Awards Rule Research Articles

Stable partitions for proportional generalized claims problems

We consider a set of agents who have claims on an endowment that is not large enough to cover all claims. Agents can form coalitions but a minimal coalition size θ is required to have positive coalitional funding that is proportional to the sum of the claims of its members. We analyze the structure of stable partitions when coalition members use well-behaved rules to allocate coalitional endowments, e.g., the well-known constrained equal awards rule (CEA) or the constrained equal losses rule (CEL). For continuous, (strictly) resource monotonic, and consistent rules, stable partitions with (mostly) θ-size coalitions emerge. For CEA and CEL we provide algorithms to construct such a stable partition formed by (mostly) θ-size coalitions.

A new fuzzy approach and bankruptcy theory in risk estimation in Waste Load Allocation.

In this paper, we developed a simulator-optimizer model based on risk analysis to determine Waste Load Allocation (WLA). A new Fuzzy index as Fuzzy Risk Index (FRI) was linked with multi-objective optimization to minimize FRI for the environmental stakeholder and the total cost of sewage treatment for the polluting industries as the other collective stakeholder. Afterwards, the conflict was resolved with the help of Nash bargaining and bankruptcy approach (Constrained Equal Awards Rule). The model was run using quantitative/qualitative data for the KhoramAbad River. To check the efficiency of FRI, the process followed for WLA was reimplemented by the Monte Carlo simulation (MCS). A comparison between the two approaches revealed that the outcomes derived from Fuzzy arithmetic across all aspects, encompassing river qualitative simulation, nondominated curve, Nash bargaining's agreed point, and bankruptcy output, closely mirrored the results of MCS. The notable distinction lies in the drastic reduction of the model's execution time by a factor of 450.

Divide and choose: An informationally robust strategic approach to bankruptcy problems

This paper proposes a simple and general strategic approach for analyzing bankruptcy problems. We construct three strategic bargaining games and show that they yield unique subgame perfect equilibrium (SPE) outcomes that coincide with the allocations given by the three prominent solution concepts, the constrained equal awards rule, the constrained equal losses rule and the Talmud rule, respectively. We also discuss the robustness of the result in the presence of certain incomplete information. The approach can be readily extended to study alternative solutions for bankruptcy problems or other settings such as surplus sharing problems, and is further enriched by considering a voting stage. Central to all these bargaining protocols is an extended and context-fitting “divide-and-choose” mechanism.

Sustainability public Procurement using new procedures of the 2014 Directives

It is common knowledge that the current directives on public contracts 2014/23/EU, 2014/24/EU and 2014/25/EU allow the use of award rules to foster sustainability. In particular, the main directive on public procurement, i.e. Directive 2014/24/EU, states that ‘this Directive clarifies how the contracting authorities can contribute to the protection of the environment and the promotion of sustainable development while ensuring that they can obtain the best value for money for their contracts’ (recital 91). It stems from it that this new ‘horizontal’ objective must be conciled with the core of public procurement rules, best value encapsulating free access to public contracts, equal access and transparency. In other words, there might be situations where those core principles may limit the use of public procurement for enhancing sustainability. Bearing in mind this potential conflict, can the new award procedures put in place in 2014 be an efficient tool to promote the sustainability objective? Here lies the question we propose to deal with in this article. One must first make clear what the expression of new award procedures covers since the 2014/24/EU directive does not refer to any ‘new procedures”. When it comes to novelties, it only refers to ‘new rules’ for cross border joint procurement (recital 72). But making no reference to any new procedures does not necessarily means that no new award procedure was introduced. Indeed, at least one may be ranked in this category. Strictly speaking, the only real new procedure introduced in 2014 is the innovation partnership. It is aimed ‘at the development of an innovative product, service or works and the subsequent purchase of the resulting supplies, services or works, provided that they correspond to the performance levels and maximum costs agreed between the contracting authorities and the participants’ (article 31.2 of directive 2014/24). ‘In the procurement documents, the contracting authority shall identify the need for an innovative product, service or works that cannot be met by purchasing products, services or works already available on the market. It shall indicate which elements of this description define the minimum requirements to be met by all tenders. The information provided shall be sufficiently precise to enable economic operators to identify the nature and scope of the required solution and decide whether to request to participate in the procedure’. There can be either just one or several partner in developing the innovative solutions (article 31.1 of directive 2014/24) (Cerqueira Gomes, 2021). However, two other procedures are relevant for the topic we are addressing: the competitive procedure with negotiation and the competitive dialogue. They actually existed before – the former under a different name – but they can be treated as new non just because their legal regimes have been slightly updated but because, and more importantly, the legal conditions set for their use have been considerably extended. For instance, under the 2004 directive, competitive dialogue was only allowed when a procurement contract was ‘particularly complex’ i.e. when contracting authorities where not objectively able to define the technical means capable of satisfying their needs or objectives, and/or were not objectively able to specify the legal and/or financial make-up of a project (article 1.11.c of Directive 2004/18/EU). Negotiated procedures, as they were then called, where allowed in a limited number of exceptional situations. Both procedures are now subject to the same conditions so widely drafted that they are very likely to be easily met in practice (article 26.4.a. of Directive 2014/24/EU) (Telles and Butler, 2021). The following reflections are based on the analysis of the text of the Directives, of the legal and economic literature regarding sustainable public procurement (SPP) and on a survey that the Chair on public contracts law is currently running1. This Chair uses on the field investigation methods (interviews, online surveys) in order to assess the impact of public contracts rules on the actual purchasing practice. We will first analyse why these new procedures could have been a good tool for sustainable public procurement and then why this has not the case before drawing some conclusions.

Generalizing the constrained equal awards rule

This paper studies axiomatic characterizations of the constrained equal awards rule for bankruptcy problems. We show that many results apply in a much more general context than for which they are originally formulated. In particular, we generalize several axiomatic characterizations based on symmetry, sustainability, and consistency to the domain of bankruptcy problems with nontransferable utility.

Deviation from proportionality and Lorenz-domination for claims problems

The Lorenz order is commonly used to compare rules for claims problems. In this paper, we incorporate the average of awards rule, the mean value of the set of awards vectors for a claims problem, to the ranking of the standard rules by proving some properties that are satisfied by this rule. We define a pair of coefficients, inspired by the Gini index, aimed at measuring, for any given claims problem, the discrepancy between the awards assigned by a rule and the proportional division. We generalize the proportionality deviation indices by introducing coefficients that measure the deviation between the awards selected by any two division rules. We show how these deviation indices are related to the Lorenz order.

Compensation and sacrifice in the probabilistic rationing of indivisible units

We consider the problem of randomly allocating indivisible units of a resource among agents with conflicting claims on the resource. An axiom reflecting a principle of compensation allows us to characterize the focal probabilistic uniform awards rule. A dual axiom reflecting a principle of sacrifice allows us to characterize the (dual) probabilistic uniform losses rule. The combination of two (other) axioms reflecting both principles (of compensation and sacrifice) allows us to characterize the (compromise) probabilistic concede-and-divide in the two-agent case. There is, however, no consistent extension of this rule to the general case of an arbitrary number of agents.

Families of sequential priority rules and random arrival rules with withdrawal limits

This paper deals with extensions of the family of sequential priority rules and the random arrival rule for bankruptcy problems when withdrawal limits are fixed by an arbitrator. We assume two approaches to limit withdrawals. The first is based on the principle that agents can only obtain at most a fixed part of the endowment each time they qualify for an award, and the second that agents can only receive at most a proportion of their claims each time they are attended. For each approach we introduce two pairs of families, each consisting of a sequential priority rule-like family and a random arrival rule-like family. Applying the first approach, we show that the constrained equal awards rule belongs to each of the families. In the second, we prove the same for the proportional rule. We study in detail one pair of families for each approach, and the others are examined in relation to them.

A Game-Theoretic Approach for Electric Power Distribution during Power Shortage: A Case Study in Pakistan

Power supply is the cornerstone for the sustainable socio-economic development of any country. In a developing country like Pakistan, shortage of power supply is the main obstacle to its economic growth, making it a disputed and contested resource among different administrative units/provinces and socio-economic sectors. A key challenge is allocating the limited available power among provinces with conflicting and competing needs amid the supply-demand gap. In this research, the allocation of energy during a shortage is considered as a game-theoretic bankruptcy problem. Five bankruptcy rules namely the Proportional Rule, Constraint Equal Award Rule, Constraint Equal Loss Rule, Talmud Rule and Piniles Rule are used for power allocation among the provinces of Pakistan. Each province is characterized by its power demand. A new framework is also proposed for power allocation, which synthesizes the Nash bargaining solution concept with bankruptcy theory to resolve power-related disputes among the four provinces within Pakistan. Additionally, a new method is introduced in this study to compare and contrast the different allocation rules. The results suggest that the basic power demands of the provinces can be satisfied by the proposed disagreement points among the provinces, and the bargaining weights can highlight the role of different levels of power claims, lengths of transmission lines, and variations in population among provinces. The findings also suggest that, due to the lowest dispersion, the proportionate rule is the most suitable method for power allocation among the provinces. The paper combines relevant bankruptcy rules with Nash bargaining theory to propose an algorithm for addressing power sector supply-demand mismatches in Pakistan.

A strategic justification of the constrained equal awards rule through a procedurally fair multilateral bargaining game

We propose a new game to strategically justify the constrained equal awards rule in claims problems. Our game is “procedurally fair” (claimants are treated equally) and “multilateral” (all claimants negotiate simultaneously). In addition, even if claimants cannot reach an agreement in any period, they can renegotiate in the next period. We show that, for each claims problem, the awards vector chosen by the constrained equal awards rule achieved at period 1 is the unique subgame perfect equilibrium outcome of the game.

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.

Strategic Justification in Claims Problems: Procedurally Fair and Multilateral Bargaining Game

In a claims problem, we propose a new game for strategic justification of the constrained equal awards rule. In contrast to Li and Ju (Mimeo, 2016) and Tsay and Yeh (Games and Economic Behavior, 113, 515-532, 2019), our game is procedurally fair (claimants are treated equally) and multilateral (all claimants negotiate simultaneously). In addition, even if claimants cannot reach an agreement in any period, they can renegotiate in the next period. We show that for each claims problem, the awards vector chosen by the constrained equal awards rule is the unique subgame perfect equilibrium outcome of the game.

Unravelling SMEs’ participation and success in public procurement

Purpose This paper aims to investigate the role of micro, small and medium enterprises (MSMEs) within the Canadian public procurement, by seeking to identify barriers and supporting factors of MSMEs’ participation and success in public tenders. Design/methodology/approach The empirical analysis builds on a unique survey run by the Canadian federal government, which addressed firms either participating or not participating in public tenders. Model estimation on the survey data relies on sample selection methodologies, which allow separating determinants of MSMEs’ decision to participate from determinants of success. Findings Results provide evidence that costs stemming from asset specificity and uncertainty (e.g. costs of bidding, requirements for participation, bundling of contracts and award rules based on minimum price) affect participation in public procurement. Within MSMEs, micro-firms are the most discouraged from participating. However, after controlling for factors affecting participation, micro-firms emerge as having a higher success rate, possibly because of high specialization and joint participation with larger firms. Research limitations/implications Because of the cross-sectional nature of the data used for hypotheses testing, endogeneity may arise if ex post variables affect ex ante decisions. This may apply if participation in procurement feeds on success in past tenders. Social implications Findings may inform policies for the inclusion of smaller firms in the public marketplace. Originality/value To the best of the authors’ knowledge, this study is the first attempting to disentangle determinants of participation in public tenders from determinants of success. Separating the two aspects helps fine-tune SME-friendly public procurement policies, by identifying actions that effectively facilitate success of MSMEs in public tenders.

Proportionality, equality, and duality in bankruptcy problems with nontransferable utility

This paper studies bankruptcy problems with nontransferable utility as a generalization of bankruptcy problems with monetary estate and claims. Following the theory on TU-bankruptcy, we introduce a duality notion for NTU-bankruptcy rules and derive several axiomatic characterizations of the proportional rule and the constrained relative equal awards rule.

An Experimental Game of Loss Sharing

We conduct a lab-experimental study of bargaining over the distribution of monetary losses. Groups of four differently endowed participants must agree, as a group, on the contribution each participant will make to cover a financial loss imposed on the group. The study sheds light on burden sharing and what loss allocation rules groups adopt. Furthermore, we characterize a new theoretical model which contains the proportional rule and equality of losses as special cases but collides with the constrained equal awards rule. The combination of our model and the constrained equal awards rule can explain the majority of proposals made in our experiment.

Water Allocation Using the Bankruptcy Model: A Case Study of the Missouri River

This research applies cooperative game theory—specifically, the bankruptcy model—to address conflicts arising from the scarcity of water resources shared by multiple agents. This case study addresses potential outcomes of five allocation rules applied to the apportionment of water between two agents in the Missouri River. Currently, there is no interstate compact to apportion Missouri River and frequent disputes between upstream and downstream states occur. Upstream states favor managing reservoir water levels to support reservoir recreation and downstream states want water for the downstream navigation channel. The five allocation rules studied are (1) Proportional Sharing, (2) Constrained Equal Awards, (3) Constrained Equal Losses, (4) Sequential Sharing based on Proportional Sharing, and (5) a proposed Modified Constrained Equal Awards rule. The results of the analysis of apportionment during four dry years in the 2000s show that the best approaches are the proposed Modified Constrained Equal Awards Rule and the Proportional Sharing Rule.

Disability and Occupational Labor Transitions: Evidence from South Korea

We examine how certain occupational physical requirements affect labor transitions of disabled workers by exploiting a unique feature of South Korean Disability Insurance (DI), where award rules are based solely on an applicant’s medical condition, independent of his previous occupations. We estimate the labor market response to a health shock by constructing a physical intensity measure from O*NET and applying it to longitudinal South Korean household panel data. Our results suggest that health shocks initially lead to a 14 to 20 percent drop in employment and that this effect is greater for workers who previously held physically demanding occupations. Those who remain part of the labor market exhibit higher occupational mobility toward less physically demanding jobs. These findings imply that the magnitudes of income risks associated with health shocks vary depending on occupational and skill characteristics.

Disability and Occupational Labor Transitions: Evidence from South Korea

We examine how certain occupational physical requirements affect labor transitions of disabled workers by exploiting a unique feature of South Korean Disability Insurance (DI), where award rules are based solely on an applicant’s medical condition, independent of his previous occupations. We estimate the labor market response to a health shock by constructing a physical intensity measure from O*NET and applying it to longitudinal South Korean household panel data. Our results suggest that health shocks initially lead to a 14 to 20 percent drop in employment and that this effect is greater for workers who previously held physically demanding occupations. Those who remain part of the labor market exhibit higher occupational mobility toward less physically demanding jobs. These findings imply that the magnitudes of income risks associated with health shocks vary depending on occupational and skill characteristics.

NTU-bankruptcy problems: consistency and the relative adjustment principle

This paper axiomatically studies bankruptcy problems with nontransferable utility by focusing on generalizations of consistency and the contested garment principle. On the one hand, we discuss several consistency notions and introduce the class of parametric bankruptcy rules which contains the proportional rule, the constrained relative equal awards rule, and the constrained relative equal losses rule. On the other hand, we introduce the class of adjusted bankruptcy rules and characterize the relative adjustment principle by truncation invariance, minimal rights first, and a weak form of relative symmetry.

Multiple‐Winner Award Rules in Online Procurement Auctions

This study investigates a novel mechanism—multiple‐winner award rules—that are widely used in e‐procurement auctions and crowdsourcing sites. In many e‐procurement auctions, the auctioneer (i.e., the buyer) specifies three rules before the auction starts: (i) the size of the finalist set (from which the winner[s] will be chosen); (ii) the number of winners; and (iii) the allocation of the contract among the winners. We examine how these three rules affect auction performance using a dataset of online procurement auctions across a variety of product categories. We find that the multiple‐winner award rules significantly impact the suppliers’ participation decisions, which is an important factor in determining the economic performance of the auction (i.e., buyer's savings). Most interestingly, these three rules systematically induce opposite effects on auction participation for two types of suppliers: experienced and inexperienced bidders. For example, increasing the number of winners encourages experienced suppliers, but discourages inexperienced suppliers from participating in the auction. On the other hand, raising the disparity in the contract allocation among winning bidders (e.g., from 50/50 to 90/10 split) deters experienced suppliers, but motivates inexperienced suppliers to participate. These findings provide guidelines for industrial buyers and crowdsourcing hosts on how to effectively make use of multiple‐winner design levers to promote suppliers’ participation when designing procurement auctions and crowdsourcing contests.