335 research outputs found
Finding the nucleolus of any n-person cooperative game by a single linear program
In this paper we show a new method for calculating the nucleolus by solving a unique minimization
linear program with OĂ°4n
Ă constraints whose coefficients belong to fâ1; 0; 1g. We discuss the need of having
all these constraints and empirically prove that they can be reduced to OĂ°kmax2n
Ă, where kmax is a positive
integer comparable with the number of players. A computational experience shows the applicability of our
method over (pseudo)random transferable utility cooperative games with up to 18 playersThe authors want to thank Javier Arin, Safae El Haj Ben Ali, Guillermo Owen and Johannes H. Reijnierse for their useful and valuable help. The research of the authors has been partially supported by the projects FQM-5849 (Junta de Andalucia \ FEDER), and by the project MTM2010-19576-C02-01 (MICINN, Spain). This paper was written while the second author was enjoying a grant for a short postdoctoral research visit at the Instituto Universitario de Investigacion de Matematicas de la Universidad de Sevilla (IMUS). Special thanks are due to one anonymous referee for his/her valuable comments.Puerto Albandoz, J.; Perea Rojas Marcos, F. (2013). Finding the nucleolus of any n-person cooperative game by a single linear program. Computers and Operations Research. 40(10):2308-2313. https://doi.org/10.1016/j.cor.2013.03.011S23082313401
Computing the Least-core and Nucleolus for Threshold Cardinality Matching Games
Cooperative games provide a framework for fair and stable profit allocation
in multi-agent systems. \emph{Core}, \emph{least-core} and \emph{nucleolus} are
such solution concepts that characterize stability of cooperation. In this
paper, we study the algorithmic issues on the least-core and nucleolus of
threshold cardinality matching games (TCMG). A TCMG is defined on a graph
and a threshold , in which the player set is and the profit of
a coalition is 1 if the size of a maximum matching in
meets or exceeds , and 0 otherwise. We first show that for a TCMG, the
problems of computing least-core value, finding and verifying least-core payoff
are all polynomial time solvable. We also provide a general characterization of
the least core for a large class of TCMG. Next, based on Gallai-Edmonds
Decomposition in matching theory, we give a concise formulation of the
nucleolus for a typical case of TCMG which the threshold equals . When
the threshold is relevant to the input size, we prove that the nucleolus
can be obtained in polynomial time in bipartite graphs and graphs with a
perfect matching
Cooperative game theory and its application to natural, environmental, and water resource issues : 3. application to water resources
This paper reviews various applications of cooperative game theory (CGT) to issues of water resources. With an increase in the competition over various water resources, the incidents of disputes have been in the center of allocation agreements. The paper reviews the cases of various water uses, such as multi-objective water projects, irrigation, groundwater, hydropower, urban water supply, wastewater, and transboundary water disputes. In addition to providing examples of cooperative solutions to allocation problems, the conclusion from this review suggests that cooperation over scarce water resources is possible under a variety of physical conditions and institutional arrangements. In particular, the various approaches for cost sharing and for allocation of physical water infrastructure and flow can serve as a basis for stable and efficient agreement, such that long-term investments in water projects are profitable and sustainable. The latter point is especially important, given recent developments in water policy in various countries and regional institutions such as the European Union (Water Framework Directive), calling for full cost recovery of investments and operation and maintenance in water projects. The CGT approaches discussed and demonstrated in this paper can provide a solid basis for finding possible and stable cost-sharing arrangements.Town Water Supply and Sanitation,Environmental Economics&Policies,Water Supply and Sanitation Governance and Institutions,Water Supply and Systems,Water and Industry
Cooperative game theory and its application to natural, environmental, and water resource issues : 2. application to natural and environmental resources
This paper provides a review of various applications of cooperative game theory (CGT) to issues of natural and environmental resources. With an increase in the level of competition over environmental and natural resources, the incidents of disputes have been at the center of allocation agreements. The paper reviews the cases of common pool resources such as fisheries and forests, and cases of environmental pollution such as acid rain, flow, and stock pollution. In addition to providing examples of cooperative solutions to allocation problems, the conclusion from this review suggests that cooperation over scarce environmental and natural resources is possible under a variety of physical conditions and institutional arrangements. CGT applications to international fishery disputes are especially useful in that they have been making headway in policy-related agreements among states and regions of the world. Forest applications are more local in nature, but of great relevance in solving disputes among communities and various levels of governments.Environmental Economics&Policies,Fisheries&Aquaculture,Common Property Resource Development,Economic Theory&Research,Ecosystems and Natural Habitats
Universal characterization sets for the nucleolus in balanced games
We provide a new mo dus op erandi for the computation of the nucleolus in co op-
erative games with transferable utility. Using the concept of dual game we extend
the theory of characterization sets. Dually essential and dually saturated coalitions
determine b oth the core and the nucleolus in monotonic games whenever the core
is non-empty. We show how these two sets are related with the existing charac-
terization sets. In particular we prove that if the grand coalition is vital then the
intersection of essential and dually essential coalitions forms a characterization set
itself. We conclude with a sample computation of the nucleolus of bankruptcy games
- the shortest of its kind
Horizontal collaboration in forestry: game theory models and algorithms for trading demands
In this paper, we introduce a new cooperative game theory model that we call
production-distribution game to address a major open problem for operations
research in forestry, raised by R\"onnqvist et al. in 2015, namely, that of
modelling and proposing efficient sharing principles for practical
collaboration in transportation in this sector. The originality of our model
lies in the fact that the value/strength of a player does not only depend on
the individual cost or benefit of the objects she owns but also depends on her
market shares (customers demand). We show however that the
production-distribution game is an interesting special case of a market game
introduced by Shapley and Shubik in 1969. As such it exhibits the nice property
of having a non-empty core. We then prove that we can compute both the
nucleolus and the Shapley value efficiently, in a nontrivial and interesting
special case. We in particular provide two different algorithms to compute the
nucleolus: a simple separation algorithm and a fast primal-dual algorithm. Our
results can be used to tackle more general versions of the problem and we
believe that our contribution paves the way towards solving the challenging
open problem herein
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