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Abstract We analyze the two-stage games induced by competitive equilibrium rules for the buyer–seller market of Shapley and Shubik (Int J Game Theory 1:111–130, 1972). In these procedures, first sellers and then buyers report their valuation and the outcome is determined by a competitive equilibrium outcome for the market reported by the agents. We provide results concerning buyers and sellers’ equilibrium strategies. In particular, our results point out that, by playing first, sellers are able to instigate an outcome that corresponds to the sellers’ optimal competitive equilibrium allocation for the true market.