Collusion Properties of Values

Hans Haller

International Journal of Game Theory, 1994, vol. 23, issue 3, 81 pages

Abstract: Two players may enter the game with a prior proxy or association agreement in order to strengthen their positions. There exist weighted majority voting games where a proxy agreement weakens the two players' collective power: the sum of their Shapley values with the agreement is less than without the agreement. This phenomenon cannot happen in non-trivial one man-one vote majority voting games. However, an association agreement weakens the two players' collective power in one man-one vote majority voting games with a sufficiently high quorom. In contrast, the sum of the two players' Banzhaf values turns out to be always immune against manipulation via a proxy or association agreement. Each of these neutrality properties can be used as part of an axiomatic characterization of the Banzhaf value.

Date: 1994
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