Computability of simple games: A characterization and application to the core

TL;DR

This paper characterizes computable simple games, explores their properties including violations of anonymity, and demonstrates implications for the core and rational decision-making limits.

Contribution

It provides a precise characterization of computable simple games, extends Nakamura's theorem, and shows that such games have a finite Nakamura number.

Findings

Computable games include those with finite carriers and are included in games with finite winning coalitions.

Computable games violate anonymity.

Computable games have a finite Nakamura number.

Abstract

The class of algorithmically computable simple games (i) includes the class of games that have finite carriers and (ii) is included in the class of games that have finite winning coalitions. This paper characterizes computable games, strengthens the earlier result that computable games violate anonymity, and gives examples showing that the above inclusions are strict. It also extends Nakamura's theorem about the nonemptyness of the core and shows that computable games have a finite Nakamura number, implying that the number of alternatives that the players can deal with rationally is restricted.