Abstract
We study minimal conditions for competitive behavior with few agents, adapting the strategic market game of Dubey (1982), Simon (1984) and Benassy (1986) to an indivisible good environment. We show that all Nash equilibrium outcomes with active trading are competitive if and only if there are at least two buyers and two sellers willing to trade at every competitive price. Unlike previous formulations, this condition can be verified directly by checking the set of competitive equilibria. In laboratory experiments, the condition we provide turns out to be enough to induce competitive results. Moreover, the performance of a sealed-bid auction following the rules of the strategic market game approaches that of its dynamic counterpart, the double auction, over time.
Highlights
Ever since the classic contributions of Cournot (1838) and Bertrand (1883), the question of whether a market with a small number of traders can achieve competitive outcomes has been a matter of debate
We show that all Nash equilibrium outcomes with active trading are competitive if and only if there are at least two intramarginal traders in each side of the market
We propose a strategic market game for a market with money and an indivisible good, where buyers and sellers have both prices and quantities in their strategy space and trade via a profit-maximizing clearing house
Summary
Ever since the classic contributions of Cournot (1838) and Bertrand (1883), the question of whether a market with a small number of traders can achieve competitive outcomes has been a matter of debate. The modern literature on strategic market games, pioneered by Dubey and Shubik (1980), Dubey (1982), Simon (1984) and Benassy (1986), revisits the topic of competition with few traders, paying attention to trading rules. In line with Bertrand’s model, having a large number of traders is not indispensable for the competitiveness of Nash equilibrium outcomes in strategic market games. Dubey (1982), Simon (1984) and Benassy (1986) prove that, under certain trading rules, having two active sellers and two active buyers in a Nash equilibrium is sufficient to make the outcome competitive In line with Bertrand’s model, having a large number of traders is not indispensable for the competitiveness of Nash equilibrium outcomes in strategic market games. Dubey (1982), Simon (1984) and Benassy (1986) prove that, under certain trading rules, having two active sellers and two active buyers in a Nash equilibrium is sufficient to make the outcome competitive
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