DIVIDE THE DOLLAR - 3 SOLUTIONS AND EXTENSIONS

Divide the Dollar (DD) is a game in which two players independently bi d up to 100 cents for a dollar. Each player receives his or her bid if the sum of the bids does not exceed a dollar; otherwise they receive nothing. This game has multiple Nash equilibria, including the egalita rian division of (50, 50), but this division is not compelling except for its symmetry and presumed fairness. This division is easy to induc e, however, by punishing - more severely than does DD - deviations fro m it, but these solutions are not 'reasonable'. By altering the rules of DD, however, one can induce an egalitarian division (by successive elimination of weakly dominated strategies), but no reasonable payoff scheme produces this division with egalitarian bids of 50. Three alter natives to DD are analyzed. DD1, which rewards lowest bidders first, s hows how an egalitarian outcome can be induced with equal but nonegali tarian bids. DD2, which adds a second stage that provides the players with new information vet restricts their choices at the same time, is used to introduce 'dominance inducibility'. DD3 combines the features of DD1 and DD2, is reasonable (like DD1), makes calculations transpare nt (like DD2), and induces egalitarian bids as well as the egalitarian outcome. The possible application of the different procedures to a re al-world allocation problem (setting of salaries by a team), in which there may be entitlements; is described.