Competitive fair division

Several indivisible goods are to be divided among two or more players, whos e bids for the goods determine their prices. An equitable assignment of the goods at competitive prices is given by a fair-division procedure, called the Gap Procedure, that ensures (1) nonnegative prices that never exceed th e bid of the player receiving the good; (2) Pareto optimality, though coupl ed with possible envy; (3) monotonicity, such that higher bids never hurt i n obtaining a good; (4) sincere bids that preclude negative utility; and (5 ) prices that are partially independent of the amounts bid (as in a Vickrey auction). A variety of applications are discussed.