arXiv subjects

Takaaki Abe

Publications and source records attributed to Takaaki Abe.

3 recordsLinked to original sources

arXiv2026

How outside options are incorporated into payoff distributions

This paper examines how outside options are incorporated into payoff distributions in games with coalition structures. We introduce and characterize the alpha-value, which "fully" incorporates outside options, and provide a new characterization of the Aumann-Dreze value as an allocation rule that does not incorporate outside options. We show that the chi-value (Casajus, 2009) is a component-wise convex combination of these two values and thus incorporates outside options in a discounted form.

econ.TH↗

arXiv2026

Measuring Concentration of Power in Approval Voting Games

The ratio of voting power between a permanent member and a non-permanent member of the United Nations Security Council varies substantially across indices: approximately 100 to 1 according to the Shapley-Shubik index, 10 to 1 according to the Banzhaf index, and 2.5 to 1 according to the Deegan-Packel index. Such comparisons depend on the choice of power index and are meaningful only in settings where players are divided into two types. To address these limitations, this paper proposes and characterizes a function that measures the level of power concentration in monotonic approval voting games. The proposed measure assigns a single value to each voting game, reflecting the extent to which voting power is unevenly distributed among players. The proposed measure is proportional to the sum of squared Deegan-Packel power indices and can also be interpreted as the degree of overlap among minimal winning coalitions. An application to the United Nations Security Council is also provided.

econ.TH↗

arXiv2026

Self-Duality and Transfer in Voting Games

This study examines the role of self-duality in the axiomatization of the Shapley-Shubik power index. We show that, when self-duality is imposed, the transfer axiom can be weakened to a restricted version requiring transfer only among voting games with no veto player. This result shows that self-duality can partially substitute for the transfer axiom.

econ.TH↗