Abstract: Various embodiments provide offline algorithms for resource allocation. A known set of “offline” requests may be matched to available resources using an online resource allocation algorithm that models the offline resource allocation problem as though the requests were received stochastically. Requests may be scaled and then sampled to provide random, stochastic input for the online resource allocation algorithm. For each request, resources are allocated to the request by evaluating multiple options based upon shadow costs assigned to resources associated with the different options. After each request is processed, an adjustment is made to the shadow costs for remaining resources to reflect differences in rates for allocation and/or consumption of the resources and the updated shadow costs are used for a subsequent request. A scaled resource allocation determined using sampled requests in this manner may be scaled back up to obtain a solution for the offline resource allocation problem.

Abstract: A single advertisement may provide benefits to multiple parties. The results discussed herein show that an ad auctioneer may improve both his own revenue and consumers' welfare by implementing an ad auction that allows cooperation among advertisers in a single ad while maintaining competition between ads. This may be called a “coopetitive” ad auction. An auction system may be configured to implement a coopetitive approach in which bids express complex preferences over ads. In particular, multiple bidders may be allowed to value a single ad, and a single bidder may be allowed to value multiple ads. Accordingly, an advertiser can derive value from clicks on multiple ads.

Abstract: Various embodiments provide offline algorithms for resource allocation. A known set of “offline” requests may be matched to available resources using an online resource allocation algorithm that models the offline resource allocation problem as though the requests were received stochastically. Requests may be scaled and then sampled to provide random, stochastic input for the online resource allocation algorithm. For each request, resources are allocated to the request by evaluating multiple options based upon shadow costs assigned to resources associated with the different options. After each request is processed, an adjustment is made to the shadow costs for remaining resources to reflect differences in rates for allocation and/or consumption of the resources and the updated shadow costs are used for a subsequent request. A scaled resource allocation determined using sampled requests in this manner may be scaled back up to obtain a solution for the offline resource allocation problem.

Abstract: Various embodiments provide online algorithms for resource allocation. In one or more embodiments, requests for resources from a service provider are received stochastically. For each request, different options for satisfying the request are evaluated based in part upon shadow costs (e.g., unit costs) that are assigned to resources associated with the different options. One of the options may be selected by optimizing an objective function that accounts for the shadow costs. Resources for the selected option are allocated to the request and an adjustment is made to the shadow costs for remaining resources to reflect differences in rates for allocation and/or consumption of the resources. Thereafter, resources may be allocated to a subsequent request using the updated shadow costs and the costs are adjusted again. By updating shadow costs iteratively in this manner, an increasingly more accurate analysis of the objective function is achieved.