Folk solution for simple minimum cost spanning tree problems

A minimum cost spanning tree problem analyzes how to efficiently connect a group of individuals to a source. Once the efficient tree is obtained, the addressed question is how to allocate the total cost among the involved agents. One prominent solution in allocating this minimum cost is the so-called Folk solution. Unfortunately, in general, the Folk solution is not easy to compute. We identify a class of mcst problems in which the Folk solution is obtained in an easy way. This class includes elementary cost mcst problems.Financial support from Generalitat de Catalunya (2014SGR325 and 2014SGR631) and Ministerio de Economía y Competitividad (ECO2013-43119-P) is acknowledged

The folk solution and Boruvka's algorithm in minimum cost spanning tree problems

The Boruvka's algorithm, which computes the minimum cost spanning tree, is used to define a rule to share the cost among the nodes (agents). We show that this rule coincides with the folk solution, a very well-known rule of this literature.minimum cost spanning tree; Boruvka's algorithm; folk solution

Decentralized Pricing in Minimum Cost Spanning Trees

In the minimum cost spanning tree model we consider decentralized pricing rules, i.e. rules that cover at least the efficient cost while the price charged to each user only depends upon his own connection costs. We define a canonical pricing rule and provide two axiomatic characterizations. First, the canonical pricing rule is the smallest among those that improve upon the Stand Alone bound, and are either superadditive or piece-wise linear in connection costs. Our second, direct characterization relies on two simple properties highlighting the special role of the source cost.pricing rules; minimum cost spanning trees; canonical pricing rule; stand-alone cost; decentralization

An egalitarian approach for sharing the cost of a spanning tree

A minimum cost spanning tree problem analyzes the way to efficiently connect individuals to a source. Hence the question is how to fairly allocate the total cost among these agents. Our approach, reinterpreting the spanning tree cost allocation as a claims problem defines a simple way to allocate the optimal cost with two main criteria: (1) each individual only pays attention to a few connection costs (the total cost of the optimal network and the cost of connecting himself to the source); and (2) an egalitarian criteria is used to share costs. Then, using claims rules, we define an egalitarian solution so that the total cost is allocated as equally as possible. We show that this solutions could propose allocations outside the core, a counter-intuitive fact whenever cooperation is necessary. Then we propose a modification to get a core selection, obtaining in this case an alternative interpretation of the Folk solution.Financial support from the Spanish Ministry of Economy and Competitiveness under projects ECO2016-75410-P (AEI/FEDER UE) and ECO2016-77200-P (AEI/FEDER UE), and from Universitat Rovira i Virgili and Generalitat de Catalunya under projects 2018PRF-URV-B2-53 and 2017SGR770, is gratefully acknowledged. Financial support from the Generalitat Valenciana (BEST/2019 grants) to visit the UNSW is gratefully acknowledged

Sharing the cost of maximum quality optimal spanning trees

Minimum cost spanning tree problems have been widely studied in operation research and economic literature. Multi-objective optimal spanning trees provide a more realistic representation of different actual problems. Once an optimal tree is obtained, how to allocate its cost among the agents defines a situation quite different from what we have in the minimum cost spanning tree problems. In this paper, we analyze a multi-objective problem where the goal is to connect a group of agents to a source with the highest possible quality at the cheapest cost. We compute optimal networks and propose cost allocations for the total cost of the project. We analyze properties of the proposed solution; in particular, we focus on coalitional stability (core selection), a central concern in the literature on minimum cost spanning tree problems.This work is supported by the Spanish Ministerio de Economía y Competitividad, under project ECO2016-77200-P. Financial support from the Generalitat Valenciana (BEST/2019 Grants) to visit the UNSW is also acknowledged

A non-cooperative approach to the folk rule in minimum cost spanning tree problems

This paper deals with the problem of finding a way to distribute the cost of a minimum cost spanning tree problem between the players. A rule that assigns a payoff to each player provides this distribution. An optimistic point of view is considered to devise a cooperative game. Following this optimistic approach, a sequential game provides this construction to define the action sets of the players. The main result states the existence of a unique cost allocation in subgame perfect equilibria. This cost allocation matches the one suggested by the folk rule.The authors thank the support of the Spanish Ministry of Science, Innovation and Universities, the Spanish Ministry of Economy and Competitiveness, the Spanish Agency of Research, co-funded with FEDER funds, under the projects ECO2016-77200-P, ECO2017-82241-R, ECO2017-87245-R, PID2021-128228NB-I00, Consellería d’Innovación, Universitats, Ciencia i Societat Digital, Generalitat Valenciana [grant number AICO/2021/257], and Xunta de Galicia (ED431B 2019/34)

네트워크 구조가 있는 비용 배분 문제에서의 샤플리 밸류에 관한 연구

학위논문 (박사) -- 서울대학교 대학원 : 사회과학대학 경제학부, 2021. 2. 전영섭.This study consists of three chapters. Each chapter addresses independent issues. However they are connected in that they are analyzing economic phenomena using a network structure and they investigate the distribution of benefits or costs arising from cooperation using cooperative game theory. The first chapter investigate positional queueing problem which is a generalized problem of the classical queueing problem. In this chapter, we obtain generalized versions of the minimal transfer rule and of the maximal transfer rule. We also investigate properties of each rules and axiomatically characterized them. The second chapter investigate the minimum cost spanning tree problems with multiple sources. We investigate the properties and axiomatic characterization of the Kar rule for the minimum cost spanning tree problems with multiple sources. The final chapter investigate the profit allocation in the Korean automotive industry using the buyer-supplier network among the vehicle manufacturers and its first-tier vendors from the perspective of cooperative game theory. Some models are constructed and the Shapley values of each models are calculated. We compare them with real profit allocation of the Korean automotive industry.본 연구는 3개의 장으로 구성되어 있다. 각 장은 독립적인 문제를 다루고 있지만, 경제학적 현상을 네트워크 구조를 활용하여 분석하고 있다는 것과 협력에서 발생하는 이익 또는 비용의 배분 문제를 협조적 게임이론을 활용하여 분석하고 있다는 점에서 각 장은 상호 연결성을 갖는다. 첫 번째 장에서는 고전적인 대기열게임을 일반화한 문제(positional queueing problem)에서의 최소이전규칙(minimal transfer rule)과 최대이전규칙(maximal transfer rule)의 특성을 밝힌다. 두 번째 장에서는 소스가 여러 개인 최소신장가지문제(minimum cost spanning tree problem with multiple sources)에서의 카규칙(Kar rule)의 특성을 밝힌다. 마지막 장에서는 한국의 자동차 산업에서의 완성차 기업과 1차 벤더 사이의 이윤분배 문제를 협조적 게임이론적 접근법을 통해서 분석한다. 4가지 모형을 구축하고 각 모형에서 계산된 이윤분배와 현실의 이윤분배를 비교할 때, 완성차 기업의 영향력을 가장 크게 가정한 모형의 이윤분배 결과가 현실의 이윤분배와 가장 근접한 것을 확인하였다.1. The Shapley Value in Positional Queueing Problems and axiomatic characterizations 1 1.1. Introduction 1 1.2. The Positional Queueing Problem 2 1.3. An optimistic approach and the minimal transfer rule 5 1.4. A pessimistic approach and the maximal transfer rule 8 1.5. Axioms and characterizations 21 1.6. Concluding remarks 31 Bibliography. 46 2. The Kar Solution for multi-source minimum cost spanning tree problems 49 2.1. Introduction 49 2.2. Model 50 2.3. An axiomatic characterization 51 2.4. Conclusion 62 Bibliography. 63 3. A cooperative game theoretic approach on the profit allocation of the Koreanautomotive industry 65 3.1. Introduction 65 3.2. Model 66 3.3. Analysis method 71 3.4. Analysis result 78 3.5. Conclusion 80 Bibliography. 82Docto

Sharing the cost of risky projects

Users share the cost of unreliable non-rival projects (items). For instance, industry partners pay today for R&D that may or may not deliver a cure to some viruses, agents pay for the edges of a network that will cover their connectivity needs, but the edges may fail, etc. Each user has a binary inelastic need that is served if and only if certain subsets of items are actually functioning. We ask how should the cost be divided when individual needs are heterogenous. We impose three powerful separability properties: Independence of Timing ensures that the cost shares computed ex ante are the expectation, over the random realization of the projects, of shares computed ex post. Cost Additivity together with Separability Across Projects ensure that the cost shares of an item depend only upon the service provided by that item for a given realization of all other items. Combining these with fair bounds on the liability of agents with more or less flexible needs, and of agents for whom an item is either indispensable or useless, we characterize two rules: the Ex Post Service rule is the expectation of the equal division of costs between the agents who end up served; the Needs Priority rule splits the cost first between those agents for whom an item is critical ex post, or if there are no such agents between those who end up being served