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I have been using a double-auction mechanism to solve a two-sided market where multiple agents are competing to supply/use slices of a shared resource. The owner of the resource is a trustable third-party who is not biased towards any of the traders and is not using the resource (*simplified description of the problem in the footnote). The setup and the auction algorithm works just fine.

Now, considering a new scenario, where the auctioneer (the primary supplier) joins the market as a trader, thus cannot be trusted to hold the auction, what other alternatives to auction are there to assure trust?

*A bakery bakes 1000 baguettes per day and distributes them equally among the 10 restaurants in the town every morning. However, depending on the day some of the restaurants might be short on Baguettes or have an excess supply. We have designed a sealed-bid double-auction mechanism that allows the restaurants to share their excess Baguettes with the restaurants short on baguettes and get monetary compensation for it. As we assume that the bakery is not biased towards any of the restaurants, we trust him to be the auctioneer.

The bakery buys one of the restaurants, and it cannot be trusted anymore to run the auction as it is biased. Is it possible to hold the auction without having a central trusted auctioneer and distribute the decision making to solve the trust issue? If so, how we can minimize the communication between the traders?

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  • $\begingroup$ Are the restaurant's objective functions quasi-linear in price? $\endgroup$
    – matthewoulton
    Commented May 18 at 6:31
  • $\begingroup$ Integration between the bakery and restaurant could lead to complete input foreclosure from the bakery to the other (non-integrated) restaurants, if the restaurants are homogeneous. This result would be robust to communication since the profits of the bakery and the integrated restaurants are at the monopoly level, so cannot be increased by communication. The seminal paper is Hart-Tirole (1990). This problem could be reduced if the restaurants were perhaps capacity constrained so could not serve all consumers, but this would require more information about the market structure in your model. $\endgroup$
    – Joseph Basford
    Commented May 18 at 8:32

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Using tools from cryptography this problem can potentially be solved. The domain of secure multiparty computation (MPC) deals with the problem of letting a set of distributed parties run an interactive protocol, which "simulates" an arbitrary trusted party. Depending on the precise computation that a central trusted auctioneer would perform, different MPC protocols are best.

The two main approaches to MPC are:

(1) Garbled circuits (constant number of rounds of interaction, but somewhat higher bandwidth overhead)

(2) SPDZ protocols (number of rounds depends on the depth of the circuit representing the auctioneer, but bandwidth overhead is smaller)

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  • $\begingroup$ Why would the bakery agree to this, though? $\endgroup$
    – matthewoulton
    Commented May 18 at 8:06

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