Endogenous participation costs and equilibrium abstention in voting with complete information: A three-player case

This note examines the endogenous determination of participation costs in a costly voting game with complete information when there are three voters. I Â…find that there are two types of equilibria: (1) one where a voter who has a minority opinion definitely abstains, and (2) where he or she votes with some positive probability. In either equilibrium, the voter never invests to reduce his or her participation costs. Thus, inefficiency arises solely from a free-rider problem among voters in the majority.