Cost Allocation Rules for Elastic Single-Attribute Situations

Karsten, Frank; Slikker, Marco; Borm, Peter

doi:10.2139/ssrn.2574187

Cited by 2 publications

(3 citation statements)

References 13 publications

(10 reference statements)

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“…However, their work differs from ours because we are considering allocating cost, rather than risk: our cost function is based off of probabilistic factors like the risks {r i }, but the cost is a deterministic function, rather than a random variable, as in these other papers. Closer works to ours include Karsten et al [16], which analyzes "elastic" cost functions, and Guo et al [11], an applied example around allocating resources across call centers (which has a cost function structurally similar to ours).…”

Section: Game Theorymentioning

confidence: 95%

“…Specifically, much of game theory relies on the idea of "fairness" as meaning people who bring more cost to the group should pay a larger share of the total cost. For example, Karsten et al [16] explores multiple variants of pricing schemes that attempt to enforce higher prices for those who contribute higher costs. However, as discussed in the end of Section 2.1, in many realistic cases we might say that it is "fair" to not charge a higher-risk person more.…”

Section: Game Theorymentioning

confidence: 99%

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Better Together? How Externalities of Size Complicate Notions of Solidarity and Actuarial Fairness

Donahue¹,

Barocas²

2021

Preprint

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Consider a cost-sharing game with players of different contribution to the total cost: an example might be an insurance company calculating premiums for a population of mixed-risk individuals. Two natural and competing notions of fairness might be to a) charge each individual the same price or b) charge each individual according to the cost that they bring to the pool. In the insurance literature, these general approaches are referred to as solidarity and actuarial fairness and are commonly viewed as opposites. However, in insurance (and many other natural settings), the cost-sharing game also exhibits externalities of size: all else being equal, larger groups have lower average cost. In the insurance case, we analyze a model with externalities of size due to a reduction in the variability of losses. We explore how this complicates traditional understandings of fairness, drawing on literature in cooperative game theory.First, we explore solidarity: we show that it is possible for both groups (high and low risk) to strictly benefit by joining an insurance pool where costs are evenly split, as opposed to being in separate risk pools. We build on this by producing a pricing scheme that maximally subsidizes the high risk group, while maintaining an incentive for lower risk people to stay in the insurance pool. Next, we demonstrate that with this new model, the price charged to each individual has to depend on the risk of other participants, making naive actuarial fairness inefficient. Furthermore, we prove that stable pricing schemes must be ones where players have the anti-social incentive of desiring riskier partners, contradicting motivations for using actuarial fairness. Finally, we describe how these results relate to debates about fairness in machine learning and potential avenues for future research.

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Section: Game Theorymentioning

confidence: 95%

Section: Game Theorymentioning

confidence: 99%

Better Together? How Externalities of Size Complicate Notions of Solidarity and Actuarial Fairness

Donahue¹,

Barocas²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…According to Swoveland (1975), piecewise concave cost functions are a realistic representation of returns to scale in a production environment. Cost sharing problems with (almost) concave functions are studied in Karsten, Slikker, and Borm (2017), from the perspective of coalitional rationality and benefit ordering.…”

Section: Introductionmentioning

confidence: 99%

Cost Sharing Methods for Capacity Restricted Cooperative Purchasing Situations

2020

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This paper analyzes cooperative purchasing situations with two suppliers with limited supply capacity. In these capacity restricted cooperative purchasing (CRCP) situations we consider a group of cooperating purchasers for whom it turns out to be optimal as a group to order as much as possible at one supplier and the possible remainder at the other. To find suitable cost allocations of the total purchasing costs, a CRCP-situation is modeled as a cost sharing problem, in which the corresponding cost function is piecewise concave and the intervals of concavity are determined by the restricted capacity of the suppliers. It is seen that in the setting with piecewise concave cost functions, standard cost sharing mechanisms lose their axiomatic appeal, e.g. the serial cost sharing mechanism will neither satisfy unit cost monotonicity (UCM) nor monotonic vulnerability for the absence of the smallest player (MOVASP). In fact, it is shown that these two properties are incompatible now. We introduce a new context specific class of piecewise serial rules, in which the vector of order quantities is divided into separate vectors for the different intervals of concavity, using a bankruptcy rule and subsequently apply the serial rule to each interval. We show that the proportional rule is the only bankruptcy rule for which the corresponding piecewise serial rule satisfies UCM. Moreover, we show that the piecewise serial rule corresponding to the constrained equal losses rule satisfies MOVASP.

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Cost Allocation Rules for Elastic Single-Attribute Situations

Cited by 2 publications

References 13 publications

Better Together? How Externalities of Size Complicate Notions of Solidarity and Actuarial Fairness

Better Together? How Externalities of Size Complicate Notions of Solidarity and Actuarial Fairness

Cost Sharing Methods for Capacity Restricted Cooperative Purchasing Situations

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