On totally balanced games arising from cooperation in fair division

Legut, Jerzy

doi:10.1016/0899-8256(90)90013-k

Cited by 14 publications

(14 citation statements)

References 18 publications

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“…Totally balanced games arise from a wide range of applications. They coincide with market games (Shapley and Shubik, 1969); also with a special case of market games with a continuum of indivisible commodities: cooperation in fair division (Legut, 1990); they are equivalent to a class of maximum flow problems (Kalai and Zemel, 1982a); and also to permutation games of less than four players (Tijs, Parthasarathy, Potters, and Prassad, 1984). Moreover, totally balanced games are generated by linear production games (Owen, 1975), generalized network problems (Kalai and Zemel, 1982b), and controlled mathematical programming problems (Dubey and Shapley, 1982).…”

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confidence: 99%

Stable allocations of risk

Csóka

Herings

Kóczy

2009

Games and Economic Behavior

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Measuring risk can be axiomatized by the concept of coherent measures of risk. A risk environment specifies some individual portfolios' realization vectors and a coherent measure of risk. We consider sharing the risk of the aggregate portfolio by studying transferable utility cooperative games: risk allocation games. We show that the class of risk allocation games coincides with the class of totally balanced games. As a limit case the aggregate portfolio can have the same payoff in all states of nature. We prove that the class of risk allocation games with no aggregate uncertainty coincides with the class of exact games. JEL: C 71Keywords: Abstract Measuring risk can be axiomatized by the concept of coherent measures of risk. A risk environment specifies some individual portfolios' realization vectors and a coherent measure of risk. We consider sharing the risk of the aggregate portfolio by studying transferable utility cooperative games: risk allocation games.We show that the class of risk allocation games coincides with the class of totally balanced games. As a limit case the aggregate portfolio can have the same payoff in all states of nature. We prove that the class of risk allocation games with no aggregate uncertainty coincides with the class of exact games.

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confidence: 99%

Stable allocations of risk

Csóka

Herings

Kóczy

2009

Games and Economic Behavior

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“…There is no interaction of sorts between the two stages, so that in the trading phase any division, no matter how unfair, would be considered just fine. The discrepancy was already noted by Legut, Potters and Tijs (1994) who kept the name of "fair division game" for the exchange model they analyzed, but noted in a footnote that "this name does not seem to be very appropriate in the present situation but in Legut (1990) this term has been introduced for games of this kind where the initial endowment [. .…”

Section: Introductionmentioning

confidence: 98%

“…The use of transferable utility is inherited from Legut (1990). Such assumption is often criticized in the classical context of fair division where children attending the division are not supposed to handle money.…”

Section: Introductionmentioning

confidence: 99%

“…In these works, great care is devoted to the formal description of the preferences, which departs from the classical measure theoretic settings in fair division to take into account non-additivity and the preference for shape and location of the plots. Legut (1990) defines a model of cooperation within the classical framework of fair division. Similarly to the model for land division, children attending the division of the cake may redistribute the total amount of cake within a group in order to maximize the joint utility of the group.…”

Section: Introductionmentioning

confidence: 99%

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Cooperation in dividing the cake

Dall’Aglio

Brânzei

Tijs

2009

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This paper defines models of cooperation among players partitioning a completely divisible good (such as a cake or a piece of land). The novelty of our approach lies in the players' ability to form coalitions before the actual division of the good with the aim to maximize the average utility of the coalition. A social welfare function which takes into account coalitions drives the division. In addition, we derive a cooperative game which measures the performance of each coalition. This game is compared with the game in which players start cooperating only after the good has been portioned and has been allocated among the players. We show that a modified version of the game played before the division outperforms the game played after the division.

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“…Brams and Taylor [6] discuss the issue of the manipulability of the preferences: in most cases children may benefit from declaring false preferences. A different approach takes into account the possibility for the children to form coalitions after (Legut [15] and Legut et al [16]) or before (Dall'Aglio et al [8]) the division of the cake. In both cases coalitional games are defined and analysed.…”

Section: Introductionmentioning

confidence: 99%