We discuss a procurement problem with transportation losses and piecewise linear production costs. We first provide an algorithm based on Knaster-Tarski’s fixed point theorem to solve the allocation problem in the quadratic losses case. We then identify a monotony condition on the types distribution under which the Bayesian cost minimizing mechanism takes a simple form.
@article{heymannReverseAuctionsTransportation2024,title={Reverse Auctions with Transportation and Convex Costs},author={Heymann, Benjamin and Jofr{\'e}, Alejandro},year={2024},journal={Computational Management Science},volume={21},number={1},pages={20},issn={1619-6988},doi={10.1007/s10287-023-00498-4}}
We use a fixed point gradient flow algorithm to compute the equilibria of first-price procurement auctions in the presence of losses and Bayesian priors. We use this efficient algorithm to compare optimal, first-price and VCG auctions. This allows us to numerically estimate the social cost of sub-optimality of the nodal pricing mechanism in wholesale electricity markets. We also derive a closed form expression of the optimal mechanism procurement cost when the types are uniformly distributed.
@article{10.1007/s10287-024-00513-2,year={2024},title={{Procurement auctions with losses}},author={Heymann, Benjamin and Jofré, Alejandro},journal={Computational Management Science},issn={1619-697X},doi={10.1007/s10287-024-00513-2},pages={38},number={2},volume={21},}
Maximizing the Success Probability of Policy Allocations in Online Systems
Artem Betlei, Mariia Vladimirova, Mehdi Sebbar, and 3 more authors
In Proceedings of the AAAI Conference on Artificial Intelligence, 2024
The effectiveness of advertising in e-commerce largely depends on the ability of merchants to bid on and win impressions for their targeted users. The bidding procedure is highly complex due to various factors such as market competition, user behavior, and the diverse objectives of advertisers. In this paper we consider the problem at the level of user timelines instead of individual bid requests, manipulating full policies (i.e. pre-defined bidding strategies) and not bid values. In order to optimally allocate policies to users, typical multiple treatments allocation methods solve knapsack-like problems which aim at maximizing an expected value under constraints. In the industrial contexts such as online advertising, we argue that optimizing for the probability of success is a more suited objective than expected value maximization, and we introduce the SuccessProbaMax algorithm that aims at finding the policy allocation which is the most likely to outperform a fixed reference policy. Finally, we conduct comprehensive experiments both on synthetic and real-world data to evaluate its performance. The results demonstrate that our proposed algorithm outperforms conventional expectedvalue maximization algorithms in terms of success rate.
@inproceedings{betlei2024maximizing,title={Maximizing the Success Probability of Policy Allocations in Online Systems},author={Betlei, Artem and Vladimirova, Mariia and Sebbar, Mehdi and Urien, Nicolas and Rahier, Thibaud and Heymann, Benjamin},booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},volume={38},number={10},pages={11061--11068},year={2024},}
Fixed Point Label Attribution for Real-Time Bidding
Martin Bompaire, Antoine Désir, and Benjamin Heymann
Manufacturing & Service Operations Management, 2024
Problem definition: Most of the display advertising inventory is sold through real-time auctions. The participants of these auctions are typically bidders (Google, Criteo, RTB House, and Trade Desk for instance) that participate on behalf of advertisers. In order to estimate the value of each display opportunity, they usually train advanced machine learning algorithms using historical data. In the labeled training set, the inputs are vectors of features representing each display opportunity, and the labels are the generated rewards. In practice, the rewards are given by the advertiser and are tied to whether a particular user converts. Consequently, the rewards are aggregated at the user level and never observed at the display level. A fundamental task that has, to the best of our knowledge, been overlooked is to account for this mismatch and split, or attribute, the rewards at the right granularity level before training a learning algorithm. We call this the label attribution problem. Methodology/results: In this paper, we develop an approach to the label attribution problem, which is both theoretically justified and practical. In particular, we develop a fixed point algorithm that allows for large-scale implementation and showcase our solution using a large-scale publicly available data set from Criteo, a large demand-side platform. We dub our approach the fixed point label attribution algorithm. Managerial implications: There is often a hidden leap of faith when transforming the advertiser’s signal into display labeling. Demand Side Platforms providers should be careful when building their machine learning pipeline and carefully solve the label attribution step.
@article{doi:10.1287/msom.2021.0611,author={Bompaire, Martin and D\'{e}sir, Antoine and Heymann, Benjamin},title={Fixed Point Label Attribution for Real-Time Bidding},journal={Manufacturing \& Service Operations Management},volume={26},number={3},pages={1043-1061},year={2024},doi={10.1287/msom.2021.0611},url={
https://doi.org/10.1287/msom.2021.0611
},eprint={
https://doi.org/10.1287/msom.2021.0611
}}
2022
Kuhn’s equivalence theorem for games in product form
Benjamin Heymann, Michel De Lara, and Jean-Philippe Chancelier
Games and Economic Behavior, 2022
2021
Causal models for real time bidding with repeated user interactions
Martin Bompaire, Alexandre Gilotte, and Benjamin Heymann
In Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining, 2021
2020
How to bid in unified second-price auctions when requests are duplicated
