Budget-balanced mechanism

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Auction Room, Christie's, circa 1808.
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In

surplus
. The term budget-balanced mechanism is sometimes used as a shorthand for WBB, and sometimes as a shorthand for SBB.

Weak budget balance

A simple example of a WBB mechanism is the Vickrey auction, in which the operator wants to sell an object to one of n potential buyers. Each potential buyer bids a value, the highest bidder wins an object and pays the second-highest bid. As all bids are positive, the total payment is trivially positive too.

As an example of a non-WBB mechanism, consider its extension to a

Pareto-efficient
truthful mechanism must incur a deficit.

McAfee[1] developed a solution to this problem for a large market (with many potential buyers and sellers): McAfee's mechanism is WBB, truthful and almost Pareto-efficient - it performs all efficient deals except at most one. McAfee's mechanism has been extended to various settings, while keeping its WBB property.[2][3] See double auction for more details.

Strong budget balance

In a strongly-budget-balanced (SBB) mechanism, all payments are made between the participants themselves.[4][5] An advantage of SBB is that all the gain from trade remains in the market; thus, the long-term welfare of the traders is larger and their tendency to participate may be higher.

McAfee's double-auction mechanism is WBB but not SBB - it may have a surplus, and this surplus may account for almost all the gain from trade. There is a simple SBB mechanism for bilateral trading: trade occurs iff b > s, and in this case the buyer pays (b+s)/2 to the seller. Since the payment goes directly from the buyer to the seller, the mechanism is SBB; however, it is not truthful, since the buyer can gain by bidding b' < b and the seller can gain by bidding s' > s. Recently, some truthful SBB mechanisms for double auction have been developed.[6][7][8][9][10] Some of them have been generalized to multi-sided markets.[11]

See also

References

  1. doi:10.1016/0022-0531(92)90091-u
    .
  2. ISSN 0167-9236
    .
  3. ISSN 0041-1655
    .
  4. ISBN 978-3-540-46243-9
    .
  5. ISBN 978-0-9817381-7-8
    .
  6. ISBN 978-1-61197-433-1
    .
  7. S2CID 217190707
    .
  8. S2CID 14358074
    .
  9. arXiv:1712.06848 [cs.GT
    ].
  10. ISBN 978-0-9992411-2-7
    .
  11. ISSN 2374-3468
    .
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