Sharing Rules Research Articles

Strategic Bilateral Exchange with Joint Harm: a Comparison of Three Liability Sharing Rules

Strategic Bilateral Exchange with Joint Harm: a Comparison of Three Liability Sharing Rules

Intrahousehold Resources Allocation in Thailand: Sharing Rules and Determinants

Intrahousehold Resources Allocation in Thailand: Sharing Rules and Determinants

Experimental evidence on sharing rules and additionality in transfer payments

This study presents novel evidence showing that group payments distributed proportional to effort are as effective as payments targeted to individuals in increasing public good provision. The decision setting includes donors who make transfer payments to public good providers. The institutions under consideration are motivated primarily by payments for ecosystem services (PES), such as payments for climate protection. The decision settings, however, capture attributes of many forms of charitable giving where NGO type organizations support activities that provide public good externalities beyond those who directly benefit. Results are presented from two studies, varying the sharing rules for transfers among group members (equal share, proportional share, and individual targeting) and the presence of additionality, whereby transfers are received contingent on public good provision being at a level higher than in initial decision periods. The sharing rules studied result in significant differences in cooperation levels. Supported by higher transfer subsides, both the proportional share and targeted-transfers to individuals lead to greater public good provision relative to the equal share rule. Contrary to its alleged relevance in the literature, additionality does not lead to sustained increases in public good provision. Yet, additionality may improve the cost-effectiveness of transfer programs by precluding transfer payments when the subsidies are not effective in increasing public good provision.

Prize Sharing Rules in Collective Contests: When Does Group Size Matter?

In this paper we deal with situations of collective contests between two groups over a private prize. A well known way to divide the prize within the winning group is the prize sharing rule introduced by Nitzan, 1991. Since its introduction it has become a standard in the collective contests literature. We generalize this rule by introducing a restriction we call norms of competitiveness of a group. We fully characterize how group sizes interact with such norms. What we show is that the smaller group is generally aggressive, but the larger group needs to have really egalitarian norms to behave aggressively in the contest. We also take up the question of how group welfare relates to group sizes under the stated norms. We provide a complete set of conditions under which the larger group fares worse in the contest, a phenomenon called Group Size Paradox (GSP) in the literature.

Prize Sharing Rules in Collective Contests: Towards Strategic Foundations

In this paper we deal with situations of collective contests between two groups over a private prize. A well known way to divide the prize within the winning group is the prize sharing rule introduced by Nitzan, 1991. Since its introduction it has become a standard in the collective contests literature. Despite its popularity this rule is ad hoc. In this paper we try to provide strategic foundations to it. To achieve that aim we introduce another rule which represents intra-group cooperation. We give both the groups a choice between the prize sharing rules and cooperative rules in an appropriately constructed game. We find that the prize sharing rules may indeed be chosen by both groups in an equilibrium of a Coordination game, where the other equilibrium is both groups choosing the cooperative rule. However, the equilibrium with cooperative rules payoff dominates the one with the prize sharing rules. But, when we subject the equilibria to the selection criterion of risk dominance and security principle, we find that indeed the equilibrium with the prize sharing rules may be chosen under certain circumstances. This helps us establish robust strategic foundations of the prize sharing rules introduced in Nitzan, 1991.

Linear Versus Nonlinear Allocation Rules in Risk Sharing Under Financial Fairness

In a risk exchange, participants trade a privately owned risk for a share in a pool. If participants agree on a valuation rule, it can be decided whether or not, according to the given rule, these trades take place at equal value. If equality holds for all participants, then the exchange is said to be fair. It has been shown by Buehlmann and Jewell (1979) that, under mild assumptions, the constraint of financial fairness singles out a unique solution among the set of all Pareto efficient risk exchanges. In this paper, we find that an analogous statement is true if we limit ourselves to linear exchanges. Conditions are provided for existence and uniqueness of linear sharing rules that are both financially fair and Pareto efficient among all linear sharing rules. We compare the performance of the linear rule to that of the general (nonlinear) rule in a number of specific cases.

The Shapley Value, Proper Shapley Value, and Sharing Rules for Cooperative Ventures

Moulin (1987) studies the equal and proportional sharing rule for a special class of cooperative games that he calls joint venture games. Proportionality is an important principle in allocation problems. Besides some special cases, it is not obvious how proportionality should be applied in cooperative TU-games. Such special cases, where proportionality is obvious, are inessential games and cooperative joint venture games. In this paper, we discuss an explicit axiom that shows that proper Shapley values can be seen as an appropriate way to express proportionality in value allocation in cooperative TU-games. We characterize positive proper Shapley values by affine invariance and an axiom that requires proportional allocation according to the individual singleton worths in generalized joint venture games. As a counterpart, we show that affine invariance and an axiom that requires equal allocation of the surplus in generalized joint venture games, characterize the positive part of the Shapley value among the single-valued solutions.

Production Sharing Rules and Optimality of Planted-Shared Farming Contracts

Production Sharing Rules and Optimality of Planted-Shared Farming Contracts

Allocation of Liability: On the Efficiency of Composite Sharing Rules

Distributing liability according to injurers' relative fault produces incentives for rent-seeking (excessive care) or free-riding (insufficient care) if precautions are complements or substitutes. We show that composite sharing rules consisting of different weights of proportional and equal allocations calibrate injurers' incentives. The optimal weight of the proportional relative to the equal allocation increases with the degree of substitutability between injurers' precautions. As the number of injurers increases, the optimal composite rule tends to an equal allocation if precautions are pure complements or one where the most careless injurer is liable for the entire harm if precautions are pure substitutes.

Allocation of Liability: On the Efficiency of Composite Sharing Rules

Allocation of Liability: On the Efficiency of Composite Sharing Rules

Allocation of Liability: On the Efficiency of Composite Sharing Rules

Allocation of Liability: On the Efficiency of Composite Sharing Rules

Developing new scenarios for water allocation negotiations: a case study of the Euphrates River Basin

Abstract. Mismanagement and uneven distribution of water may lead to or increase conflict among countries. Allocation of water among trans-boundary river neighbours is a key issue in utilization of shared water resources. The bankruptcy theory is a cooperative Game Theory method which is used when the amount of demand of riparian states is larger than total available water. In this study, we survey the application of seven methods of Classical Bankruptcy Rules (CBRs) including Proportional (CBR-PRO), Adjusted Proportional (CBR-AP), Constrained Equal Awards (CBR-CEA), Constrained Equal Losses (CBR-CEL), Piniles (CBR-Piniles), Minimal Overlap (CBR-MO), Talmud (CBR-Talmud) and four Sequential Sharing Rules (SSRs) including Proportional (SSR-PRO), Constrained Equal Awards (SSR-CEA), Constrained Equal Losses (SSR-CEL) and Talmud (SSR-Talmud) methods in allocation of the Euphrates River among three riparian countries: Turkey, Syria and Iraq. However, there is not a certain documented method to find more equitable allocation rule. Therefore, in this paper, a new method is established for choosing the most appropriate allocating rule which seems to be more equitable than other allocation rules to satisfy the stakeholders. The results reveal that, based on the new propose model, the CBR-AP seems to be more equitable to allocate the Euphrates River water among Turkey, Syria and Iraq.

Voting for Burden Sharing Rules in Public Goods Games

In this experiment, we endogenize the choice of which contribution scheme is implemented in a public goods game. We investigate three rule-based contribution schemes. In a first step, players agree on a common group provision level using the principle of the smallest common denominator. Subsequently, this group investment is allocated according to a specific rule to individual minimum contributions. The game is implemented either as a Single- or a Multi-Phase Game. In the Single-Phase Game, the contribution schemes are exogenously implemented. In the Multi-Phase Game, we let subjects vote on the rule-based contribution schemes. If a scheme obtains a sufficient majority it is implemented. In case no sufficient majority is reached, subjects have to make their contributions to the public good using the voluntary contribution mechanism (VCM). Our results suggest that the endogenous choice of a contribution scheme has an impact on the level of contributions. In case of a rule-based contribution scheme which equalizes payoffs, contributions are higher if subjects choose the scheme than in case the scheme is implemented exogenously. In contrast, contributions are higher if the VCM is implemented exogenously than in case a sufficient majority cannot be obtained and, therefore, subjects have to play the VCM.

Voting for Burden Sharing Rules in Public Goods Games

We experimentally investigate whether groups of heterogeneous agents can reach an agreement on how to share the costs of providing a public good. Thereby, we explore the performance of different burden sharing rules being implemented either endogenously or exogenously. In case of an endogenously implemented burden sharing rule, subjects vote for different burden sharing schemes either by unanimity or majority vote. Despite the fact that preferences for the allocation schemes differ among agents, most groups agree upon a common scheme, and consequently avoid an uncoordinated action. Our results reveal both the opportunities and risks of burden sharing negotiations. We find average efficiency levels to increase in case an agreement is reached. If groups however fail to agree upon a common rule, cooperation collapses and efficiency levels decrease compared to a voluntary contribution mechanism being exogenously imposed. Most importantly, agents who face a voting decision on average receive higher payoffs than agents in an exogenously implemented voluntary contribution mechanism and do not earn less than participants in any externally determined burden sharing rule.

Endogenous Group Formation in Contests: Unobservable Sharing Rules

We study contests in which players compete by expending irreversible effort to win a prize, the prize is awarded to one of the players, the winner shares the prize with other players in his group, if any, and each group's sharing rule is unobservable to the other groups and the singletons, if any, when the players expend their effort. The number of groups, their sizes, and the number of singletons are exogenous in the first model, whereas they are endogenous in the second model. We show that group formation occurs if the number of players is four or smaller, but does not occur otherwise. We examine the effect of endogenous group formation on total effort level and the profitability of endogenous group formation. In each of the two models, comparing the outcomes of the case of unobservable sharing rules with those of the case of observable sharing rules, we show that the two cases yield quite different outcomes.

Reallocating Water: An Application of Sequential Sharing Rules to Cyprus

Water scarcity has become a major constraint on economic development in many regions of the world and sectoral water reallocation is now widely recognized as an essential step toward the sustainable management of water resources. This paper offers an approach to the reallocation of water among sectors based on sequential sharing rules. An essential feature of this approach is that it takes jointly into account a multiplicity of aspects which are critical to many water reallocation problems, but have often been neglected by the theoretical literature. Such aspects include pre-existing customary (or other) rights, scarcity constraints, the chronological order of sectors’ arrivals and environmental water demand. In doing so, our framework can help achieve a solution which is not only more efficient, but also perceived as legitimate and fair. Sequential sharing rules can be used to support or complement other approaches to water allocation, including those based on water markets. Our framework is illustrated using an application to inter-sectoral water reallocation in Cyprus.

On the Importance of Uniform Sharing Rules for Efficient Matching

The paper aims to provide a possible explanation for the occurrence of uniform, fixed-proportion rules for sharing surplus in two-sided markets. We study a two-sided matching model with transferable utility where agents are characterized by privately known, multi-dimensional attributes that jointly determine the surplus of each potential partnership. We ask the following question: for what divisions of surplus within matched pairs is it possible to implement the efficient (surplus-maximizing) matching? Our main result shows that the only robust rules compatible with efficient matching are those that divide realized surplus in a fixed proportion, independently of the attributes of the pair's members: each agent must expect to get the same fixed percentage of surplus in every conceivable match. A more permissive result is obtained for one-dimensional attributes and supermodular surplus functions.

Negotiating Weights for Burden Sharing Rules Among Heterogeneous Parties: Empirical Evidence from a Survey Among Delegates in International Climate Negotiations

Given the vital and controversial debate on fairness concerns in international climate negotiations, the acceptance of a climate treaty may be fostered if the distribution of costs and benefits from global environmental protection is perceived to be “fair”. Since an agreement must be acceptable to all negotiating countries, it is likely that no single burden sharing concept will gain unconditional support from all parties. We have conducted a world-wide survey among participants in international climate negotiations to address the question whether negotiating weights for different fairness concepts may enlarge the bargaining space among heterogeneous agents and overcome the currently dominating self-interested use of fairness claims. Even though our empirical results confirm different positions on burden sharing among key regions, there is evidence that a broad majority favors allocations that are based on a variety of fairness rules. Turning the debate rather towards justice claims based on needs than towards culpability may serve as a fruitful starting point to depart from a purely egoistic use of equity rules in international climate negotiations.

The Filtering Effect of Sharing Rules

Sharing rules have a filtering effect on violations: they prevent the most harmful violations and let the least harmful ones occur. We show under what conditions the filtering effect improves social welfare and argue that this may explain why, in most areas of the law, sharing rules are, in general, preferred to rules that entirely burden one party. Our analysis applies to comparative negligence, communal liability, the allocation of police investigation efforts, contract remedies for non-verifiable breaches such as those that may occur in marriage and employment contracts, and to the distribution of shares in partnerships.

The Cake-Eating Problem: Non-Linear Sharing Rules

Consider the most simple problem in microeconomics, a maximization problem with an additive separable utility function over bundles of two goods which provide equal satisfaction to an agent. Although simple, this framework allows for a very wide range of applications, from the Arrow-Debreu contingent claims case to the risk-sharing problem, including standard portfolio choice, intertemporal individual consumption, demand for insurance and tax evasion. We show that any Engel curve can be generated through such a simple program and the necessary and sufficient restrictions on the demand system to be the outcome of such a maximisation process. Moreover, we identify three classes of utility function that generate non-linear sharing rules. The gap between the two expenditure shares increases in absolute, average or marginal terms with the total amount of wealth, depending on whether DARA, DRRA and convex risk tolerance are considered. The extension of the different results to the case of more than two goods is provided.