Seminario: "Ordinal aspects of coalitional games"

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Abstract:

A game on a finite set of players assigns a real number to any coalition of players, the worth of the coalition.  In applications, the players are economic agents (people or companies).  The worths reflect the values of the various coalitions; but how to derive from them rewards to the individual players?  A scoring provides an answer by specifying how to compute, for any game, a real number for each player, the score of the player.  Classical examples are the Banzhaf scoring and the Shapley scoring and their generalizations as semivalues, all of them being linear scorings (that is, linear as a function of the game). 
In a game where the data are uncertain, it makes sense to rely only on the ranking (a weak ordering) induced on the coalitions by the hazy worths.  Consequently then, the final goal of the scoring consists in a ranking of the players (reflecting their dubious scores).  For a given scoring, the games for which the player ranking depends only on the coalition ranking are thus of particular interest; we call them stable w.r.t. the scoring.  We characterize the games that are stable for a given linear scoring.  To check whether a game is stable for a specific semivalue, it suffices to inspect the ordering of the coalitions and to perform some direct computation based on the semivalue parameters.  The latter computation becomes remarkably easy for the Banzhaf scoring.

 

Referente DEI: Prof. Alfio Giarlotta