Population Monotonic Allocation Schemes in Bankruptcy Games

doi:10.1023/A:1016316622277

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Population Monotonic Allocation Schemes in Bankruptcy Games

Journal Article•DOI•

Population Monotonic Allocation Schemes in Bankruptcy Games

Sofia Grahn¹, Mark Voorneveld²•Institutions (2)

Uppsala University¹, Stockholm School of Economics²

01 Jan 2002-Annals of Operations Research (Springer)-Vol. 109, Iss: 1, pp 317-329

TL;DR: Rules satisfying these axioms are shown to yield population monotonic allocation schemes and the thieve property for bankruptcy problems.

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Abstract: The USA Bankruptcy Code legislates the bankruptcy of firms. Any allocation mechanism that is legal according to the Bankruptcy Code is necessarily population monotonic. Bankruptcy rules yielding a population monotonic allocation scheme in the associated bankruptcy game are characterized by efficiency, reasonability (each claimant receives a nonnegative amount not exceeding his claim), and the thieve property. The thieve property for bankruptcy problems entails that if a claimant manages to escape with his claim, the amount allocated to each remaining claimant is not larger than his share in the original problem. Many bankruptcy rules studied in the literature are efficient, reasonable, self-consistent, and monotonic. Rules satisfying these axioms are shown to yield population monotonic allocation schemes.

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Journal Article•DOI•

Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: an update

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William Thomson¹•Institutions (1)

University of Rochester¹

01 Jul 2003-Mathematical Social Sciences

TL;DR: This essay is an update of Thomson (2003), a survey of the literature devoted to the study of such problems as a group of agents having claims on a resource but there is not enough of it to honor all of the claims.

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577 citations

Journal Article•DOI•

Selecting permit allocation rules for agricultural pollution control: a bargaining solution

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Athanasios Kampas¹, Ben White²•Institutions (2)

Agricultural University of Athens¹, University of Western Australia²

01 Dec 2003-Ecological Economics

TL;DR: In this article, an asymmetric Nash bargaining framework is employed to characterise agents' co-operative behaviour and explain their likely preferences over permit allocation rules, and some potential links between ex-ante and ex-post equity criteria were also discussed.

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50 citations

Cites background from "Population Monotonic Allocation Sch..."

...Finally, the AP rule initially allocates the agents’ minimal rights and then divides the remainder according to their claims (Grahn and Voorneveld, 2002)....
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...The second group of allocation rules stems from so-called ‘bankruptcy games’, a situation where the agents demands exceed the value of goods or rights to be divided (Grahn and Voorneveld, 2002)....
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Journal Article•DOI•

A proportional approach to claims problems with a guaranteed minimum

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José-Manuel Giménez-Gómez, Josep E. Peris

01 Jan 2014-European Journal of Operational Research

TL;DR: It is obtained that the recursive application of this process finishes at the Constrained Equal Awards solution (CEA), and it is shown that the most egalitarian compromise fulfilling this restriction ensures a minimum amount to each agent.

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32 citations

Cites methods from "Population Monotonic Allocation Sch..."

...We name this operation Self-composition, since it is related to the Self-consistency property (see for instance Grahn and Voorneveld (2002)).14 In particular, Self-composition proposes a “recursive” distribution of the resources starting from agent 1....
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...We name this operation Self-composition, since it is related to the Self-consistency property (see for instance Grahn and Voorneveld (2002))....
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Journal Article•DOI•

Mediation in claims problems

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José-Manuel Giménez-Gómez, Josep E. Peris

10 May 2014-Series

TL;DR: This paper provides a natural way of coming to agreements in claims problems by combining a set of fair properties and a criterion for delimiting the admissible manners of distributing the endowment that concludes at the midpoint between the two dual points of view.

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Abstract: Mediation is a dispute resolution process whereby agents reach a mutually acceptable agreement among different proposals that satisfy a set of principles. This paper provides a natural way of coming to such agreements in claims problems. In our approach, mediation combines (i) a set of fair properties (legitimate principles); and (ii) a criterion for delimiting the admissible manners of distributing the endowment, that is determined by the mediator expressing the two (dual) points of view to face such problems: awards and losses. These dual views define a lower and an upper bounds on awards, which are used to implement the so-called Double Recursive Process. We find that this process concludes at the midpoint between the two dual points of view. Finally, we argue that the criterion of the mediator could be established throughout Lorenz domination. In so doing, we retrieve the average of old and well-known rules.

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4 citations

Cites background from "Population Monotonic Allocation Sch..."

...2 For instance, “any bankruptcy rule that is in line with the existing laws as described in the USA Bankruptcy Code is necessarily population monotonic” (Grahn and Voorneveld 2002)....
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Posted Content•

A Proportional Approach to Bankruptcy Problems with a guaranteed minimum.

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M. Gim, Josep E. Peris

22 Mar 2012-Research Papers in Economics

TL;DR: In this article, a convex combination of the proportional and the egalitarian division is proposed to solve the problem of the constrained equal awards rule in bankruptcy, where no agent receives more than her claim, and the remaining estate is distributed in a proportional way.

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Abstract: In a distribution problem, and specically in bankruptcy issues, the Proportional (P ) and the Egalitarian (EA) divisions are two of the most popular ways to resolve the conict. The Constrained Equal Awards rule (CEA) is introduced in bankruptcy literature to ensure that no agent receives more than her claim, a problem that can arise when using the egalitarian division. We propose an alternative modication, by using a convex combination of P and EA. The recursive application of this new rule nishes at the CEA rule. Our solution concept ensures a minimum amount to each agent, and distributes the remaining estate in a proportional way.

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4 citations

Additional excerpts

...12 for instance Grahn and Voorneveld (2002))....
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Journal Article•DOI•

Game theoretic analysis of a bankruptcy problem from the Talmud

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Robert J. Aumann¹, Michael Maschler¹•Institutions (1)

Hebrew University of Jerusalem¹

01 Aug 1985-Journal of Economic Theory

TL;DR: For three different bankruptcy problems, the 2000-year old Babylonian Talmud prescribes solutions that equal precisely the nucleoli of the corresponding coalitional games, and a rationale for these solutions that is independent of game theory is given in this article.

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950 citations

"Population Monotonic Allocation Sch..." refers background in this paper

...This is done by adopting an axiomatic approach, as suggested in the opening chapter of Patrone et al. [7], where Maschler [5] provides “some tips concerning application of game theory to real problems” and states: “. . . when we make a recommendation on a cooperative-type real issue we are faced with a problem of choosing the right solution concept....
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...It can be seen in Aumann and Maschler [2, pp. 201, 202, 205)] that the rules PR, TAL, CEA, and CEL (to which Aumann and Maschler refer as the “dual” of CEA), satisfy monotonicity, self-consistency, efficiency, and reasonability....
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...Bankruptcy problems and their associated cooperative games were introduced and studied in O’Neill [6], Aumann and Maschler [2], and Curiel, Maschler, and Tijs [3], among other papers....
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...Curiel, Maschler and Tijs [3] gave a much more involved, indirect proof of this result....
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...The proof above simplifies that of Curiel, Maschler and Tijs ([3], theorem 6, p. 154, using theorem 2 on p. 151), who give a more involved, indirect proof of this result....
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Journal Article•DOI•

A problem of rights arbitration from the Talmud

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Barry O'Neill¹•Institutions (1)

Northwestern University¹

01 Jun 1982-Mathematical Social Sciences

TL;DR: The method endorsed here regards the problem as one of rights arbitration in which the division is based on interpreting the applicable rules, rather than on weighing the parties' powers and possible benefits.

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779 citations

"Population Monotonic Allocation Sch..." refers background or methods in this paper

...O’Neill [6] was the first to associate a cooperative game with a bankruptcy problem....
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...Bankruptcy problems and their associated cooperative games were introduced and studied in O’Neill [6], Aumann and Maschler [2], and Curiel, Maschler, and Tijs [3], among other papers....
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...The Shapley rule is used in O’Neill [6] and is referred to as the recursive completion rule....
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Journal Article•DOI•

Population monotonic allocation schemes for cooperative games with transferable utility

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Yves Sprumont¹•Institutions (1)

Virginia Tech¹

01 Dec 1990-Games and Economic Behavior

TL;DR: In this paper, the authors show that a game has a population monotonic allocation scheme (PMAS) if and only if it is a positive linear combination of simple games with veto control.

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326 citations

Journal Article•DOI•

On Dividing an Amount According to Individual Claims or Liabilities

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H. Peyton Young¹•Institutions (1)

University of Maryland, College Park¹

01 Aug 1987-Mathematics of Operations Research

TL;DR: Every consistent, continuous taxation method optimizes an additively separable objective function and optimal allocations may be computed by a simple Lagrange multiplier technique.

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Abstract: A basic principle of distributive justice states that if an allocation among a group of individuals is fair, then it should be perceived as fair when restricted to each subgroup of individuals. This 'consistency' principle applies in particular to methods for allocating taxes among citizens according to their ability to pay. Every consistent, continuous taxation method optimizes an additively separable objective function. Optimal allocations may be computed by a simple Lagrange multiplier technique. Similar results hold for allocating assets among creditors according to their claims. The techniques are illustrated by constructing an objective function for a bankruptcy method from the Babylonian Talmud.

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250 citations

"Population Monotonic Allocation Sch..." refers background in this paper

...Young [10], for instance, suggests a dual interpretation, where the estate is to be considered as a tax that is to be paid and the claims correspond with the individuals’ ability to pay....
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Journal Article•DOI•

Bankruptcy games

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I. J. Curiel¹, M. Maschler², Stef Tijs¹•Institutions (2)

The Catholic University of America¹, Hebrew University of Jerusalem²

01 Sep 1987

TL;DR: In this paper, the authors considered bankruptcy problems from a game theoretic point of view and provided necessary and sufficient conditions for a division rule for bankruptcy problems to be a game-theoretic rule.

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Abstract: Bankruptcy problems are considered from a game theoretic point of view. Solution concepts from cooperative game theory are studied for bankruptcy games. A necessary and sufficient condition for a division rule for bankruptcy problems to be a game theoretic rule is given. A new division rule which is an adjustment of the proportional rule is given. This rule coincides with theT-value for bankruptcy games. Properties of the new rule are treated and a set of characterizing properties is given.

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209 citations