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Bankruptcy Problem
A bankruptcy problem, also called a claims problem, is a problem of distributing a homogeneous divisible good (such as money) among people with different claims. The focus is on the case where the amount is insufficient to satisfy all the claims. The canonical application is a bankrupt firm that is to be liquidated. The firm owes different amounts of money to different creditors, but the total worth of the company's assets is smaller than its total debt. The problem is how to divide the scarce existing money among the creditors. Another application would be the division of an estate amongst several heirs, particularly when the estate cannot meet all the deceased's commitments. A third application is ''tax assessment''. One can consider the claimants as taxpayers, the claims as the incomes, and the endowment as the total after-tax income. Determining the allocation of total after-tax income is equivalent to determining the allocation of tax payments. Definitions The amount ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fair Division Of A Single Homogeneous Resource
Fair division of a single homogeneous resource is one of the simplest settings in fair division problems. There is a single resource that should be divided between several people. The challenge is that each person derives a different utility from each amount of the resource. Hence, there are several conflicting principles for deciding how the resource should be divided. A primary conflict is between efficiency and equality. Efficiency is represented by the ''utilitarian'' rule, which maximizes the sum of utilities; equality is represented by the ''egalitarian'' rule, which maximizes the minimum utility. Setting In a certain society, there are: * t units of some divisible resource. * n agents with different "utilities". * The utility of agent i is represented by a function u_i; when agent i receives y_i units of resource, he derives from it a utility of u_i(y_i). This setting can have various interpretations. For example: * The resource is wood, the agents are builders, and the ut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cooperative Bargaining
Cooperative bargaining is a process in which two people decide how to share a surplus that they can jointly generate. In many cases, the surplus created by the two players can be shared in many ways, forcing the players to negotiate which division of payoffs to choose. Such surplus-sharing problems (also called bargaining problem) are faced by management and labor in the division of a firm's profit, by trade partners in the specification of the terms of trade, and more. The present article focuses on the ''normative'' approach to bargaining. It studies how the surplus ''should'' be shared, by formulating appealing axioms that the solution to a bargaining problem should satisfy. It is useful when both parties are willing to cooperate in implementing the fair solution. The five axioms, any Nash Bargaining Solution should satisfy are Pareto Optimality (PAR), Individual Rationality (IR), Independent of Expected Utility Representations (INV), Independence of Irrelevant Alternatives (IIA) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bankruptcy Theory
Bankruptcy is a legal process through which people or other entities who cannot repay debts to creditors may seek relief from some or all of their debts. In most jurisdictions, bankruptcy is imposed by a court order, often initiated by the debtor. Bankrupt is not the only legal status that an insolvent person may have, and the term ''bankruptcy'' is therefore not a synonym for insolvency. Etymology The word ''bankruptcy'' is derived from Italian ''banca rotta'', literally meaning "broken bank". The term is often described as having originated in renaissance Italy, where there allegedly existed the tradition of smashing a banker's bench if he defaulted on payment so that the public could see that the banker, the owner of the bench, was no longer in a condition to continue his business, although some dismiss this as a false etymology. History In Ancient Greece, bankruptcy did not exist. If a man owed and he could not pay, he and his wife, children or servants were forced into " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strategic Bankruptcy Problem
A strategic bankruptcy problem is a variant of a bankruptcy problem (also called ''claims problem'') in which claimants may act strategically, that is, they may manipulate their claims or their behavior. There are various kinds of strategic bankruptcy problems, differing in the assumptions about the possible ways in which claimants may manipulate. Definitions There is a divisible resource, denoted by ''E'' (=Estate or Endowment). There are ''n'' people who claim this resource or parts of it; they are called ''claimants''. The amount claimed by each claimant ''i'' is denoted by ''c_i''. Usually, \sum_^n c_i > E, that is, the estate is insufficient to satisfy all the claims. The goal is to allocate to each claimant an amount ''x_i'' such that \sum_^n x_i = E. Unit-selection game O'Neill describes the following game. * The estate is divided to small units (for example, if all claims are integers, then the estate can be divided into ''E'' units of size 1). * Each claimant ''i'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proportional Cake-cutting With Different Entitlements
In the fair cake-cutting problem, the partners often have different entitlements. For example, the resource may belong to two shareholders such that Alice holds 8/13 and George holds 5/13. This leads to the criterion of ''weighted proportionality'' (WPR): there are several weights w_i that sum up to 1, and every partner i should receive at least a fraction w_i of the resource by their own valuation. In contrast, in the simpler proportional cake-cutting setting, the weights are equal: w_i=1/n for all i Several algorithms can be used to find a WPR division. Cloning Suppose all the weights are rational numbers, with common denominator D. So the weights are p_1/D,\dots,p_n/D, with p_1+\cdots+p_n=D. For each player i, create p_i clones with the same value-measure. The total number of clones is D. Find a proportional cake allocation among them. Finally, give each partner i the pieces of his p_i clones. Robertson and Webb show a simpler procedure for two partners: Alice cuts the cake ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entitlement (fair Division)
Entitlement in fair division describes that proportion of the resources or goods to be divided that a player can expect to receive. In many fair division settings, all agents have ''equal entitlements'', which means that each agent is entitled to 1/''n'' of the resource. But there are practical settings in which agents have ''different entitlements''. Some examples are: * In partnership resolution settings, each partner is entitled to a fraction of the common assets in proportion to his/her investment in the partnership. * In inheritance settings, the law in some jurisdictions prescribes a different share to each heir according to his/her proximity to the deceased person. For example, according to the Bible, the firstborn son must receive twice as much as every other son. In contrast, according to the Italian law, when there are three heirs - parent, brother and spouse - they are entitled to 1/4, 1/12 and 2/3 respectively. * In parliamentary democracies, each party is entitled to a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anonymity (social Choice)
In social choice theory, Anonymity is a basic requirement of a social choice rule. It says that the rule does not discriminate apriori between different voters. In other words, the rule returns the same outcome (whatever this outcome may be) if the vector of votes is permuted arbitrarily.{{Cite book, last=Felix Brandt, chapter-url=https://books.google.com/books?id=0qY8DwAAQBAJ&dq=multiwinner++voting+a+new+challenge&pg=PA27, title=Trends in Computational Social Choice, date=2017-10-26, publisher=Lulu.com, isbn=978-1-326-91209-3, editor-last=Endriss, editor-first=Ulle, language=en, chapter=Roling the Dice: Recent Results in Probabilistic Social Choice Anonymous rules Most voting rules are anonymous by design. For example, plurality voting is anonymous, since only counts the number of votes received by each candidates, regardless of who cast these votes. Similarly, the utilitarian rule and egalitarian rule are both anonymous, since the only consider the set of utilities, regardless ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prenucleolus
In game theory, a cooperative game (or coalitional game) is a game with competition between groups of players ("coalitions") due to the possibility of external enforcement of cooperative behavior (e.g. through contract law). Those are opposed to non-cooperative games in which there is either no possibility to forge alliances or all agreements need to be self-enforcing (e.g. through credible threats). Cooperative games are often analysed through the framework of cooperative game theory, which focuses on predicting which coalitions will form, the joint actions that groups take and the resulting collective payoffs. It is opposed to the traditional non-cooperative game theory which focuses on predicting individual players' actions and payoffs and analyzing Nash equilibria. Cooperative game theory provides a high-level approach as it only describes the structure, strategies and payoffs of coalitions, whereas non-cooperative game theory also looks at how bargaining procedures will aff ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shapley Value
The Shapley value is a solution concept in cooperative game theory. It was named in honor of Lloyd Shapley, who introduced it in 1951 and won the Nobel Memorial Prize in Economic Sciences for it in 2012. To each cooperative game it assigns a unique distribution (among the players) of a total surplus generated by the coalition of all players. The Shapley value is characterized by a collection of desirable properties. Hart (1989) provides a survey of the subject. The setup is as follows: a coalition of players cooperates, and obtains a certain overall gain from that cooperation. Since some players may contribute more to the coalition than others or may possess different bargaining power (for example threatening to destroy the whole surplus), what final distribution of generated surplus among the players should arise in any particular game? Or phrased differently: how important is each player to the overall cooperation, and what payoff can he or she reasonably expect? The Shapley val ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Core (game Theory)
In cooperative game theory, the core is the set of feasible allocations that cannot be improved upon by a subset (a ''coalition'') of the economy's agents. A coalition is said to ''improve upon'' or ''block'' a feasible allocation if the members of that coalition are better off under another feasible allocation that is identical to the first except that every member of the coalition has a different consumption bundle that is part of an aggregate consumption bundle that can be constructed from publicly available technology and the initial endowments of each consumer in the coalition. An allocation is said to have the ''core property'' if there is no coalition that can improve upon it. The core is the set of all feasible allocations with the core property. Origin The idea of the core already appeared in the writings of , at the time referred to as the ''contract curve''. Even though von Neumann and Morgenstern considered it an interesting concept, they only worked with zero-sum ga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Games
In game theory, a cooperative game (or coalitional game) is a game with competition between groups of players ("coalitions") due to the possibility of external enforcement of cooperative behavior (e.g. through contract law). Those are opposed to non-cooperative games in which there is either no possibility to forge alliances or all agreements need to be self-enforcing (e.g. through credible threats). Cooperative games are often analysed through the framework of cooperative game theory, which focuses on predicting which coalitions will form, the joint actions that groups take and the resulting collective payoffs. It is opposed to the traditional non-cooperative game theory which focuses on predicting individual players' actions and payoffs and analyzing Nash equilibria. Cooperative game theory provides a high-level approach as it only describes the structure, strategies and payoffs of coalitions, whereas non-cooperative game theory also looks at how bargaining procedures will aff ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cooperative Game Theory
In game theory, a cooperative game (or coalitional game) is a game with competition between groups of Player (game), players ("coalitions") due to the possibility of external enforcement of cooperative behavior (e.g. through contract law). Those are opposed to non-cooperative games in which there is either no possibility to forge alliances or all agreements need to be Self-enforcing agreement, self-enforcing (e.g. through credible threats). Cooperative games are often analysed through the framework of cooperative game theory, which focuses on predicting which coalitions will form, the joint actions that groups take and the resulting collective payoffs. It is opposed to the traditional Non-cooperative game, non-cooperative game theory which focuses on predicting individual players' actions and payoffs and analyzing Nash equilibria. Cooperative game theory provides a high-level approach as it only describes the structure, strategies and payoffs of coalitions, whereas non-cooperativ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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