Search

This paper proposes a new refinement of Nash equilibria. Where most existing refinements are based on a thought experiment which imposes a certain ‘imperfection’ on the choices of individual players, we consider a thought experiment in which the imperfections occur on a global, ‘system’ level. If an imperfection occurs, the actions as prescribed by the players’ strategic choices are blocked for all players simultaneously, rather than for individual players. The idea behind this is that after players submit their strategies, some entity or system converts these strategies into actions leading to payoffs. In this new thought experiment, with small probability, this entity makes an error that blocks the chosen combination of actions instead of implementing them, and chooses a random combination of the remaining actions. We refer to an equilibrium based on this thought experiment as an entangled equilibrium. Focusing on bimatrix games, we show that the set of entangled equilibria is non-empty and the union of a finite number of polytopes. Finally, we discuss a geometriccombinatorial approach to efficiently determine all entangled equilibria of 2 × n bimatrix games, gaining practical insight in the exact workings of the underlying thought experiment.

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 article models the inherent cooperative and non-cooperative incentives of stakeholders in investment projects in a novel way by combining concepts from co operative game theory and real options theory. As stakeholders have outside options, in the sense that they may terminate negotiations with the current coalition and join another, we introduce and analyze a coalitional and dynamic stability concept. We show that investment projects, in which cooperation between stakeholders is necessary, are more prone to coalitional instability when there are insufficient synergies between the stakeholders. We characterize the proportional investment scheme as the investment scheme that maximizes the total project value and that results in the earliest investment timing. A failure to implement proportional investing leads to the formation of a smaller, less efficient, coalition. The vulnerability to fail is exacerbated in a market that is characterized by high profit growth and low profit uncertainty, or vice versa. Finally, we explicitly consider one-leader investment projects and characterize the prioritized investment scheme that maximizes the value of the leader. We show that the same market conditions govern the stability of the prioritized investment scheme, which contributes to the robustness of our results.

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.

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

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.

This paper studies a new type of interactive Operations Research problem, called a graph machine scheduling problem (GMS-problem). A GMS-problem combines aspects from minimum cost spanning tree problems 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 cost allocation of such an optimal order among the players involved. We restrict attention to GMS-problems on trees and propose a recursive method to solve these tree GMS-problems integrated with an allocation approach. This latter mechanism consistently and recursively uses myopic reference orders to determine potential cost savings, which will then be appropriately allocated. Interestingly, the transition process from a myopic reference order to an optimal one will be smooth using the switching of blocks of agents based on the basic notion of merge segments.