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In this article, I develop a simple bidding model in which collusion is endogenous. Buyers at a first-price sealed-bid auction decide whether to rig their bids given that they face the threat of government prosecution. A legal authority chooses whether to investigate the buyers on the basis of the bids tendered. In the unique sequential equilibrium of the game, buyers rig their bids with positive probability, but the legal authority can never ascertain, on the basis of the bids alone, that a conspiracy has formed.
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Chantale LaCasse (1995) studied this question.
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