior. This paper addresses the stability of the grand coalition of
transmitters signaling over a multiple access channel using the framework of
cooperative game theory. The external interference experienced by each TX is
represented accurately by modeling the cooperation game between the TXs in
\emph{partition form}. Single user decoding and successive interference
cancelling strategies are examined at the receiver. In the absence of
coordination costs, the grand coalition is shown to be \emph{sum-rate optimal}
for both strategies. Transmitter cooperation is \emph{stable}, if and only if
the core of the game (the set of all divisions of grand coalition utility such
that no coalition deviates) is nonempty. Determining the stability of
cooperation is a co-NP-complete problem in general. For a single user decoding
receiver, transmitter cooperation is shown to be \emph{stable} at both high and
low SNRs, while for an interference cancelling receiver with a fixed decoding
order, cooperation is stable only at low SNRs and unstable at high SNR. When
time sharing is allowed between decoding orders, it is shown using an
approximate lower bound to the utility function that TX cooperation is also
stable at high SNRs. Thus, this paper demonstrates that ideal zero cost TX
cooperation over a MAC is stable and improves achievable rates for each
individual user.Comment: in review for publication in IEEE Transactions on Signal Processin
Matchings with externalities and attitudes
Two-sided matchings are an important theoretical tool used to model markets and social interactions. In many real-life problems the utility of an agent is influenced not only by their own choices, but also by the choices that other agents make. Such an influence is called an externality. Whereas fully expressive representations of externalities in matchings require exponential space, in this paper we propose a compact model of externalities, in which the influence of a match on each agent is computed additively. Under this framework, we analyze many-to-many matchings and one-to-one matchings where agents take different attitudes when reasoning about the actions of others. In particular, we study optimistic, neutral and pessimistic attitudes and provide both computational hardness results and polynomial-time algorithms for computing stable outcomes
The Least-core and Nucleolus of Path Cooperative Games
Cooperative games provide an appropriate framework for fair and stable profit
distribution in multiagent systems. In this paper, we study the algorithmic
issues on path cooperative games that arise from the situations where some
commodity flows through a network. In these games, a coalition of edges or
vertices is successful if it enables a path from the source to the sink in the
network, and lose otherwise. Based on dual theory of linear programming and the
relationship with flow games, we provide the characterizations on the CS-core,
least-core and nucleolus of path cooperative games. Furthermore, we show that
the least-core and nucleolus are polynomially solvable for path cooperative
games defined on both directed and undirected network
The complexity of the nucleolus in compact games
This is the author accepted manuscript. The final version is available from ACM via the DOI in this recordThe nucleolus is a well-known solution concept for coalitional games to fairly distribute the total available worth among the players. The nucleolus is known to be NP-hard to compute over compact coalitional games, that is, over games whose functions specifying the worth associated with each coalition are encoded in terms of polynomially computable functions over combinatorial structures. In particular, hardness results have been exhibited over minimum spanning tree games, threshold games, and flow games. However, due to its intricate definition involving reasoning over exponentially many coalitions, a nontrivial upper bound on its complexity was missing in the literature and looked for. This article faces this question and precisely characterizes the complexity of the nucleolus, by exhibiting an upper bound that holds on any class of compact games, and by showing that this bound is tight even on the (structurally simple) class of graph games. The upper bound is established by proposing a variant of the standard linear-programming based algorithm for nucleolus computation and by studying a framework for reasoning about succinctly specified linear programs, which are contributions of interest in their own. The hardness result is based on an elaborate combinatorial reduction, which is conceptually relevant for it provides a "measure" of the computational cost to be paid for guaranteeing voluntary participation to the distribution process. In fact, the pre-nucleolus is known to be efficiently computable over graph games, with this solution concept being defined as the nucleolus but without guaranteeing that each player is granted with it at least the worth she can get alone, that is, without collaborating with the other players. Finally, this article identifies relevant tractable classes of coalitional games, based on the notion of type of a player. Indeed, in most applications where many players are involved, it is often the case that such players do belong in fact to a limited number of classes, which is known in advance and may be exploited for computing the nucleolus in a fast way.Part of E. Malizia’s work was supported by the European Commission through the European Social Fund
and by Calabria Regio
Complexity bounds for relational algebra over document spanners
We investigate the complexity of evaluating queries in Relational Algebra (RA) over the relations extracted by regex
formulas (i.e., regular expressions with capture variables)
over text documents. Such queries, also known as the regular document spanners, were shown to have an evaluation
with polynomial delay for every positive RA expression (i.e.,
consisting of only natural joins, projections and unions);
here, the RA expression is fixed and the input consists of
both the regex formulas and the document. In this work, we
explore the implication of two fundamental generalizations.
The first is adopting the “schemaless” semantics for spanners, as proposed and studied by Maturana et al. The second
is going beyond the positive RA to allowing the difference
operator.
We show that each of the two generalizations introduces
computational hardness: it is intractable to compute the natural join of two regex formulas under the schemaless semantics, and the difference between two regex formulas under
both the ordinary and schemaless semantics. Nevertheless,
we propose and analyze syntactic constraints, on the RA
expression and the regex formulas at hand, such that the
expressive power is fully preserved and, yet, evaluation can
be done with polynomial delay. Unlike the previous work on
RA over regex formulas, our technique is not (and provably cannot be) based on the static compilation of regex formulas, but rather on an ad-hoc compilation into an automaton
that incorporates both the query and the document. This
approach also allows us to include black-box extractors in
the RA expression
K-balanced games and capacities
In this paper, we present a generalization of the concept of balanced game for finite games. Balanced games are those having a nonempty core, and this core is usually considered as the solution of game. Based on the concept of k-additivity, we define to so-called k-balanced games and the corresponding generalization of core, the k-additive core, whose elements are not directly imputations but k-additive games. We show that any game is k-balanced for a suitable choice of k, so that the corresponding k-additive core is not empty. For the games in the k-additive core, we propose a sharing procedure to get an imputation and a representative value for the expectations of the players based on the pessimistic criterion. Moreover, we look for necessary and sufficient conditions for a game to be k-balanced. For the general case, it is shown that any game is either balanced or 2-balanced. Finally, we treat the special case of capacities.Coopertaive games, k-additivity, balanced games, capacities, core.
On some cost allocation problems in communication networks
New technologies prompted an explosion in the development of
communication networks. Modern network optimization techniques usually lead to a design of the most profitable, or the least cost network that will provide some service to customers. There are various costs and gains associated with building and using a communication network. Moreover, the involved multiple network users and/or owners possibly have conflicting objectives. However, they might cooperate in order to decrease their joint cost or increase their joint profit. Clearly, these individuals or organizations will support a globally \u27attractive\u27 solution(s) only if their expectations for a \u27fair share\u27 of the cost or profit are met. Consequently,
providing network developers, users and owners with efficiently computable \u27fair\u27 cost allocation solution procedures is of great importance for strategic management. This work is an overview of some recent results (some already published as well as some new) in the development of cooperative game theory based mechanisms to efficiently compute \u27attractive\u27 cost allocation solutions for several important classes of communication networks
- …