A fair rule in minimum cost spanning tree problems

We study minimum cost spanning tree problems and define a cost sharing rule that satisfies many more properties than other rules in the literature. Furthermore, we provide an axiomatic characterization based on monotonicity properties.minimum cost spanning tree, cost sharing

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)

Defining Rules in Cost Spanning Tree Problems Through the Canonical Form

We define the canonical form of a cost spanning tree problem. The canonical form has the property that reducing the cost of any arc, the minimal cost of connecting agents to the source is also reduced. We argue that the canonical form is a relevant concept in this kind of problems and study a rule using it. This rule satisfies much more interesting properties than other rules in the literature. Furthermore we provide two characterizations. Finally, we present several approaches to this rule without using the canonical form.Cost spanning tree, Rules, Canonical form

Defining rules in cost spanning tree problems through the canonical form

We define the canonical form of a cost spanning tree problem. The canonical form has the property that reducing the cost of any arc, the minimal cost of connecting agents to the source is also reduced. We argue that the canonical form is a relevant concept in this kind of problems and study a rule using it. This rule satisfies much more interesting properties than other rules in the literature. Furthermore we provide two characterizations. Finally, we present several approaches to this rule without using the canonical form.cost spanning tree problems canonical form rules

Applying the Shapley value to the tuna fishery

The tuna fishing sector has faced important regulatory restrictions for years, mainly based on the number of fish aggregating devices (FADs) allowed per vessel, which has threatened the survival of many tuna firms. Various academics have studied this issue, proposing various solutions based on the reassignment and sharing of FADs. However, previous research has focused primarily on the use of FADs and their implications, rather than actually helping to optimize the tuna fleet’s fishing activity, and possibly for this reason, none of these proposals has impacted current fishing practices. In light of this situation, our research proposes a more equitable approach: we have modeled the tuna vessel problem as a cooperative game, reallocating FADs among vessels, studying the Shapley value, and comparing the results achieved with previous proposals. Although our approach is fairly standard in the literature, it is a novel solution to a deep-rooted problem in this sector that also leads to a significant reduction in emissions associated with fuel consumption. In fact, the application of our theoretical results to real data shows that there is not only a significant scope for improvement for firms and their vessels –both gain more revenue– but also a beneficial contribution to the environment in terms of reduced fuel consumption.Agencia Estatal de Investigación | Ref. PID2020-113440GB-I00Xunta de Galicia | Ref. ED431B2022/03Universidade de Vigo/CISU

Cooperative games for minimum cost spanning tree problems

Minimum cost spanning tree problems are well known problems in the Operations Research literature. Some agents, located at different geographical places, want a service provided by a common supplier. Agents will be served through costly connections. Some part of the literature has focused, mainly, in studying how to allocate the connection cost among the agents. We review the papers that have addressed the allocation problem using cooperative game theory

Smooth Multibidding Mechanisms

We propose a smooth multibidding mechanism for environments where a group of agents have to choose one out of several projects. Our proposal is related to the multibidding mechanism (Pérez-Castrillo and Wettstein, 2002) but it is “smoother” in the sense that small variations in an agent’s bids do not lead to dramatic changes in the probability of selecting a project. This mechanism is shown to possess several interesting properties. First, the equilibrium outcome is unique. Second, it ensures an equal sharing of the surplus that it induces. Finally, it enables reaching an outcome as close to efficiency as is desired.mechanism design, NIMBY

Minimum cost connection networks: Truth-telling and implementation

In the present paper we consider the allocation of costs in connection networks. Agents have connection demands in form of pairs of locations they want to have connected. Connections between locations are costly to build. The problem is to allocate costs of networks satisfying all connection demands. We use a few axioms to characterize allocation rules that truthfully implement cost minimizing networks satisfying all connection demands in a game where: (1) a central planner announces an allocation rule and a cost estimation rule; (2) every agent reports her own connection demand as well as all connection costs; (3) the central planner selects a cost minimizing network satisfying reported connection demands based on the estimated costs; and, (4) the planner allocates the true costs of the selected network. It turns out that an allocation rule satisfies the axioms if and only if relative cost shares are fixed

Smooth multibidding mechanisms

We propose a smooth multibidding mechanism for environments where a group of agents have to choose one out of several projects (possibly with the help of a social planner). Our proposal is related to the multibidding mechanism (Pérez-Castrillo and Wettstein, 2002) but it is "smoother" in the sense that small variations in an agent's bids do not lead to dramatic changes in the probability of selecting a project. This mechanism is shown to possess several interesting properties. Unlike in the study by Pérez Castrillo and Wettstein (2002), the equilibrium outcome is unique. Second, it ensures an equal sharing of the surplus that it induces. Finally, it enables reaching an outcome as close to effciency as is desired