Poisson voting games under proportional rule

We analyze strategic voting under proportional rule and two parties, embedding the basic spatial model into the Poisson framework of population uncertainty. We prove that there exists a unique Nash equilibrium. We show that it is characterized by a cutpoint in the policy space that is always located between the average of the two parties’ positions and the median of the distribution of voters’ types. We also show that, as the expected number of voters goes to infinity, the equilibrium converges to that of the case with deterministic population size.

Characterizing NTU-bankruptcy rules using bargaining axioms

This paper takes an axiomatic bargaining approach to bankruptcy problems with nontransferable utility, by using properties from bargaining theory in order to characterize bankruptcy rules. In particular, we derive new axiomatic characterizations of the proportional rule, the truncated proportional rule, and the constrained relative equal awards rule, using properties which concern changes in the estate or in the claims.

An Axiomatization of the Proportional Rule in Financial Networks

The most important rule to determine payments in real-life bankruptcy problems is the proportional rule. Many such bankruptcy problems are characterized by network aspects, and the values of the agents’ assets are endogenous as they depend on the extent to which claims on other agents can be collected. These network aspects make an axiomatic analysis challenging. This paper is the first to provide an axiomatization of the proportional rule in financial networks. Our main axiom is invariance to mitosis. The other axioms are claims boundedness, limited liability, priority of creditors, continuity, and impartiality. This paper was accepted by Manel Baucells, decision analysis.

Agricultural Water Allocation under Cyclical Scarcity: The Role of Priority Water Rights

Water is becoming an increasingly scarce resource worldwide, suggesting that water rationing methods should be revised to improve water allocation efficiency, especially during cyclical scarcity events (droughts). The proportional rule is the most widely used rationing method to allocate water in cases of water scarcity. However, this method fails to achieve Pareto-efficient allocation arrangements. Economic theory and international experience demonstrate that implementing security-differentiated water rights could improve allocative efficiency during cyclical scarcity periods. Moreover, it has been proven that this kind of priority rights regime is an efficient instrument to share risks related to water supply reliability, and can thus be considered as an adaptation measure to climate change. This evidence has enabled the development of an operational proposal for the implementation of security-differentiated water rights in the irrigation sector in Spain, as an alternative to the current rights based on the proportional rule. This proposal draws on the Australian case study, which is the most successful experience worldwide. Nevertheless, the insights obtained from the analysis performed and the proposal for reforming the water rights regime are applicable to any country with a mature water economy.

Robust Model of Discrete Competitive Facility Location Problem with Partially Proportional Rule

When consumers faced with the choice of competitive chain facilities that offer exclusive services, current rules cannot describe these customers’ behaviors very well. So we propose a partially proportional rule to represent this kind of customer behavior. In addition, the exact demands of customers in many real-world environments are often difficult to determine. This is contradicting to the assumption in most studies of the competitive facility location problem. For the competitive facility location problem with the partially proportional rule, we establish a robust optimization model to handle the uncertainty of customers’ demands. We propose two methods to solve the robust model by studying the properties of the counterpart problem. The first method MIP is presented by solving a mixed-integer optimization model of the counterpart problem directly. The second method SAS is given by embedding a sorting subalgorithm into the simulated annealing framework, in which the sorting subalgorithm can easily solve the subproblem. The effects of the budget and the robust control parameter to the location scheme are analyzed in a quasi-real example. The result shows that changes in the robust control parameter can affect the customer demands that were captured by the new entrants, thereby changing the optimal solution for facility location. In addition, there is a threshold of the robust control parameter for any given budget. Only when the robust control parameter is larger than this threshold, the market share captured by the new entering firm increases with the increases of this parameter. Finally, numerical experiments show the superiority of the algorithm SAS in large-scare competitive facility location problems.