Cost allocation rules for elastic single‐attribute situations

Many cooperative games, especially ones stemming from resource pooling in queueing or inventory systems, are based on situations in which each player is associated with a single attribute (a real number representing, say, a demand) and in which the cost to optimally serve any sum of attributes is described by an elastic function (which means that the per‐demand cost is non‐increasing in the total demand served). For this class of situations, we introduce and analyze several cost allocation rules: the proportional rule, the serial cost sharing rule, the benefit‐proportional rule, and various Shapley‐esque rules. We study their appeal with regard to fairness criteria such as coalitional rationality, benefit ordering, and relaxations thereof. After showing the impossibility of combining coalitional rationality and benefit ordering, we show for each of the cost allocation rules which fairness criteria it satisfies. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 271–286, 2017     

Probabilistic resource pooling games

We study a setting with a single type of resource and with several players, each associated with a single resource (of this type). Unavailability of these resources comes unexpectedly and with player‐specific costs. Players can cooperate by reallocating the available resources to the ones that need the resources most and let those who suffer the least absorb all the costs. We address the cost savings allocation problem with concepts of cooperative game theory. In particular, we formulate a probabilistic resource pooling game and study them on various properties. We show that these games are not necessarily convex, do have non‐empty cores, and are totally balanced. The latter two are shown via an interesting relationship with Böhm‐Bawerk horse market games. Next, we present an intuitive class of allocation rules for which the resulting allocations are core members and study an allocation rule within this class of allocation rules with an appealing fairness property. Finally, we show that our results can be applied to a spare parts pooling situation.     

Relaxed sequencing games have a nonempty core

We study sequencing situations with a fixed initial order and linear cost functions. Cost savings can be obtained by rearranging jobs. Next to finding an optimal order, an additional issue is formed by the division of these savings. Cooperative game theory studies this issue. A common assumption states that cooperation between players is restricted to groups that are connected according to the initial order. The value of disconnected groups is defined additively over their connected components. In this paper we allow players in disconnected coalitions to switch places as long as they do not hurt the players not in the coalition under consideration. The resulting games are called relaxed sequencing games. Although they have been studied before, no general results on stable profit divisions have been derived so far. In this paper we prove that relaxed sequencing games have a nonempty core, i.e., they all have stable profit divisions. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Coherent systems based on sequential order statistics

The sequential order statistics (SOS) are a good way to model the lifetimes of the components in a system when the failure of a component at time t affects the performance of the working components at this age t. In this article, we study properties of the lifetimes of the coherent systems obtained using SOS. Specifically, we obtain a mixture representation based on the signature of the system. This representation is used to obtain stochastic comparisons. To get these comparisons, we obtain some ordering properties for the SOS, which in this context represent the lifetimes of k‐out‐of‐n systems. In particular, we show that they are not necessarily hazard rate ordered. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

New results on rendezvous search on the interval

In a rendezvous search problem, two players are placed in a network and must try to meet each other in the least possible expected time. We look at rendezvous search on a discrete interval in which the players are initially placed using independent draws (usually assumed to be from the same distribution). Some optimal solutions are known if this distribution is uniform, and also for certain other special types of distribution. In this article, we present two new results. First, we characterize the complete set of solutions for the uniform case, showing that all optimal strategies must have two specific properties (namely, of being swept and strictly geodesic). Second, we relate search strategies on the interval to proper binary trees, and use this correspondence to derive a recurrence relation for solutions to the symmetric rendezvous problem for any initial distribution. This relation allows us to solve any such problem computationally by dynamic programming. Finally, some ideas for future research are discussed. © Wiley Periodicals, Inc. Naval Research Logistics 60: 454–467, 2013     

A Nonlinear Model of Military Expenditure Convergence: Evidence From Estar Nonlinear Unit Root Test

The paper builds a model to empirically test military expenditure convergence in a nonlinear set up. We assert that country A chooses a military strategy of catching up with the military expenditure of its rivals, subject to public spending constraints on public investments, including health and education, leading to decrease in long-term economic welfare. This implies nonlinear convergence path: only when the military expenditure gap between countries reaches the threshold level, will it provide incentives to catch up with rival’s military expenditures. We test this nonlinear catching up hypothesis for 37 countries spanning from 1988 to 2012. Results from individual nonlinear cross-sectionally augmented Dickey–Fuller (NCADF) regression indicate that 53% of countries converge to world’s average military expenditure: where 39% of countries converge to Germany; 33% of countries converge to China; 22% of countries converge to the USA, and 11% of countries converge to Russia. Interestingly, USA does not exhibit nonlinear military expenditure convergence toward world’s average level. For panel NCADF regression, the result suggests that on average, there is evidence for countries converging to USA’s military expenditure at 10% significance level. For the convergence to the world’s average, the statistical significance is at the 1% significance level.     

Inventory pooling games for expensive,low‐demand spare parts

We consider several independent decision makers who stock expensive, low‐demand spare parts for their high‐tech machines. They can collaborate by full pooling of their inventories via free transshipments. We examine the stability of such pooling arrangements, and we address the issue of fairly distributing the collective holding and downtime costs over the participants, by applying concepts from cooperative game theory. We consider two settings: one where each party maintains a predetermined stocking level and one where base stock levels are optimized. For the setting with fixed stocking levels, we unravel the possibly conflicting effects of implementing a full pooling arrangement and study these effects separately to establish intuitive conditions for existence of a stable cost allocation. For the setting with optimized stocking levels, we provide a simple proportional rule that accomplishes a population monotonic allocation scheme if downtime costs are symmetric among participants. Although our whole analysis is motivated by spare parts applications, all results are also applicable to other pooled resource systems of which the steady‐state behavior is equivalent to that of an Erlang loss system. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Conflict circuit breakers in the Great Lakes Region of Africa

Conflict resolution in the African Great Lakes Region has been linked to the protocols and projects agreed upon at the Second International Conference on the Great Lakes Region (ICGLR). The ICGLR created a continental-wide framework of conflict circuit breakers focused on resolving the structural and surface situational causes of the 1996 to 2003 armed conflicts that drew in at least six nations and destabilised the entire region. The implementation of these protocols and projects will serve as a test for the African Great Lakes Region to move away from conflict and into a cooperation and development phase; however, the effort to bring peace, stability and development will face obstacles not only in the security sector, but also in developing infrastructure, civil society, and good governance. In summary, this article contends that peace in the Great Lakes Region will depend equally on two factors: internal governance and building civil society institutions, and focused regional interlocking circuit-breaking institutions.     

Military spending and budget deficits: the impact of US military spending on public debt in Europe (1988–2013)

The aim of this paper is to study the relationship between military spending and sovereign debt in a panel of 13 European countries. In particular, under the assumption of the interdependence of military spending between US and European countries, we analyse whether US military spending affected European sovereign debt in the period 1988–2013. The empirical estimation is based on different steps: (i) a unit root test; (ii) an Arellano–Bond panel estimation and a linear fixed effect model; and (iii) a FMOLS estimation to highlight the long run relationship between debt and relevant variables. General results highlight that debt burden of European countries is: (1) positively associated with US military burden and (2) negatively associated with average military burden of other European countries.     

Solving partially observable agent‐intruder games with an application to border security problems

In this paper, we introduce partially observable agent‐intruder games (POAIGs). These games model dynamic search games on graphs between security forces (an agent) and an intruder given possible (border) entry points and high value assets that require protection. The agent faces situations with dynamically changing, partially observable information about the state of the intruder and vice versa. The agent may place sensors at selected locations, while the intruder may recruit partners to observe the agent's movement. We formulate the problem as a two‐person zero‐sum game, and develop efficient algorithms to compute each player's optimal strategy. The solution to the game will help the agent choose sensor locations and design patrol routes that can handle imperfect information. First, we prove the existence of ?‐optimal strategies for POAIGs with an infinite time horizon. Second, we introduce a Bayesian approximation algorithm to identify these ?‐optimal strategies using belief functions that incorporate the imperfect information that becomes available during the game. For the solutions of large POAIGs with a finite time horizon, we use a solution method common to extensive form games, namely, the sequence form representation. To illustrate the POAIGs, we present several examples and numerical results.