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Abraham Ravid allowable prices analysis ARBITRAGE ASYMMETRIC INFORMATION BQ.i Chichilnisky and Geoffrey competing quoters cont corner solution discrete prices discreteness of prices ECONOMIES equilibrium expected profits expected trading profits EXPONENTIAL UTILITY FINANCIAL finer prices Franklin gains from trade Glosten Goetzmann Graciela Chichilnisky Hasbrouck increase investors January large traders larger number Lawrence marginal valuation Mark Broadie MARKET MAKERS market order users Matthew Spiegel Ming-Jer Chen MONOPOLISTIC COMPETITION Nagarajan Nathaniel H number of competing number of quoters offer schedule optimal trade order condition Paolo Fulghieri price discreteness price pj prices get finer private information profit per trade providing quotes quantity chosen quantity offered restricted to 1/8's risk aversion risk neutral schedule of bids set of allowable set of prices Sid Browne Silverio Foresi small traders spread step function approximation trader of type trading on pennies trading on private typical quoter U.S. dollars welfare Yasushi Hamao York Stock Exchange zero