Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for increasing advertiser utility in broad match auctions. In one aspect, a method includes receiving, from an advertiser, a set of keywords; accessing a linear program for a keyword language auction; determining a solution to the linear program; determining, based on the solution to the linear program, a proper subset of the keywords that increases the advertiser's utility relative to the advertiser's utility for the set of keywords; and generating utility bids for each of the keywords in the subset, each utility bid corresponding to one of the keywords in the subset and being a bid price for the keywords.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for allocating resources. In one aspect, a method includes receiving an advertisement request and identifying eligible advertisements that are eligible to be provided in response to the advertisement request. For each of the eligible advertisements an impression score corresponding to the advertisement request is received and a discount factor for each eligible advertisement is computed. The discount factor can be computed based on a function of previous impression scores for previous advertisement requests for which the eligible advertisement was provided. Using the impression scores and the discount factors for the eligible advertisements an allocation score is computed for each eligible advertisement. Using the allocation scores, an eligible advertisement is selected and provided in response to the request.

Abstract: Systems and methods for allocating and providing advertisements in response to impression events (e.g., a request for a placement of an advertisement) corresponding to forecasted impressions (e.g., a forecast of a request for a placement of an advertisement). The advertisements are allocated according to solution data that includes two disjoint solution sets, with each solution set identifying an advertisement that can be allocated to a forecasted impression.

Abstract: Systems and methods for providing advertisements in response to impression events (e.g., a request for a placement of an advertisement) corresponding to forecasted impressions (e.g., a forecast of a request for a placement of an advertisement). The advertisements are allocated according to solution data that respects frequency caps on the number of times the advertisement can be presented to a particular user population.

Abstract: An item is allocated among two bidders that value the item very differently. The allocation is based on a probability that each of the bidders is allocated the item. The probability that each bidder is allocated the item is determined based on a non-linear function that is applied to bids that are received from the bidders. The item can be allocated semi-randomly subject to the probability that each bidder is allocated the item. A bidder can be required to pay its bid price only when allocated the item or each bidder can be required to pay an all-pay price regardless of which bidder is allocated the item. If the item is allocated in multiple auctions, the bidders can be ensured allocation of the item a minimum number of integer times based on the probabilities.