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2. Price of anarchy in auctions - Wikipedia

   en.wikipedia.org/wiki/Price_of_anarchy_in_auctions

   Case 3: subadditive buyers, 2nd-price auctions. [3] Under a strong-no-overbidding assumption: With complete information, the welfare of every pure Nash equilibrium is at least 1/2 the optimum, so the PoA is at most 2. With incomplete information, there exist Bayes-Nash equilibria with welfare less than 1/2 the optimum, so the BPoA is more than 2.

3. Revenue equivalence - Wikipedia

   en.wikipedia.org/wiki/Revenue_equivalence

   A classic example is the pair of auction mechanisms: first price auction and second price auction. First-price auction has a variant which is Bayesian-Nash incentive compatible; second-price auction is dominant-strategy-incentive-compatible, which is even stronger than Bayesian-Nash incentive compatible. The two mechanisms fulfill the ...

4. Unique bid auction - Wikipedia

   en.wikipedia.org/wiki/Unique_bid_auction

   In a 2012 study Pigolotti et al. conducted a thorough study of the unique bid auction in the grand canonical ensemble, finding a theoretical expression for the Nash equilibrium distribution and showing that real-world players play according to this distribution when the number of players in the auction is low. [14] Nash equilibrium distribution ...

5. Price of anarchy - Wikipedia

   en.wikipedia.org/wiki/Price_of_anarchy

   Usually the system is modeled as a game and the efficiency is some function of the outcomes (e.g. maximum delay in a network, congestion in a transportation system, social welfare in an auction, etc.). Different concepts of equilibrium can be used to model the selfish behavior of the agents, among which the most common is the Nash equilibrium.

6. All-pay auction - Wikipedia

   en.wikipedia.org/wiki/All-pay_auction

   The dollar auction is a two player Tullock auction, or a multiplayer game in which only the two highest bidders pay their bids. Another practical examples are the bidding fee auction and the penny raffle (pejoratively known as a "Chinese auction" [6]).

7. 9 Antique Items You Could Sell for Thousands of Dollars

   www.aol.com/9-antique-items-could-sell-190033573...

   A 2019 pristine copy of Harry Potter and the Philosopher’s Stone was sold for roughly $90,000 at auction. One of the 22 known first-edition copies of Alice’s Adventures in Wonderland, with one ...