A CONJECTURE OF SHAPLEY AND SHUBIK ON COMPETITIVE OUTCOMES IN THE CORES OF NTU MARKET GAMES

It is shown that for every NTU market game, there is a market that rep resents the game whose competitive payoff vectors completely fill up t he inner core of the game. It is also shown that for every NTU market game and for any point in its inner core, there is a market that repre sents the game and further has the given inner core point as its uniqu e competitive payoff vector. These results prove a conjecture of Shapl ey and Shubik.