The axiomatic approach to three values in games with coalition structure

We study three values for transferable utility games with coalition structure, including the Owen coalitional value and two weighted versions with weights given by the size of the coalitions. We provide three axiomatic characterizations using the properties of Efficiency, Linearity, Independence of Null Coalitions, and Coordination, with two versions of Balanced Contributions inside a Coalition and Weighted Sharing in Unanimity Games, respectively.coalition structure; coalitional value

Stability in shortest path problems

We study three remarkable cost sharing rules in the context of shortest path problems, where agents have demands that can only be supplied by a source in a network. The demander rule requires each demander to pay the cost of their cheapest connection to the source. The supplier rule charges to each demander the cost of the second-cheapest connection and splits the excess payment equally between her access suppliers. The alexia rule averages out the lexicographic allocations, each of which allows suppliers to extract rent in some pre-specified order. We show that all three rules are anonymous and demand-additive core selections. Moreover, with three or more agents, the demander rule is characterized by core selection and a specific version of cost additivity. Finally, convex combinations of the demander rule and the supplier rule are axiomatized using core selection, a second version of cost additivity and two additional axioms that ensure the fair compensation of intermediaries

Stability in shortest path problems

We study three remarkable cost sharing rules in the context of shortest path problems, where agents have demands that can only be supplied by a source in a network. The demander rule requires each demander to pay the cost of their cheapest connection to the source. The supplier rule charges to each demander the cost of the second-cheapest connection and splits the excess payment equally between her access suppliers. The alexia rule averages out the lexicographic allocations, each of which allows suppliers to extract rent in some pre-specified order. We show that all three rules are anonymous and demand-additive core selections. Moreover, with three or more agents, the demander rule is characterized by core selection and a specific version of cost additivity. Finally, convex combinations of the demander rule and the supplier rule are axiomatized using core selection, a second version of cost additivity and two additional axioms that ensure the fair compensation of intermediaries

Stable and weakly additive cost sharing in shortest path problems

In a shortest path problem, agents seek to ship their respective demands; and the cost on a given arc is linear in the flow. Previous works have proposed cost allocations falling in the core of the associated cooperative game. The present work combines core selection with weak versions of the additivity axiom, which allows to characterize a new family of rules. The demander rule charges each demander the cost of their shortest path, and the supplier rule charges the cost of the second-cheapest path while splitting the excess payment equally between access suppliers. With three or more agents, the demander rule is characterized by core selection and a specific version of cost additivity. Convex combinations of the demander rule and the supplier rule are axiomatized using core selection, a second version of cost additivity, and two additional axioms that ensure the fair compensation of intermediaries. With three or more agents, the demander rule is characterized by core selection and a specific version of cost additivity. Finally, convex combinations of the demander rule and the supplier rule are axiomatized using core selection, a second version of cost additivity, and two additional fairness properties.Agencia Estatal de Investigación | Ref. TED2021-130241A-I00Agencia Estatal de Investigación | Ref. PID2020-113440GB-I00Xunta de Galicia | Ref. GPC-ED431B 2022/0

Sharing the costs of cleaning a river: the Upstream Responsibility rule

The cleaning up of waste present in transboundary rivers, which requires the cooperation of di erent authorities, is a problematic issue, especially when responsibility for the discharge of the waste is not well-defined. Following Ni and Wang [12] we assume that a river is a segment divided into several regions from upstream to downstream. We show that when the transfer rate of the waste is unknown, the clean-up cost vector provides useful information for estimating some limits in regard to the responsibility of each region. We propose a cost allocation rule, the Upstream Responsibility rule, which takes into account these limits in distributing costs \fairly" and we provide an axiomatic characterization of this rule via certain properties based on basic ideas concerning the responsibility of regions

Allocating the costs of cleaning a river: expected responsibility versus median responsibility

We consider the problem of cleaning a transboundary river, proposed by Ni and Wang (Games Econ Behav 60:176–186, 2007). A river is modeled as a segment divided into subsegments, each occupied by one region, from upstream to downstream. The waste is transferred from one region to the next at some rate. Since this transfer rate may be unknown, the social planner could have uncertainty over each region’s responsibility. Two natural candidates to distribute the costs in this setting would be the method that assigns to each region its expected responsibility and the one that assigns to each region its median responsibility. We show that the latter is equivalent to the Upstream Responsibility method (Alcalde-Unzu et al. in Games Econ Behav 90:134–150, 2015) and the former is a new method that we call Expected Responsibility. We compare both solutions and analyze them in terms of a new property of monotonicity.Jorge Alcalde-Unzu acknowledges the financial support from the Spanish Government through projects PGC2018-093542-B-I00 and ECO2017-91589-EXP. María Gómez-Rúa acknowledges the financial support from the Spanish Government through projects ECO2014-52616-R and ECO2017-82241-R and the Galician Government through projects GRC 2015/014 and ED431B 2019/34. Elena Molis acknowledges the financial support from the Spanish Government through projects ECO2015-67519-P and PID2019-110783GB-I00, the Basque Government through project IT-568-13 and the Andalusian Government through the projects SEJ1436 and SEJ492

A monotonic and merge-proof rule in minimum cost spanning tree situations

We present a new model for cost sharing in minimum cost spanning tree problems, so that the planner can identify the agents that merge. Under this new framework, and as opposed to the traditional model, there exist rules that satisfy merge-proofness. Besides, by strengthening this property and adding some other properties, such as population-monotonicity and solidarity, we characterize a unique rule that coincides with the weighted Shapley value of an associated cost game

Risk prevention of land flood: A cooperative game theory approach.

Protection against flood risks becomes increasingly difficult for economic and hydrological reasons. Therefore, it is necessary to improve water retention throughout catchment with a more comprehensive approach. Strategies in the land use and measures that are designed to prevent flood risks involve land owners. So, justice issues appear. This paper studies the application of game theory through a cooperative game in order to contribute the resolution of possible agreements among owners and to establish cost / benefit criteria. It is a methodological contribution where land use management for flood retention is analyzed. Specifically, we concentrate on enhancing upstream water retention focusing on the role that forests have as natural water retention measures. This study shows a framework for allocating the compensations among participants based on cooperative game theory and taking into account a principle of stability. We show that it is possible to establish distribution rules that encourage stable payments among land owners. This contribution shows the suitability of this method as a flood risk management tool and as a guide to help decision-making. Compensations and benefits could be established to raise awareness and encourage land owners to cooperate

Risk prevention of land flood: A cooperative game theory approach.

Protection against flood risks becomes increasingly difficult for economic and hydrological reasons. Therefore, it is necessary to improve water retention throughout catchment with a more comprehensive approach. Strategies in the land use and measures that are designed to prevent flood risks involve land owners. So, justice issues appear. This paper studies the application of game theory through a cooperative game in order to contribute the resolution of possible agreements among owners and to establish cost / benefit criteria. It is a methodological contribution where land use management for flood retention is analyzed. Specifically, we concentrate on enhancing upstream water retention focusing on the role that forests have as natural water retention measures. This study shows a framework for allocating the compensations among participants based on cooperative game theory and taking into account a principle of stability. We show that it is possible to establish distribution rules that encourage stable payments among land owners. This contribution shows the suitability of this method as a flood risk management tool and as a guide to help decision-making. Compensations and benefits could be established to raise awareness and encourage land owners to cooperate