Limited lottery insurance

A method for conducting a lottery for at least one item comprising:

• for each of a plurality of buyers:
• receiving a buyer's declared valuation for each of at least one item being offered in a lottery by a seller, the item having an assigned non-deterministic probability of being allocated to the buyer, and
• calculating, by a computer processor, insured prices for outcomes of the lottery which are a function of the buyer's declared valuation of the at least one item;
• randomly drawing an allocation of each of the at least one item to a respective one of the buyers, based on its assigned non-deterministic probability;
• and
• allocating the insured prices to the buyers based on respective outcomes of the random drawing,
• wherein there are n+1 possible outcomes and the insured prices for each of the buyers are set based on the following equation:
• p
• i
• :=
• p
• +
• v
• i
• -
• ∑
• j
• =
• 1
• n
• +
• 1
• ⁢
• z
• j
• ⁢
• v
• j
• ,
• where pi is the insured price of an item i=1, 2, . . . , n;
• vi is the buyer's declared valuation for item i;
• p is an average price set by the seller for the item i;
• zi is the probability of being allocated the item i;
• zj is the probability of being allocated an item other than item i, and vj is the buyer's declared valuation for that other item;
• and
• v
• n
• +
• 1
• =
• 0
• ,
• ⁢
• z
• n
• +
• 1
• =
• 1
• -
• ∑
• i
• =
• 1
• n
• ⁢
• z
• i
• is used to model the possibility that nothing is allocated to the buyer.

A system for conducting a lottery for at least one item comprising:

• memory which stores instructions which, upon execution by a processor:
• for a plurality of buyers, receive a buyer's declared valuation for each of at least one item being offered in a lottery by a seller, the item having an assigned non-deterministic probability of being allocated to the buyer and calculate insured prices for different outcomes of the lottery, the insured price pi, for each of the items being based on an equation which incorporates:
• the average price p for the respective item i,
• the probability zi of winning the item i, the buyer's declared valuation vi for the item i, and
• corresponding probabilities zj and the buyer's valuations vj for items other than i offered in the lottery,
• randomly draw an allocation of each of the at least one item to a respective one of the buyers, based on its assigned non-deterministic probability, and
• allocate the insured prices to the buyers based on respective outcomes of the random drawing;
• and
• the processor in communication with the memory for executing the instructions.

A computer program product comprising a non-transitory computer-readable medium storing instructions which, when executed by a computer, perform a method comprising:

• for each of a plurality of buyers:
• receiving a buyer's declared valuation for each of at least one item being offered in a lottery by a seller, the item having an assigned non-deterministic probability of being allocated to the buyer;
• and
• calculating an insured price for each of a plurality of different outcomes of the lottery, each of the insured prices being a function of the buyer's declared valuation of the at least one item, wherein there are n+1 possible outcomes and the insured prices for the buyer are set based on the following equation:
• p
• i
• :=
• p
• +
• v
• i
• -
• ∑
• j
• =
• 1
• n
• +
• 1
• ⁢
• z
• j
• ⁢
• v
• j
• ,
• where pi is the insured price of an item i=1, 2, . . . , n;
• vi is the buyer's declared valuation for item i;
• p is an average price set by the seller for the item i;
• zi is the probability of being allocated the item i;
• zj is the probability of being allocated an item other than item i, and vj is the buyer's declared valuation for that other item;
• and
• randomly drawing an allocation of each of the at least one item to a respective one of the buyers, based on its assigned non-deterministic probability;
• and
• allocating the insured prices to the buyers based on respective outcomes of the random drawing.