{"type":"ScholarlyArticle","title":"Differentiable Economics for Randomized Affine Maximizer Auctions","authors":[{"name":"Michael Curry","slug":"michael-curry","given":"Michael","family":"Curry","affiliation":"University of Zurich , ETH AI Center"},{"name":"Tuomas Sandholm","slug":"tuomas-sandholm","given":"Tuomas","family":"Sandholm","affiliation":"Carnegie Mellon University , Optimized Markets, Inc. , Strategic Machine, Inc. , Strategy Robot, Inc."},{"name":"John Dickerson","slug":"john-dickerson","given":"John","family":"Dickerson","affiliation":"University of Maryland"}],"abstract":"A recent approach to automated mechanism design, differentiable economics, represents auctions by rich function approximators and optimizes their performance by gradient descent. The ideal auction architecture for differentiable economics would be perfectly strategyproof, support multiple bidders and items, and be rich enough to represent the optimal (i.e. revenue-maximizing) mechanism. So far, such an architecture does not exist. There are single-bidder approaches (MenuNet, RochetNet) which are always strategyproof and can represent optimal mechanisms. RegretNet is multi-bidder and can approximate any mechanism, but is only approximately strategyproof. We present an architecture that supports multiple bidders and is perfectly strategyproof, but cannot necessarily represent the optimal mechanism. This architecture is the classic affine maximizer auction (AMA), modified to offer lotteries. By using the gradient-based optimization tools of differentiable economics, we can now train lottery AMAs, competing with or outperforming prior approaches in revenue.","doi":"10.24963/ijcai.2023/293","url":"https://ijcai.org/proceedings/2023/293","pdf":"https://ijcai.org/proceedings/2023/0293.pdf","markdown":"https://ijcai.org/proceedings/2023/293.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/293","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":293,"pages":{"first":2633,"last":2641},"keywords":["Game Theory and Economic Paradigms: GTEP: Auctions and market-based systems","Multidisciplinary Topics and Applications: MDA: Economics","Game Theory and Economic Paradigms: GTEP: Mechanism design"],"videos":[],"references":[{"position":1,"raw":"[Armstrong, 2000] Mark Armstrong. Optimal multi-object auctions. Review of Economic Studies, 67:455-481, 2000.","title":"Optimal multi-object auctions","authors":"Mark Armstrong","year":"2000","venue":"Review of Economic Studies","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Avery and Hendershott, 2000] Christopher Avery and Ter- rence Hendershott. Bundling and optimal auctions of mul- tiple products. Review of Economic Studies, 67:483-497, 2000.","title":"Christopher Avery and Terrence Hendershott. Bundling and optimal auctions of multiple products","authors":"Hendershott Avery","year":"2000","venue":"Review of Economic Studies","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Bachrach et al., 2021] Yoram Bachrach, Ian Gemp, Marta Garnelo, Janos Kramar, Tom Eccles, Dan Rosenbaum, and Thore Graepel. A neural network auction for group de- cision making over a continuous space. In International Joint Conference on Artificial Intelligence (IJCAI), 2021.","title":"A neural network auction for group decision making over a continuous space","authors":"Yoram Bachrach, Ian Gemp, Marta Garnelo, Janos Kramar, Tom Eccles, Dan Rosenbaum, Thore Graepel","year":"2021","venue":"International Joint Conference on Artificial Intelligence (IJCAI)","doi":null,"url":null,"internal_url":"/proceedings/2021/706"},{"position":4,"raw":"[Balcan et al., 2016] Maria-Florina F Balcan, Tuomas Sand- holm, and Ellen Vitercik. Sample complexity of automated mechanism design. In NeurIPS, 2016.","title":"Sample complexity of automated mechanism design","authors":"Maria-Florina F Balcan, Tuomas Sandholm, Ellen Vitercik","year":"2016","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Balcan et al., 2018] Maria-Florina Balcan, Tuomas Sand- holm, and Ellen Vitercik. A general theory of sample com- plexity for multi-item profit maximization. In Economics and Computation (EC), 2018.","title":"A general theory of sample complexity for multi-item profit maximization","authors":"Maria-Florina Balcan, Tuomas Sandholm, Ellen Vitercik","year":"2018","venue":"Economics and Computation (EC)","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Balcan et al., 2021] Maria-Florina Balcan, Dan DeBlasio, Travis Dick, Carl Kingsford, Tuomas Sandholm, and Ellen Vitercik. How much data is sufficient to learn high- performing algorithms? Generalization guarantees for data-driven algorithm design. In ACM Symposium on The- ory of Computing (STOC), 2021.","title":"How much data is sufficient to learn highperforming algorithms? Generalization guarantees for data-driven algorithm design","authors":"Maria-Florina Balcan, Dan Deblasio, Travis Dick, Carl Kingsford, Tuomas Sandholm, Ellen Vitercik","year":"2021","venue":"ACM Symposium on Theory of Computing (STOC)","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Bradbury et al., 2018] James Bradbury, Roy Frostig, Peter Hawkins, Matthew James Johnson, Chris Leary, Dougal Maclaurin, George Necula, Adam Paszke, Jake Vander- Plas, Skye Wanderman-Milne, and Qiao Zhang. JAX: composable transformations of Python+NumPy programs, 2018.","title":"JAX: composable transformations of Python+NumPy programs","authors":"James Bradbury, Roy Frostig, Peter Hawkins, Matthew James Johnson, Chris Leary, Dougal Maclaurin, George Necula, Adam Paszke, Jake Vander-Plas, Skye Wanderman-Milne, Qiao Zhang","year":"2018","venue":null,"doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Brero et al., 2019a] Gianluca Brero, Sébastien Lahaie, and Sven Seuken. Fast iterative combinatorial auctions via bayesian learning. In AAAI Conference on Artificial In- telligence (AAAI), 2019.","title":"Fast iterative combinatorial auctions via bayesian learning","authors":"Brero","year":"2019","venue":"AAAI Conference on Artificial Intelligence (AAAI)","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Brero et al., 2019b] Gianluca Brero, Benjamin Lubin, and Sven Seuken. Machine learning-powered iterative combi- natorial auctions. arXiv preprint arXiv:1911.08042, 2019.","title":"Machine learning-powered iterative combinatorial auctions","authors":"Brero","year":"2019","venue":null,"doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Brero et al., 2021] Gianluca Brero, Alon Eden, Matthias Gerstgrasser, David Parkes, and Duncan Rheingans-Yoo. Reinforcement learning of sequential price mechanisms. In AAAI Conference on Artificial Intelligence (AAAI), 2021.","title":"Reinforcement learning of sequential price mechanisms","authors":"Gianluca Brero, Alon Eden, Matthias Gerstgrasser, David Parkes, Duncan Rheingans-Yoo","year":"2021","venue":"AAAI Conference on Artificial Intelligence (AAAI)","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Briest et al., 2010] Patrick Briest, Shuchi Chawla, Robert Kleinberg, and S Matthew Weinberg. Pricing randomized allocations. In ACM-SIAM Symposium on Discrete Algo- rithms (SODA), 2010.","title":"Pricing randomized allocations","authors":"Patrick Briest, Shuchi Chawla, Robert Kleinberg, Matthew Weinberg","year":"2010","venue":"ACM-SIAM Symposium on Discrete Algorithms (SODA)","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Cai and Zhao, 2017] Yang Cai and Mingfei Zhao. Simple mechanisms for subadditive buyers via duality. In ACM Symposium on Theory of Computing (STOC), 2017.","title":"Simple mechanisms for subadditive buyers via duality","authors":"Zhao ; ] Cai, Yang Cai, Mingfei Zhao","year":"2017","venue":"ACM Symposium on Theory of Computing (STOC)","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Cai et al., 2012a] Yang Cai, Constantinos Daskalakis, and S Matthew Weinberg. An algorithmic characterization of multi-dimensional mechanisms. In ACM Symposium on Theory of Computing (STOC), 2012.","title":"An algorithmic characterization of multi-dimensional mechanisms","authors":"Cai","year":"2012","venue":"ACM Symposium on Theory of Computing (STOC)","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Cai et al., 2012b] Yang Cai, Constantinos Daskalakis, and S Matthew Weinberg. Optimal multi-dimensional mech- anism design: Reducing revenue to welfare maximiza- tion. In Symposium on Foundations of Computer Science (FOCS), 2012.","title":"Optimal multi-dimensional mechanism design: Reducing revenue to welfare maximization","authors":"Cai","year":"2012","venue":"Symposium on Foundations of Computer Science (FOCS)","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Cai et al., 2013] Yang Cai, Constantinos Daskalakis, and S Matthew Weinberg. Understanding incentives: Mech- anism design becomes algorithm design. In Symposium on Foundations of Computer Science (FOCS), 2013.","title":"Understanding incentives: Mechanism design becomes algorithm design","authors":"Yang Cai, Constantinos Daskalakis, Matthew Weinberg","year":"2013","venue":"Symposium on Foundations of Computer Science (FOCS)","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Cai et al., 2016] Yang Cai, Nikhil R. Devanur, and S. Matthew Weinberg. A Duality-Based Unified Ap- proach to Bayesian Mechanism Design. In ACM Symposium on Theory of Computing (STOC), 2016.","title":"A Duality-Based Unified Approach to Bayesian Mechanism Design","authors":"Yang Cai, Nikhil R Devanur, S Matthew Weinberg","year":"2016","venue":"ACM Symposium on Theory of Computing (STOC)","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Chawla et al., 2010] Shuchi Chawla, Jason D Hartline, David L Malec, and Balasubramanian Sivan. Multi- parameter mechanism design and sequential posted pric- ing. In ACM Symposium on Theory of Computing (STOC), 2010.","title":"Multiparameter mechanism design and sequential posted pricing","authors":"Shuchi Chawla, Jason D Hartline, David L Malec, Balasubramanian Sivan","year":"2010","venue":"ACM Symposium on Theory of Computing (STOC)","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Clarke, 1971] Edward H Clarke. Multipart pricing of public goods. Public Choice, pages 17-33, 1971.","title":"Multipart pricing of public goods","authors":"Clarke Edward","year":"1971","venue":"Public Choice","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Conitzer and Sandholm, 2002] Vincent Conitzer and Tuo- mas Sandholm. Complexity of mechanism design. In Un- certainty in Artificial Intelligence (UAI), 2002.","title":"Complexity of mechanism design","authors":"Sandholm ; Conitzer, Tuomas Conitzer, Sandholm","year":"2002","venue":"Uncertainty in Artificial Intelligence (UAI)","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Conitzer and Sandholm, 2007] Vincent Conitzer and Tuo- mas Sandholm. Incremental mechanism design. In In- ternational Joint Conference on Artificial Intelligence (IJ- CAI), 2007.","title":"Vincent Conitzer and Tuomas Sandholm","authors":"Sandholm Conitzer","year":"2007","venue":"International Joint Conference on Artificial Intelligence (IJ-CAI)","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Curry et al., 2020] Michael Curry, Ping-yeh Chiang, Tom Goldstein, and John P. Dickerson. Certifying strategyproof auction networks. In NeurIPS, 2020.","title":"Certifying strategyproof auction networks","authors":"Curry","year":"2020","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Curry et al., 2021] Michael J Curry, Uro Lyi, Tom Gold- stein, and John Dickerson. Learning revenue-maximizing auctions with differentiable matching. In International Conference on Artificial Intelligence and Statistics (AIS- TATS), 2021.","title":"Learning revenue-maximizing auctions with differentiable matching","authors":"J Michael, Uro Curry, Tom Lyi, John Goldstein, Dickerson","year":"2021","venue":"International Conference on Artificial Intelligence and Statistics (AIS-TATS)","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Daskalakis et al., 2017] Constantinos Daskalakis, Alan Deckelbaum, and Christos Tzamos. Strong duality for a multiple-good monopolist. Econometrica, 85(3):735-767, 2017.","title":"Strong duality for a multiple-good monopolist","authors":"Constantinos Daskalakis, Alan Deckelbaum, Christos Tzamos","year":"2017","venue":"Econometrica","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Deng et al., 2021] Yuan Deng, Jieming Mao, Vahab Mir- rokni, and Song Zuo. Towards efficient auctions in an auto-bidding world. In The Web Conference, 2021.","title":"Towards efficient auctions in an auto-bidding world","authors":"Yuan Deng, Jieming Mao, Vahab Mirrokni, Song Zuo","year":"2021","venue":"The Web Conference","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Duan et al., 2022] Zhijian Duan, Jingwu Tang, Yutong Yin, Zhe Feng, Xiang Yan, Manzil Zaheer, and Xiaotie Deng. A context-integrated transformer-based neural network for auction design. arXiv preprint arXiv:2201.12489, 2022.","title":"A context-integrated transformer-based neural network for auction design","authors":"Zhijian Duan, Jingwu Tang, Yutong Yin, Zhe Feng, Xiang Yan, Manzil Zaheer, Xiaotie Deng","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Duetting et al., 2019] Paul Duetting, Zhe Feng, Harikrishna Narasimhan, David C. Parkes, and Sai Srivatsa Ravin- dranath. Optimal auctions through deep learning. In ICML, 2019.","title":"Optimal auctions through deep learning","authors":"Paul Duetting, Zhe Feng, Harikrishna Narasimhan, David C Parkes, Sai Srivatsa Ravindranath","year":"2019","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Feng et al., 2018] Zhe Feng, Harikrishna Narasimhan, and David C. Parkes. Deep learning for revenue-optimal auctions with budgets. In International Conference on Autonomous Agents and MultiAgent Systems (AAMAS), 2018.","title":"Deep learning for revenue-optimal auctions with budgets","authors":"Zhe Feng, Harikrishna Narasimhan, David C Parkes","year":"2018","venue":"International Conference on Autonomous Agents and MultiAgent Systems (AAMAS)","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Frankle and Carbin, 2019] Jonathan Frankle and Michael Carbin. The lottery ticket hypothesis: Finding sparse, trainable neural networks. In ICLR, 2019.","title":"The lottery ticket hypothesis: Finding sparse, trainable neural networks","authors":"Carbin Frankle, Jonathan Frankle, Michael Carbin","year":"2019","venue":"ICLR","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Golowich et al., 2018] Noah Golowich, Harikrishna Narasimhan, and David C. Parkes. Deep learning for multi-facility location mechanism design. In International Joint Conference on Artificial Intelligence (IJCAI), 2018.","title":"Deep learning for multi-facility location mechanism design","authors":"Golowich","year":"2018","venue":"International Joint Conference on Artificial Intelligence (IJCAI)","doi":null,"url":null,"internal_url":"/proceedings/2018/36"},{"position":30,"raw":"[Groves, 1973] Theodore Groves. Incentives in teams. Econometrica: Journal of the Econometric Society, pages 617-631, 1973.","title":"Theodore Groves. Incentives in teams","authors":"Groves","year":"1973","venue":"Econometrica: Journal of the Econometric Society","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Guo et al., 2017] Mingyu Guo, Hideaki Hata, and Ali Babar. Optimizing affine maximizer auctions via lin- ear programming: an application to revenue maximizing mechanism design for zero-day exploits markets. In Inter- national Conference on Principles and Practice of Multi- Agent Systems, 2017.","title":"Optimizing affine maximizer auctions via linear programming: an application to revenue maximizing mechanism design for zero-day exploits markets","authors":"Mingyu Guo, Hideaki Hata, Ali Babar","year":"2017","venue":"International Conference on Principles and Practice of Multi-Agent Systems","doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Hart and Nisan, 2019] Sergiu Hart and Noam Nisan. Sell- ing multiple correlated goods: Revenue maximization and menu-size complexity. Journal of Economic Theory, 183:991-1029, 2019.","title":"Selling multiple correlated goods: Revenue maximization and menu-size complexity","authors":"Sergiu Hart, Noam Nisan","year":"2019","venue":"Journal of Economic Theory","doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Hartline and Roughgarden, 2009] Jason D Hartline and Tim Roughgarden. Simple versus optimal mechanisms. In Eco- nomics and Computation (EC), 2009.","title":"Simple versus optimal mechanisms","authors":"Jason D Hartline, Tim Roughgarden","year":"2009","venue":"Economics and Computation (EC)","doi":null,"url":null,"internal_url":null},{"position":34,"raw":"[Hennigan et al., 2020] Tom Hennigan, Trevor Cai, Tamara Norman, and Igor Babuschkin. Haiku: Sonnet for JAX, 2020.","title":"Haiku: Sonnet for JAX","authors":"Hennigan","year":"2020","venue":null,"doi":null,"url":null,"internal_url":null},{"position":35,"raw":"[Hessel et al., 2020] Matteo Hessel, David Budden, Fabio Viola, Mihaela Rosca, Eren Sezener, and Tom Hennigan. Optax: composable gradient transformation and optimisa- tion, in jax!, 2020.","title":"Optax: composable gradient transformation and optimisation","authors":"Matteo Hessel, David Budden, Fabio Viola, Mihaela Rosca, Eren Sezener, Tom Hennigan","year":"2020","venue":"jax!","doi":null,"url":null,"internal_url":null},{"position":36,"raw":"[Ivanov et al., 2022] Dmitry Ivanov, Iskander Safiulin, Kse- nia Balabaeva, and Igor Filippov. Optimal-er auctions through attention. In NeurIPS, 2022.","title":"Optimal-er auctions through attention","authors":"Dmitry Ivanov, Iskander Safiulin, Ksenia Balabaeva, Igor Filippov","year":"2022","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":37,"raw":"[Kash and Frongillo, 2016] Ian A Kash and Rafael M Frongillo. Optimal auctions with restricted allocations. In Economics and Computation (EC), 2016.","title":"Optimal auctions with restricted allocations","authors":"Ian A Kash, Rafael M Frongillo","year":"2016","venue":"Economics and Computation (EC)","doi":null,"url":null,"internal_url":null},{"position":38,"raw":"[Kolesnikov et al., 2022] Alexander V. Kolesnikov, Fedor Sandomirskiy, Aleh Tsyvinski, and Alexander P. Zimin. Beckmann's approach to multi-item multi-bidder auctions. (arXiv:2203.06837), September 2022.","title":"Beckmann's approach to multi-item multi-bidder auctions","authors":"Alexander V Kolesnikov, Fedor Sandomirskiy, Aleh Tsyvinski, Alexander P Zimin","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":39,"raw":"[Kuo et al., 2020] Kevin Kuo, Anthony Ostuni, Elizabeth Horishny, Michael J. Curry, Samuel Dooley, Ping yeh Chiang, Tom Goldstein, and John P. Dickerson. Propor- tionNet: Balancing fairness and revenue for auction de- sign with deep learning. arXiv preprint arXiv:2010.06398, 2020.","title":"Propor-tionNet: Balancing fairness and revenue for auction design with deep learning","authors":"Kevin Kuo, Anthony Ostuni, Elizabeth Horishny, Michael J Curry, Samuel Dooley, Ping Yeh Chiang, Tom Goldstein, John P Dickerson","year":"2020","venue":null,"doi":null,"url":null,"internal_url":null},{"position":40,"raw":"[Lavi et al., 2003] R Lavi, Ahuva Mu'alem, and N Nisan. Towards a characterization of truthful combinatorial auc- tions. In Symposium on Foundations of Computer Science (FOCS), October 2003.","title":"Towards a characterization of truthful combinatorial auctions","authors":"Ahuva Lavi, Mu'alem, Nisan","year":"2003","venue":"Symposium on Foundations of Computer Science (FOCS)","doi":null,"url":null,"internal_url":null},{"position":41,"raw":"[Likhodedov and Sandholm, 2004] Anton Likhodedov and Tuomas Sandholm. Methods for boosting revenue in com- binatorial auctions. In AAAI Conference on Artificial In- telligence (AAAI), 2004.","title":"Methods for boosting revenue in combinatorial auctions","authors":"Sandholm Likhodedov, Anton Likhodedov, Tuomas Sandholm","year":"2004","venue":"AAAI Conference on Artificial Intelligence (AAAI)","doi":null,"url":null,"internal_url":null},{"position":42,"raw":"[Likhodedov and Sandholm, 2005] Anton Likhodedov and Tuomas Sandholm. Approximating revenue-maximizing combinatorial auctions. In AAAI Conference on Artificial Intelligence (AAAI), 2005.","title":"Anton Likhodedov and Tuomas Sandholm. Approximating revenue-maximizing combinatorial auctions","authors":"Sandholm Likhodedov","year":"2005","venue":"AAAI Conference on Artificial Intelligence (AAAI)","doi":null,"url":null,"internal_url":null},{"position":43,"raw":"[Maskin and Riley, 1989] Eric Maskin and John Riley. Op- timal multi-unit auctions. In Frank Hahn, editor, The Economics of Missing Markets, Information, and Games, chapter 14, pages 312-335. Clarendon Press, Oxford, 1989.","title":"Optimal multi-unit auctions","authors":"Riley ; Maskin, Eric Maskin, John Riley","year":"1989","venue":"The Economics of Missing Markets, Information, and Games","doi":null,"url":null,"internal_url":null},{"position":44,"raw":"[Myerson, 1981] Roger B Myerson. Optimal auction design. Mathematics of Operations Research, 6(1):58-73, 1981.","title":"Optimal auction design","authors":"Roger B Myerson","year":"1981","venue":"Mathematics of Operations Research","doi":null,"url":null,"internal_url":null},{"position":45,"raw":"[Pavlov, 2011] Gregory Pavlov. Optimal mechanism for sell- ing two goods. The BE Journal of Theoretical Economics, 11(1), 2011.","title":"Optimal mechanism for selling two goods","authors":"Gregory Pavlov","year":"2011","venue":"The BE Journal of Theoretical Economics","doi":null,"url":null,"internal_url":null},{"position":46,"raw":"[Peri et al., 2021] Neehar Peri, Michael J Curry, Samuel Dooley, and John P Dickerson. Preferencenet: Encoding human preferences in auction design with deep learning. In NeurIPS, 2021.","title":"Preferencenet: Encoding human preferences in auction design with deep learning","authors":"Peri","year":"2021","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":47,"raw":"[Rahme et al., 2021a] Jad Rahme, Samy Jelassi, Joan Bruna, and S Matthew Weinberg. A permutation-equivariant neu- ral network architecture for auction design. In AAAI Con- ference on Artificial Intelligence (AAAI), 2021.","title":"A permutation-equivariant neural network architecture for auction design","authors":"Rahme","year":"2021","venue":"AAAI Conference on Artificial Intelligence (AAAI)","doi":null,"url":null,"internal_url":null},{"position":48,"raw":"[Rahme et al., 2021b] Jad Rahme, Samy Jelassi, and S Matthew Weinberg. Auction learning as a two-player game. In ICLR, 2021.","title":"Auction learning as a two-player game","authors":"Rahme","year":"2021","venue":"ICLR","doi":null,"url":null,"internal_url":null},{"position":49,"raw":"[Ravindranath et al., 2021] Sai Srivatsa Ravindranath, Zhe Feng, Shira Li, Jonathan Ma, Scott D Kominers, and David C Parkes. Deep learning for two-sided matching. arXiv preprint arXiv:2107.03427, 2021.","title":"Deep learning for two-sided matching","authors":"Ravindranath","year":"2021","venue":null,"doi":null,"url":null,"internal_url":null},{"position":50,"raw":"[Roberts, 1979] Kevin Roberts. The characterization of im- plementable choice rules. Aggregation and Revelation of Preferences, 12(2):321-348, 1979.","title":"The characterization of implementable choice rules","authors":"Kevin Roberts","year":"1979","venue":"Aggregation and Revelation of Preferences","doi":null,"url":null,"internal_url":null},{"position":51,"raw":"[Rochet, 1987] Jean-Charles Rochet. A necessary and suffi- cient condition for rationalizability in a quasi-linear con- text. Journal of Mathematical Economics, 16(2):191-200, 1987.","title":"A necessary and sufficient condition for rationalizability in a quasi-linear context","authors":"Jean-Charles Rochet","year":"1987","venue":"Journal of Mathematical Economics","doi":null,"url":null,"internal_url":null},{"position":52,"raw":"[Sandholm and Likhodedov, 2015] Tuomas Sandholm and Anton Likhodedov. Automated design of revenue- maximizing combinatorial auctions. Operations Research, 63(5):1000-1025, 2015.","title":"Automated design of revenuemaximizing combinatorial auctions","authors":"Likhodedov Sandholm, Tuomas Sandholm, Anton Likhodedov","year":"2015","venue":"Operations Research","doi":null,"url":null,"internal_url":null},{"position":53,"raw":"[Sandholm, 2003] Tuomas Sandholm. Automated mecha- nism design: A new application area for search algorithms. In International Conference on Principles and Practice of Constraint Programming, 2003.","title":"Automated mechanism design: A new application area for search algorithms","authors":"Tuomas Sandholm, Sandholm","year":"2003","venue":"International Conference on Principles and Practice of Constraint Programming","doi":null,"url":null,"internal_url":null},{"position":54,"raw":"[Shen et al., 2019] Weiran Shen, Pingzhong Tang, and Song Zuo. Automated mechanism design via neural networks. In International Conference on Autonomous Agents and MultiAgent Systems (AAMAS), 2019.","title":"Automated mechanism design via neural networks","authors":"Shen","year":"2019","venue":"International Conference on Autonomous Agents and MultiAgent Systems (AAMAS)","doi":null,"url":null,"internal_url":null},{"position":55,"raw":"[Soumalias et al., 2022] Ermis Soumalias, Behnoosh Za- manlooy, Jakob Weissteiner, and Sven Seuken. Ma- chine learning-powered course allocation. arXiv preprint arXiv:2210.00954, 2022.","title":"Machine learning-powered course allocation","authors":"Ermis Soumalias, Behnoosh Zamanlooy, Jakob Weissteiner, Sven Seuken","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":56,"raw":"[Tacchetti et al., 2019] Andrea Tacchetti, DJ Strouse, Marta Garnelo, Thore Graepel, and Yoram Bachrach. A neural architecture for designing truthful and efficient auctions. arXiv preprint arXiv:1907.05181, 2019.","title":"A neural architecture for designing truthful and efficient auctions","authors":"Andrea Tacchetti, Marta Strouse, Thore Garnelo, Yoram Graepel, Bachrach","year":"2019","venue":null,"doi":null,"url":null,"internal_url":null},{"position":57,"raw":"[Tang and Sandholm, 2012] Pingzhong Tang and Tuomas Sandholm. Mixed-bundling auctions with reserve prices. In International Conference on Autonomous Agents and MultiAgent Systems (AAMAS), 2012.","title":"Mixed-bundling auctions with reserve prices","authors":"Sandholm Tang, Pingzhong Tang, Tuomas Sandholm","year":"2012","venue":"International Conference on Autonomous Agents and MultiAgent Systems (AAMAS)","doi":null,"url":null,"internal_url":null},{"position":58,"raw":"[Vickrey, 1961] William Vickrey. Counterspeculation, auc- tions, and competitive sealed tenders. The Journal of Fi- nance, 16(1):8-37, 1961.","title":"Counterspeculation, auctions, and competitive sealed tenders","authors":"William Vickrey","year":"1961","venue":"The Journal of Finance","doi":null,"url":null,"internal_url":null},{"position":59,"raw":"[Weissteiner and Seuken, 2020] Jakob Weissteiner and Sven Seuken. Deep learning-powered iterative combinatorial auctions. In AAAI Conference on Artificial Intelligence (AAAI), 2020.","title":"Deep learning-powered iterative combinatorial auctions","authors":"Seuken Weissteiner, Jakob Weissteiner, Sven Seuken","year":"2020","venue":"AAAI Conference on Artificial Intelligence (AAAI)","doi":null,"url":null,"internal_url":null},{"position":60,"raw":"[Weissteiner et al., 2020] Jakob Weissteiner, Chris Wendler, Sven Seuken, Ben Lubin, and Markus Püschel. Fourier analysis-based iterative combinatorial auctions. arXiv preprint arXiv:2009.10749, 2020.","title":"Fourier analysis-based iterative combinatorial auctions","authors":"Jakob Weissteiner, Chris Wendler, Sven Seuken, Ben Lubin, Markus Püschel","year":"2020","venue":null,"doi":null,"url":null,"internal_url":"/proceedings/2022/78"},{"position":61,"raw":"[Yao, 2014] Andrew Chi-Chih Yao. An n-to-1 Bidder Re- duction for Multi-item Auctions and its Applications. In ACM-SIAM Symposium on Discrete Algorithms (SODA), 2014.","title":"An n-to-1 Bidder Reduction for Multi-item Auctions and its Applications","authors":"Chi-Chih Andrew, Yao","year":"2014","venue":"ACM-SIAM Symposium on Discrete Algorithms (SODA)","doi":null,"url":null,"internal_url":null},{"position":62,"raw":"[Yao, 2017] Andrew Chi-Chih Yao. Dominant-strategy ver- sus bayesian multi-item auctions: Maximum revenue de- termination and comparison. In Economics and Computa- tion (EC), 2017.","title":"Dominant-strategy versus bayesian multi-item auctions: Maximum revenue determination and comparison","authors":"Chi-Chih Andrew, Yao","year":"2017","venue":"Economics and Computation (EC)","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}