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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 amoun ... [...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] |
Nash Bargaining Solution
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. Such solutions, particularly the Nash solution, were used to solve concrete economic problems, such as management–labor conflicts, on numerous occasions. An alternative approach to bargaining is the ''positive'' appr ... [...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, meaning the term ''bankruptcy'' is not a synonym for insolvency. Etymology The word ''bankruptcy'' is derived from Italian , literally meaning . 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. However, the existence of such a ritual is doubted. 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 "debt slavery" until the creditor recouped losses through their physical labour. Many city-states in ancient Greece limited debt slavery to a period of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pari Passu
''Pari passu'' is a Latin phrase that literally means "with an equal step" or "on equal footing". It is sometimes translated as "ranking equally", "hand-in-hand", "with equal force", or "moving together", and by extension, "fairly", "without partiality". Etymology *'' pari'' is the ablative singular masculine (since it must grammatically agree with ''passu'') of the adjective ''par'', "equal". If it were nominative, "an equal step" it would be ''par passus''. *'' passu'' is the ablative of the Latin noun ''passus'', "step". In legal terms, pari passu means "on equal footing." It refers to creditors, claimants, or shareholders receiving equal treatment without preference. Common in bankruptcy and finance, it ensures proportional distribution of assets, rights, or obligations among parties. This term is commonly used in law. '' Black's Law Dictionary'' (8th ed., 2004) defines ''pari passu'' as "proportionally; at an equal pace; without preference". Usage In inheritance In inh ... [...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)
In fair division, a person's entitlement is the value of the goods they are owed or deserve, i.e. the total value of the goods or resources that a player would ideally receive. For example, in party-list proportional representation, a party's seat entitlement (sometimes called its seat quota) is equal to its share of the vote, times the number of seats in the legislature. Dividing money Even when only money is to be divided and some fixed amount has been specified for each recipient, the problem can be complex. The amounts specified may be more or less than the amount of money, and the profit or loss will then need to be shared out. The proportional rule is normally used in law nowadays, and is the default assumption in the theory of bankruptcy. However, other rules can also be used. For example: * The Shapley value is one common method of deciding bargaining power, as can be seen in the airport problem. * Welfare economics on the other hand tries to determine allocations de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anonymity (social Choice)
In economics and social choice, a function satisfies anonymity, neutrality, or symmetry if the rule does not discriminate between different participants ahead of time. For example, in an election, a voter-anonymous function is one where it does not matter who casts which vote, i.e. all voters' ballots are equal ahead of time. Formally, this is defined by saying the rule returns the same outcome (whatever this may be) if the votes are "relabeled" arbitrarily, e.g. by swapping votes #1 and #2. Similarly, outcome-neutrality says the rule does not discriminate between different outcomes (e.g. candidates) ahead of time. Formally, if the labels assigned to each outcome are permuted arbitrarily, the returned result is permuted in the same way. Some authors reserve the term anonymity for agent symmetry and neutrality for outcome-symmetry, but this pattern is not perfectly consistent.{{Rp, 75 Examples Most voting rules are anonymous and neutral by design. For example, plurality voting i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prenucleolus
In game theory, a cooperative game (or coalitional game) is a game with groups of players who form binding “coalitions” with external enforcement of cooperative behavior (e.g. through contract law). This is different from 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 analysed by focusing on coalitions that can be formed, and the joint actions that groups can take and the resulting collective payoffs. Mathematical definition A cooperative game is given by specifying a value for every coalition. Formally, the coalitional game consists of a finite set of players N , called the ''grand coalition'', and a ''characteristic function'' v : 2^N \to \mathbb from the set of all possible coalitions of players to a set of payments that satisfies v( \emptyset ) = 0 . The function describes how much collective payoff a set of players can gain by fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shapley Value
In cooperative game theory, the Shapley value is a method (solution concept) for fairly distributing the total gains or costs among a group of players who have collaborated. For example, in a team project where each member contributed differently, the Shapley value provides a way to determine how much credit or blame each member deserves. 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. The Shapley value determines each player's contribution by considering how much the overall outcome changes when they join each possible combination of other players, and then averaging those changes. In essence, it calculates each player's average marginal contribution across all possible coalitions. It is the only solution that satisfies four fundamental properties: efficiency, symmetry, additivity, and the dummy player (or null player) property, which are widely accepted as defining a fair distribution. This m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Core (game Theory)
In cooperative game theory, the core is the set of feasible allocations or imputations where no coalition of agents can benefit by breaking away from the grand coalition. An allocation is said to be in the ''core'' of a game if there is no coalition that can improve upon it. The core is then the set of all feasible allocations. 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 games where the core is always empty. The modern definition of the core is due to Gillies. Definition Consider a transferable utility cooperative game (N,v) where N denotes the set of players and v is the characteristic function. An imputation x\in\mathbb^N is ''dominated'' by another imputation y if there exists a coalition C, such that each player in C weakly-prefers y (x_i\leq y_i for all i\in C) and there exists i\in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Games
In game theory, a cooperative game (or coalitional game) is a game with groups of players who form binding “coalitions” with external enforcement of cooperative behavior (e.g. through contract law). This is different from 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 analysed by focusing on coalitions that can be formed, and the joint actions that groups can take and the resulting collective payoffs. Mathematical definition A cooperative game is given by specifying a value for every coalition. Formally, the coalitional game consists of a finite set of players N , called the ''grand coalition'', and a ''characteristic function'' v : 2^N \to \mathbb from the set of all possible coalitions of players to a set of payments that satisfies v( \emptyset ) = 0 . The function describes how much collective payoff a set of players can gain by fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
