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A Way to Play Claims Problems
Abstract
Commitment among agents is always difficult, especially when a scarce resource is to be shared. On the one hand, there are many possible ways to assign the available amount; on the other hand, each agent is motivated to propose a distribution that maximizes her award. In this paper, we propose a mechanism that combines the diminishing claims (Chun in Math Soc Sci 17(3):245–261, 1989) and the unanimous concessions (Herrero in Advances in economic design. Springer, Berlin, 2003) procedures, thereby obtaining a new justification of rules based on averaging.
Supplementary resource (1)
... These rules satisfy several desirable properties, and each rule can be used in different bankruptcy scenarios. Bankruptcy theory and Nash bargaining has been applied to various resource allocation scenarios by various researchers [5,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. ...
For the sustainable socio-economic growth, the energy supply is one of the foundations for any country. The gas shortage is one of the most significant impediments to any emerging country’s economic progress, making it a contested and disputed resource. In the middle of a supply–demand mismatch, distributing limited available gas across administrative units/provinces with competing requirements is a key challenge. In this work, an asymmetric gas allocation bargaining model is proposed under gas shortage to resolve natural gas-related disputes among Pakistan’s administrative units/provinces. Each administrative unit/province is characterized by its gas demand. Results show that the Nash bargaining theory, when applied under equal and bargaining weights, can address the supply–demand mismatches of the gas sector in Pakistan. Such an approach could help policymakers to make a fair gas-supply management system during gas shortage periods and would help in resolving the disputes between the provinces.
This paper presents a sequential partition method for non-cooperative games of bankruptcy problems. Based on the ascending order of claims, two consequential games are introduced, called the divide-and-choose game and the divide-and-object game. We prove that the unique Nash equilibrium outcome of each game is consistent with the allocation of the constrained equal awards rule.
Power supply is one of the main backbones of sustainable socio-economic development. In developing countries with rapidly growing economies one of the main problem and obstacle for economic development is shortage of power supply. This makes it a contested resource among different socio-economic sectors. Therefore, distribution of power to different socio-economic sectors with overlapping power demands during power shortage requires careful and strategic decision making in order to maximize the socio-economic benefit that can be obtained out of limited power supply while maintaining equitable distribution. This research article proposed approaching power supply allocation problem during power shortage as game theoretic bankruptcy problem. Then the allocation of power during power scarcity among different socio-economic sectors using the classical bankruptcy allocation techniques was proposed. Each sector is characterized by its power demand. Such an approach could help make power allocation decisions which maximizes the socio-economic benefits from limited power supply by distributing it in a way that can be a base for efficient, reasonable and fair power supply management schemes during periods of power shortage.
A group of agents have claims on a resource but there is not enough of it to honor all of the claims. How should it be divided? A group of agents decide to undertake a public project that they can jointly afford. How much should each of them contribute? This essay is an update of Thomson (2003), a survey of the literature devoted to the study of such problems. (C) 2015 Published by Elsevier B.V.
Mediation is a dispute resolution process where agents reach a mutually acceptable agreement among prominent proposals. This paper provides a natural way of coming to this agreement in bankruptcy problems. The central fact is that such problems can be faced from two different (focal) points of view: awards and losses. Given this views, we assume that agents decide a group of principles on which the distribution of the available resources should be based. Next we define a double recursive process by the application of both a lower and an upper bound on awards. Finally, we obtain that this process concludes at the midpoint between the two focal rules. By applying the result to some possible sets of principles we retrieve the average of old and well known bankruptcy rules.
For three different bankruptcy problems, the 2000-year old Babylonian Talmud prescribes solutions that equal precisely the nucleoli of the corresponding coalitional games. A rationale for these solutions that is independent of game theory is given in terms of the Talmudic principle of equal division of the contested amount; this rationale leads to a unique solution for all bankruptcy problems, which always coincides with the nucleolus. Two other rationales for the same rule are suggested, in terms of other Talmudic principles. (Needless to say, the rule in question is not proportional division).
Consider a two-person bargaining problem, where both agents have a particular notion of what would be a just solution outcome. In case their opinions differ, a procedure which leads to a compromise between t,he two different views is needed. In this paper we propose a mechanism to solve this kind of conflict. Furthermore, we characterize it axiomatically.
It is well known that, in distributions problems, "Fairness" rarely leads to a single viewpoint (see Young (1994) and Moulin (1988) among many others). This paper provides, in this context, interesting basis in defense of intermediate agreements when two prominent proposals, representing different sets of "Equity Principles", highlight a discrepancy in sharing resources. Specifically, we formalize such a conflicting situation by associating it with a "natural" cooperative game, called the Bifocal Distribution game, to show that both the Nucleolus, introduced by Schmeidler (1969), and the Shapley value, proposed by Shapley (1953), agree on recommending the "average of the two focal solutions". Finally, applying our analysis to bankruptcy problems, which have been analyzed extensively by Thomson (2003) and Moulin (2002), provides new "reasonable" solutions.
The solution for the Contested Garment Problemproposed in the Babylonic Talmud,one of the most important sources of inspiration for solving situations where demandovercomes supply of some resources, suggests that each agent should receive at least somepart of the available amount when facing these situations. This idea has underlied thetheoretical analysis of bankruptcy problems from its beginning (ONeill, 1982) to presentday (Dominguez and Thomson, 2006). In this context, starting from the fact that a societyestablishes its own set of Commonly Accepted Equity Principles, we propose a new lowerbound on awards de
ned, for each agent, as the minimum amount she gets according toall the admissible rules for such a society. Moreover, we analyze the recursive applicationof this new bound, since it will not exhaust the resources, in general.
We propose an elementary game form that allows to obtain the allocations proposed by any acceptable bankruptcy rule as the unique payoff vector of the corresponding Nash equilibria.
For the problem of adjudicating conflicting claims, a rule is consistent if the choice it makes for each problem is always
in agreement with the choice it makes for each “reduced problem” obtained by imagining that some claimants leave with their
awards and reassessing the situation from the viewpoint of the remaining claimants. We develop a general technique to determine
whether a given two-claimant rule admits a consistent extension to general populations, and to identify this extension if
it exists. We apply the technique to a succession of examples.
Consider the following nine rules for adjudicating conflicting claims: the proportional, constrained equal awards, constrained equal losses, Talmud, Piniles’, constrained egalitarian, adjusted proportional, random arrival, and minimal overlap rules. For each pair of rules in this list, we examine whether or not the two rules are Lorenz comparable. We allow the comparison to depend upon whether the amount to divide is larger or smaller than the half-sum of claims. In addition, we provide Lorenz-based characterizations of the constrained equal awards, constrained equal losses, Talmud, Piniles’, constrained egalitarian, and minimal overlap rules.
This paper focuses on bankruptcy problems and duality. By introducing the idea of dual properties, we obtain a new characterization of the Constrained Equal Losses rule by means of well-known properties. “Dual” procedures to solve discrepancies can also be used to support, noncoopera-tively, the Constrained Equal Awards and the Constrained Equal Losses rules, respectively.
C onsid er th e follow ing nine ru les for ad ju d icating conî icting claims: th e p ro- p ortional, constrained eq u al aw ard s, constrained eq u al losses, T almu d , P inilesê, constrained eg alitarian, ad ju sted p rop ortional, rand om arriv al, and minimal ov erlap ru les. F or each p air of ru les in th is list, w e ex amine w h eth er or not th e tw o ru les are L orenz comp arab le. W e allow th e comp arison to d ep end u p on w h eth er th e amou nt to d iv id e is larg er or smaller th an th e h alf-su m of claims. In ad d ition, w e p rov id e L orenz-b ased ch aracterizations of th e constrained eq u al aw ard s, constrained eq u al losses, T almu d , P inilesê, constrained eg alitarian, and minimal ov erlap ru les.
We consider the problem faced by players in a two-person bargaining game who have different opinions about what is the appropriate solution concept to use. A procedure is proposed to resolve such a conflict and it is shown that the Nash bargaining solution constitutes the unique equilibrium of the game induced by the procedure. As a by-product we obtain that in the axiomatic characterization of the Nash solution, the controversial “independence of irrelevant alternatives” axiom can be replaced by a much weaker recursivity axiom, which amounts to requiring independence of alternatives that cannot be obtained as an outcome of a risk sensitive solution.
When a firm goes bankrupt, how should its liquidation value be divided among its creditors? This essay is an introduction to the literature devoted to the formal analysis of such problems. We present the rules that are commonly used in practice or discussed in theoretical work. We show how many can be obtained by applying solution concepts developed in cooperative game theory (for bargaining games and for coalitional games). We formulate properties of rules, first when the population of agents is fixed, then when it may vary, compare the rules on the basis of these properties, and search for rules satisfying the greatest number of the properties together. We model the resolution of conflicting claims as strategic games, and extend the model to handle surplus sharing and situations in which the feasible set is specified in utility space. Identifying well-behaved taxation rules is formally identical to identifying rules to reconcile conflicting claims, and all of the results we present can be reinterpreted in that context.
This paper provides a comparative analysis of some classical solutions to bankruptcy problems from an axiomatic viewpoint. These rules are the constrained equal-awards rule, the constrained equal-losses rule, the proportional rule and the Talmud rule. The purpose of this study is to facilitate the understanding of their differences and to clarify the type of situations in which each of these rules is better.
We consider the problem of allocating some amount of an infinitely divisible and homogeneous resource among agents having claims on this resource that cannot be jointly honored. A “rule” associates with each such problem a feasible division. Our goal is to uncover the structure of the space of rules. For that purpose, we study “operators” on the space, that is, mappings that associate to each rule another one. Duality, claims truncation, and attribution of minimal rights are the operators we consider. We first establish a number of results linking them. Then, we determine which properties of rules are preserved under each of these operators, and which are not.
We consider a surplus sharing problem faced by a group of agents who have different opinions as to how such problems should be solved in general. We propose a procedure to resolve the conflict and show that each agent receives an equal share of the surplus in all noncooperative Nash equilibria of the game induced by the procedure.
Consider a two-person bargaining problem, where both agents have a particular notion of what would be a just solution outcome. In case their opinions differ, a procedure which leads to a compromise between t,he two different views is needed. In this paper we propose a mechanism to solve this kind of conflict. Furthermore, we characterize it axiomatically.
The paper presents a framework in which the most important single-valued solutions in the literature of TU games are jointly analyzed. None of the main results is original.
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