This article introduces the concept of duality in financial networks, which entails the division of losses versus gains. In bankruptcy problems, in which a bankrupt entity divides its non-negative assets among a group of claimants, duality is well understood. Financial networks generalize bankruptcy problems by allowing for multiple agents with individual assets interconnected by mutual claims. We argue that allowing for negative assets is imperative to adequately formulate duality for financial networks. We show that there is a linear relationship between transfer schemes based on claims rules in a financial network and transfer schemes based on the dual of those claims rules in the dual financial network. Moreover, dual financial networks enable us to define dual transfer rules and dual allocation rules. We show that both self-dual transfer rules and self-dual allocation rules have to be based on self-dual claims rules. On the other hand, we demonstrate that transfer rules based on self-dual claims rules need not be self-dual, whereas allocation rules based on self-dual claims rules are always self-dual.

This paper studies so‐called connection scheduling problems, a type of interactive operations research problem. A connection scheduling problem combines aspects from the minimum cost spanning tree and sequencing problems. Given a graph, we aim to first establish a connection order on the players such that the total cost of connecting them to a source is minimal and second to find a fair cost allocation of such an optimal order among the players involved. We restrict our attention to connection scheduling problems on trees and propose a recursive method to solve these tree connection scheduling problems integrated with an allocation approach. This latter mechanism consistently and recursively uses benchmark endogenous myopic orders to determine potential cost savings, which will then be appropriately allocated. Interestingly, the transition process from a benchmark myopic order to an optimal one will be smooth using the switching of blocks of agents based on the basic notion of merge segments.

This paper examines cost allocation rules for minimum cost spanning tree (MCST) problems, focusing on the properties of merge-proofness and coalitional stability. Merge-proofness ensures that no coalition of agents has the incentive to merge before participating in the cost allocation process. On the other hand, coalitional stability ensures that no coalition has the incentive to withdraw from the cost allocation process after the cost allocation proposal is made. We propose a novel class of rules called induced rules, which are derived recursively from base rules designed for two-person MCST problems. We demonstrate that induced rules exhibit both merge-proofness and coalitional stability within a restricted domain, provided that the corresponding base rules satisfy specific conditions.

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This paper provides a multi-actor perspective on the realization of new infrastructures, motivated by the necessity for infrastructures to support the ongoing climate and energy transition in general, and CO2 transport infrastructures for carbon capture, utilization and storage (CCUS) in particular. We develop a general model to represent infrastructures that allows for a unique decomposition into 'elementary infrastructure components' based on heterogeneous user requirements. Notably, it incorporates a cost function with a very generic and adaptable structure, for which we can still explicitly determine the costs of each individual component. As a direct consequence an intuitive cost allocation rule is obtained: equal component cost sharing. This allocation rule is in line with existing game-theoretic concepts and satisfies the desirable properties of advantageous scaling and coalitional rationality. Advantageous scaling guarantees that the costs allocated to each existing user do not increase if the number of users grows larger and coalitional rationality ensures that there is no subgroup of infrastructure users that would have a financial reason to object to the cost allocation. Additionally, we examine the application of our model to a prospective CO2 transport infrastructure for CCUS in the port of Rotterdam and the adjoining industry area.

Clearing payments are payments between agents to settle their mutual liabilities. The interdependence between agents in financial networks complicates the analysis of clearing payments as the extent to which an agent can pay its creditors depends not only on its own assets but also on the incoming payments from the other agents. Each financial network is endowed with agent-specific claims rules that prescribe how each agent pays its creditors. Consequently, our model not only captures standard principles of bankruptcy law, such as limited liability of equity, absolute priority of debt over equity, proportionality, and priority, but also allows for more general underlying payment mechanisms. A payment matrix that contains clearing payments in accordance with claims rules is a transfer scheme, which is not necessarily uniquely determined. This article is the first to provide the complete characterization of all such transfer schemes. Our characterization relies on additional cash vectors, which summarize the payments in excess of the minimum clearing payments. The set of such vectors is shown to be homeomorphic to the set of transfer schemes. We introduce a recursive procedure to compute any additional cash vector, and thereby indirectly a corresponding transfer scheme. The characterization opens up the opportunity for a network-based axiomatic analysis of transfer rules, which prescribe clearing payments for each financial network. In fact, we show that the characterization can be used to provide new axiomatizations of transfer rules in which each agent pays its creditors in accordance with the proportional claims rule.

This paper analyzes bankruptcy problems from a strategic perspective using the parameterized TAL family of bankruptcy rules. We construct a strategic game where every player selects a parameter, and the rule from the TAL family that corresponds to the mean of the chosen parameters is used to divide the estate. We prove the existence of Nash equilibria for this strategic game. In particular, we provide the set of all Nash equilibria for two players, and for more players, we prove existence by constructing a Nash equilibrium of a particular form based on the notion of a pivotal player.

This paper provides a multi-actor perspective on the realization of new infrastructures, motivated by the necessity for infrastructures to support the ongoing climate and energy transition in general, and CO2 transport infrastructures for carbon capture, utilization and storage (CCUS) in particular. We develop a general model to represent infrastructures that allows for a unique decomposition into ‘elementary infrastructure components’ based on heterogeneous user requirements. Notably, it incorporates a cost function with a very generic and adaptable structure, for which we can still explicitly determine the costs of each individual component. As a direct consequence an intuitive cost allocation rule is obtained: equal component cost sharing. This allocation rule is in line with existing game-theoretic concepts and satisfies the desirable properties of advantageous scaling and coalitional rationality. Advantageous scaling guarantees that the costs allocated to each existing user do not increase if the number of users grows larger and coalitional rationality ensures that there is no subgroup of infrastructure users that would have a financial reason to object to the cost allocation. Additionally, we examine the application of our model to a prospective CO2 transport infrastructure for CCUS in the port of Rotterdam and the adjoining industry area.

We analyze clearing mechanisms in financial networks in which agents may have both monetary individual assets and mutual liabilities. A clearing mechanism prescribes mutual payments between agents in a financial network to settle their mutual liabilities. The corresponding payments, summarized in a payment matrix, are made in accordance with agent-specific claims rules that stem from the vast literature on claims situations. The bottom payment matrix is the payment matrix that contains the minimal amount of payments required to clear the network. We explicitly characterize the bottom payment matrix as the result of a recursive centralized mechanism. We subsequently show that several types of decentralized clearing mechanisms lead to the bottom payment matrix as well. In fact, we show that this unification of centralized and decentralized clearing mechanisms relies on the composition property of the underlying agent-specific claims rules that dictate the payment mechanism.

We consider a model of influence over a network with finite-horizon opinion dynamics. The network consists of agents that update their opinions via a trust structure as in the DeGroot dynamics. The model considers two potential external influencers that have fixed and opposite opinions. They aim to maximally impact the aggregate state of opinions at the end of the finite horizon by targeting with precision one agent in one specific time period. In the case of only one influencer, we characterize optimal targets on the basis of two features: shift and amplification. Also, conditions are provided under which a specific target is optimal: the maximum-amplification target. In the case of two influencers, we focus on the existence and characterization of pure strategy equilibria in the corresponding two-person strategic zero-sum game. Roughly speaking, if the initial opinions are not too much in favour of either influencer, the influencers’ equilibrium behaviour is also driven by the amplification of targets.

We analyze applications of biform games to linear production (LP) and sequencing processes. Biform games, as introduced by Brandenburger and Stuart (2007), apply to problems in which strategic decisions are followed by some cooperative game, where the specific environment of the cooperative game that is played, is in turn determined by these strategic decisions. We extend the work on LP-processes by allowing firms to compete for resources that are scarce or hard to produce, rather than assuming these resource bundles are simply given. With strategy dependent resource bundles that can be obtained from two locations, we show that the induced strategic game has a (pure) Nash equilibrium, using the Owen set or any game-theoretic solution concept that satisfies anonymity to solve the cooperative LP-game. To analyze competition in sequencing processes, we no longer assume an initial processing order is given. Instead, this initial order is strategically determined. Solving the second-stage cooperative sequencing game using a gain splitting rule, we fully determine the set of Nash equilibria of the induced strategic game.

This paper studies the nucleolus of graph-restricted games as an alternative for the Shapley value to evaluate communication situations. We focus on the inheritance of properties of cooperative games related to the nucleolus: strong compromise admissibility and compromise stability. These two properties allow for a direct, closed formula for the nucleolus. We characterize the families of graphs for which the graph-restricted games inherit these properties from the underlying games. Moreover, for each of these two properties, we characterize the family of graphs for which the nucleolus is invariant

Supply chain collaboration has the potential to address issues of inefficiency and lack of coordination that often drives down the competitiveness of supply chains. However, collaboration in supply chains is difficult due to ever increasing complexity and conflicting objectives prevalent in supply chains, and a growing challenge is to be able to identify the optimal configuration of collaboration that benefits the supply chain as a whole. The inherent complexity of supply chains has lead to the emergence of so-called orchestrators to help coordinate supply chains and enable collaboration. In this paper we address a specific problem that an orchestrator might face: given a set of potential coalitions that could form in a given supply chain, together with the means by which collaborative benefits should be allocated, which coalition should form? We propose a new methodology based on what we call leading coalitions to address this coalition selection problem, which borrows concepts from cooperative game theory to ensure stability and fairness of the final selection. The proposed methodology is applied to linear production processes where agents collaborate by pooling their resources, and a computational study is performed on a large set of instances in order to gain insight into the working of the methodology.

We define and axiomatically characterize a new proportional influence measure for sequential projects with imperfect reliability. We consider a model in which a finite set of players aims to complete a project, consisting of a finite number of tasks, which can only be carried out by certain specific players. Moreover, we assume the players to be imperfectly reliable, i.e., players are not guaranteed to carry out a task successfully. To determine which players are most important for the completion of a project, we use a proportional influence measure. This paper provides two characterizations of this influence measure. The most prominent property in the first characterization is task decomposability. This property describes the relationship between the influence measure of a project and the measures of influence one would obtain if one divides the tasks of the project over multiple independent smaller projects. Invariance under replacement is the most prominent property of the second characterization. If in a certain task group a specific player is replaced by a new player who was not in the original player set, this property states that this should have no effect on the allocated measure of influence of any other original player.

This paper axiomatically studies bankruptcy problems with nontransferable utility by focusing on generalizations of consistency and the contested garment principle. On the one hand, we discuss several consistency notions and introduce the class of parametric bankruptcy rules which contains the proportional rule, the constrained relative equal awards rule, and the constrained relative equal losses rule. On the other hand, we introduce the class of adjusted bankruptcy rules and characterize the relative adjustment principle by truncation invariance, minimal rights first, and a weak form of relative symmetry.

This paper introduces a model to analyze individual externalities and the associated negotiation problem, which has been largely neglected in the game theoretic literature. Following an axiomatic perspective, we propose a solution, as a payoff sharing scheme, called the balanced threat agreement, for such problems. It highlights an agent’s potential influences on all agents by threatening to enter or quit. We further study the solution by investigating its consistency. We also offer a discussion on the related stability issue.

This paper studies bankruptcy problems with nontransferable utility as a generalization of bankruptcy problems with monetary estate and claims. Following the theory on TU-bankruptcy, we introduce a duality notion for NTU-bankruptcy rules and derive several axiomatic characterizations of the proportional rule and the constrained relative equal awards rule.

This paper is a reaction on Ginsburgh and Zang (2003).It reconsiders the problem where a group of museums offer a pass such that the owner can visit these museums an unlimited number of times during a fixed period of time.The problem addressed is how to share the total joint income of this pass system among the museums.Ginsburgh and Zang propose to use the Shapley value of an associated cooperative game.Arguments are provided to model this problem within the framework of bankruptcy problems.

This paper analyzes capacity restricted cooperative purchasing (CRCP) situations in which a group of cooperating purchasers face two suppliers with limited supply capacity. To minimize the total purchasing costs, we show that two extreme policies have to be compared: order everything at one supplier and the possible remainder at the other. Interestingly, as order quantities increase, various policy switches can occur. To find suitable cost allocations of the total purchasing costs, we model a CRCP-situation as a cost sharing problem. As increasing order quantities also imply concavity breaks due to a forced change in supplier, the corresponding cost function is piecewise concave. For cost sharing problems with concave cost functions, we show that the serial cost sharing mechanism satisfies two desirable properties, unit cost monotonicity (UCM) and monotonic vulnerability for the absence of the smallest player (MOVASP) . However, these properties are lost in the setting of piecewise concave cost functions. We develop a new context specific class of piecewise serial rules based on claims rules. We show that the proportional rule is the only claims rule for which the corresponding piecewise serial rule satisfies UCM. Moreover, the piecewise serial rule corresponding to the constrained equal losses rule satisfies MOVASP.