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

AbstractBoruvka’s algorithm, which computes a 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

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

A characterization of optimistic weighted Shapley rules in minimum cost spanning tree problems

Bergantiños and Lorenzo-Freire (2007) introduce optimistic weighted Shapley rules in minimum cost spanning tree problems. We present an axiomatic characterization of these rules using monotonicity properties

¿Optimistic¿ weighted Shapley rules in minimum cost spanning tree problems

We introduce optimistic weighted Shapley rules in minimum cost spanning tree problems. We define it as the weighted Shapley values of the optimistic game v+ introduced in Bergantiños and Vidal-Puga (2005b). We prove that they are obligation rules (Tijs, Branzei, Moretti, and Norde (2005)). Moreover, we present an axiomatic characterization

A Data-driven Case-based Reasoning in Bankruptcy Prediction

There has been intensive research regarding machine learning models for predicting bankruptcy in recent years. However, the lack of interpretability limits their growth and practical implementation. This study proposes a data-driven explainable case-based reasoning (CBR) system for bankruptcy prediction. Empirical results from a comparative study show that the proposed approach performs superior to existing, alternative CBR systems and is competitive with state-of-the-art machine learning models. We also demonstrate that the asymmetrical feature similarity comparison mechanism in the proposed CBR system can effectively capture the asymmetrically distributed nature of financial attributes, such as a few companies controlling more cash than the majority, hence improving both the accuracy and explainability of predictions. In addition, we delicately examine the explainability of the CBR system in the decision-making process of bankruptcy prediction. While much research suggests a trade-off between improving prediction accuracy and explainability, our findings show a prospective research avenue in which an explainable model that thoroughly incorporates data attributes by design can reconcile the dilemma

Cooperative and axiomatic approaches to the knapsack allocation problem

In the knapsack problem a group of agents want to fill a knapsack with several goods. Two issues should be considered. Firstly, to decide optimally the goods selected for the knapsack, which has been studied in many papers. Secondly, to divide the total revenue among the agents, which has been studied in few papers (including this one). We assign to each knapsack problem several cooperative games. For some of them we prove that the core is non-empty. Later, we follow the axiomatic approach. We propose two rules. The first one is based on the optimal solution of the knapsack problem. The second one is the Shapley value of the so called optimistic game. We offer axiomatic characterizations of both rules

Characterization of monotonic rules in minimum cost spanning tree problems

We characterize, in minimum cost spanning tree problems, the family of rules satisfying monotonicity over cost and population. We also prove that the set of allocations induced by the family coincides with the irreducible core