Bidding box for home-played games. Use of bidding boxes has several advantages over oral bidding: it reduces noise in the room, prevents bidding being overheard at neighboring tables, allows easier review of the auction, and reduces the opportunity to pass unauthorized information to one's partner (intentionally or not) by the manner and intonation in which one makes one's bid. A bidding box is typically a plastic box with two slots, each containing a set of bidding cards. One slot contains 35 cards with symbols of bids (5 denominations—clubs (), diamonds (), hearts (), spades (), and notrump (NT)—in seven levels of bidding,
Vickrey auction payment in the sealed second-price auction. Vickrey considered the case of two buyers and assumed that each buyer's value was an independent draw from a uniform distribution with support formula_15. With buyers bidding according to their dominant strategies, a buyer with valuation formula_12 wins if his opponent's value formula_17. Suppose that formula_12 is the high value. Then the winning payment is uniformly distributed on the interval formula_19 and so the expected payment of the winner is We now argue that in the sealed first price auction the equilibrium bid of a buyer with valuation formula_12 is That is, the payment