A market game with symmetric limit orders

Abstract

We extend the market game with symmetric limit orders studied in Weyers (2003, 2004) to a many-good setup. Our limit orders are symmetric in terms of payment and determine a unique consistent price system for every strategy profile. The limit orders studied in the previous literature—see Dubey (1982), Simon (1984) and Mertens (2003)—share none of these properties. It is shown that three mild market-thickness conditions imply that the set of symmetric Nash equilibrium outcomes coincides with the set of price-taking equilibrium outcomes. First, the Dubey and Shubik (1978) refinement is used to eliminate no-trade as an equilibrium. Second, any price-taking equilibrium has trade in each market. Third, there are at least two agents of each type, where a type is determined by preferences and endowments. The last two conditions enable applying the Bertrand argument. This paper thus provides new insights to Bertrand’s (1883) classic critique of Cournot and the associated problem of capacity constraints raised by Edgeworth (1897).