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4 Operations Research and Decisions

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Orders of criticality in voting games

Dall'Aglio M., Fragnelli V., Moretti S.

Operations Research and Decisions

2016

Vol. 26, No. 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.

Further open problems in cooperative games

Fragnelli V., Gambarelli G.

Operations Research and Decisions

2014

Vol. 24, No. 4

51--62

In 2013, the International Game Theory Review published two special issues on open problems in cooperative games: the first regarding theory and the second applications. In this paper, our aim is to present some problems currently “on our table” that were not included in the two issues mentioned above, either because the topics were too specific or they arose after publication. The problems are divided into theoretical problems, general models that may be applied to different fields and applicative problems.

Editorial

Fragnelli V., Stach I.

Operations Research and Decisions

2014

Vol. 24, No. 4

5--6

Quantitative evaluation of veto power

Chessa M., Fragnelli V.

Operations Research and Decisions

2011

Vol. 21, No. 3-4

5-19

The decisiveness index and the loose protectionism index for a single player have been introduced, starting from the decisiveness and the loose protectionism indices for a collective decisionmaking mechanism defined by Carreras. Attention was mainly focused on the latter index, being proposed as a quantitative measure of the power of veto of each agent. According to this index, a veto player has veto power equal to one, while each other player has a fractional power according to her/his likelihood of blocking a given proposal. Such an index coincides with the expected payoff at the Bayesian equilibrium of a suitable Bayesian game, which illustrates the non-cooperative point of view of a decision-making mechanism.