Punishing greediness in divide-the-dollar games

Brams and Taylor 1994 presented a version of the divide-the-dollar game (DD), which they call DD1. DD1 suffers from the following drawback: when each player demands approximately the entire dollar, then if the least greedy player is unique, then this player obtains approximately the entire dollar even if he is only slightly less greedy than the other players. I introduce a parametrized family of 2-person DD games, whose “endpoints” (the games that correspond to the extreme points of the parameter space) are (1) a variant of DD1, and (2) a game that completely overcomes the greediness-related problem. I also study an n-person generalization of this family. Finally, I show that the modeling choice between discrete and continuous bids may have far-reaching implications in DD games.