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2 Operations Research and Decisions

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Finding the Pareto optimal equitable allocation of homogeneous divisible goods among three players

100%

DALL’AGLIO M. , DI LUCA C. , MILONE L.

nr 3

35-50

We consider the allocation of a finite number of homogeneous divisible items among three players. Under the assumption that each player assigns a positive value to every item, we develop a simple algorithm that returns a Pareto optimal and equitable allocation. This is based on the tight relationship between two geometric objects of fair division: The Individual Pieces Set (IPS) and the Radon–Nykodim Set (RNS). The algorithm can be considered as an extension of the Adjusted Winner procedure by Brams and Taylor to the three-player case, without the guarantee of envy-freeness.

Orders of criticality in voting games

100%

DALL’AGLIO M. , FRAGNELLI V. , MORETTI S.

2016

tom 26

nr 2

53-67

The authors focus on the problem of investigating the blackmail power of players in simple games, which is the possibility of players of threatening coalitions to cause them loss using arguments that are (apparently) unjustified. To this purpose, the classical notion of the criticality of players has been ex-tended, in order to characterize situations where players may gain more power over the members of a coalition thanks to collusion with other players.