{'fraction_non_alphanumeric': 0.022750775594622543, 'fraction_numerical': 0.004136504653567736, 'mean_word_length': 4.761904761904762, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Collusion in Repeated Auctions with Externalities

This paper studies an infinitely repeated auction when the stage game involves negative externalities among buyers, that is, a buyer is worse off if another rival wins the good rather than if nobody wins it. It is first shown in the stage game that a cartel must be more inclusive if it wishes to enforce a rigid bidding scheme a la McAfee and McMillan (1992) due to the existence of externalities. That is, there is a trade-off between the amount of payment to the seller and the probability of sales. Then focusing on the symmetric perfect public equilibria (SPPE) of the repeated game, the paper finds that i) wars are not necessary on the equilibrium path and ii) optimal collusive bidding scheme may involve only partial rigidity for some values of externalities. The latter result contrasts with optimal collusion in the case without externalities which involves fully-rigid (i.e. bid-rotation) bidding scheme.