We introduce and study the online Bayesian recommendation problem for a platform, who can observe a utility-relevant state of a product, repeatedly interacting with a population of myopic users through an online recommendation mechanism. This paradigm is common in a wide range of scenarios in the current Internet economy. For each user with her own private preference and belief, the platform commits to a recommendation strategy to utilize his information advantage on the product state to persuade the self-interested user to follow the recommendation. The platform does not know user's preferences and beliefs, and has to use an adaptive recommendation strategy to persuade with gradually learning user's preferences and beliefs in the process. We aim to design online learning policies with no Stackelberg regret for the platform, i.e., against the optimum policy in hindsight under the assumption that users will correspondingly adapt their behaviors to the benchmark policy. Our first result is an online policy that achieves double logarithm regret dependence on the number of rounds. We then present a hardness result showing that no adaptive online policy can achieve regret with better dependency on the number of rounds. Finally, by formulating the platform's problem as optimizing a linear program with membership oracle access, we present our second online policy that achieves regret with polynomial dependence on the number of states but logarithm dependence on the number of rounds.
{"title":"Online Bayesian Recommendation with No Regret","authors":"Yiding Feng, Wei Tang, Haifeng Xu","doi":"10.1145/3490486.3538327","DOIUrl":"https://doi.org/10.1145/3490486.3538327","url":null,"abstract":"We introduce and study the online Bayesian recommendation problem for a platform, who can observe a utility-relevant state of a product, repeatedly interacting with a population of myopic users through an online recommendation mechanism. This paradigm is common in a wide range of scenarios in the current Internet economy. For each user with her own private preference and belief, the platform commits to a recommendation strategy to utilize his information advantage on the product state to persuade the self-interested user to follow the recommendation. The platform does not know user's preferences and beliefs, and has to use an adaptive recommendation strategy to persuade with gradually learning user's preferences and beliefs in the process. We aim to design online learning policies with no Stackelberg regret for the platform, i.e., against the optimum policy in hindsight under the assumption that users will correspondingly adapt their behaviors to the benchmark policy. Our first result is an online policy that achieves double logarithm regret dependence on the number of rounds. We then present a hardness result showing that no adaptive online policy can achieve regret with better dependency on the number of rounds. Finally, by formulating the platform's problem as optimizing a linear program with membership oracle access, we present our second online policy that achieves regret with polynomial dependence on the number of states but logarithm dependence on the number of rounds.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133503566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ioannis Anagnostides, Gabriele Farina, Christian Kroer, A. Celli, T. Sandholm
A recent emerging trend in the literature on learning in games has been concerned with providing faster learning dynamics for correlated and coarse correlated equilibria in normal-form games. Much less is known about the significantly more challenging setting of extensive-form games, which can capture both sequential and simultaneous moves, as well as imperfect information. In this paper we establish faster no-regret learning dynamics forextensive-form correlated equilibria (EFCE) in multiplayer general-sum imperfect-information extensive-form games. When all players follow our accelerated dynamics, the correlated distribution of play is an O(T-3/4)-approximate EFCE, where the O(·) notation suppresses parameters polynomial in the description of the game. This significantly improves over the best prior rate of O(T-1/2 ). To achieve this, we develop a framework for performing accelerated Phi-regret minimization via predictions. One of our key technical contributions---that enables us to employ our generic template---is to characterize the stability of fixed points associated with trigger deviation functions through a refined perturbation analysis of a structured Markov chain. Furthermore, for the simpler solution concept of extensive-form coarse correlated equilibrium (EFCCE) we give a new succinct closed-form characterization of the associated fixed points, bypassing the expensive computation of stationary distributions required for EFCE. Our results place EFCCE closer to normal-form coarse correlated equilibria in terms of the per-iteration complexity, although the former prescribes a much more compelling notion of correlation. Finally, experiments conducted on standard benchmarks corroborate our theoretical findings.
{"title":"Faster No-Regret Learning Dynamics for Extensive-Form Correlated and Coarse Correlated Equilibria","authors":"Ioannis Anagnostides, Gabriele Farina, Christian Kroer, A. Celli, T. Sandholm","doi":"10.1145/3490486.3538288","DOIUrl":"https://doi.org/10.1145/3490486.3538288","url":null,"abstract":"A recent emerging trend in the literature on learning in games has been concerned with providing faster learning dynamics for correlated and coarse correlated equilibria in normal-form games. Much less is known about the significantly more challenging setting of extensive-form games, which can capture both sequential and simultaneous moves, as well as imperfect information. In this paper we establish faster no-regret learning dynamics forextensive-form correlated equilibria (EFCE) in multiplayer general-sum imperfect-information extensive-form games. When all players follow our accelerated dynamics, the correlated distribution of play is an O(T-3/4)-approximate EFCE, where the O(·) notation suppresses parameters polynomial in the description of the game. This significantly improves over the best prior rate of O(T-1/2 ). To achieve this, we develop a framework for performing accelerated Phi-regret minimization via predictions. One of our key technical contributions---that enables us to employ our generic template---is to characterize the stability of fixed points associated with trigger deviation functions through a refined perturbation analysis of a structured Markov chain. Furthermore, for the simpler solution concept of extensive-form coarse correlated equilibrium (EFCCE) we give a new succinct closed-form characterization of the associated fixed points, bypassing the expensive computation of stationary distributions required for EFCE. Our results place EFCCE closer to normal-form coarse correlated equilibria in terms of the per-iteration complexity, although the former prescribes a much more compelling notion of correlation. Finally, experiments conducted on standard benchmarks corroborate our theoretical findings.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124828515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the query complexity of finding a Tarski fixed point over the k-dimensional grid {1,...,n}k. Improving on the previous best upper bound of O(log⌈2k/3⌉n)[7], we give a new algorithm with query complexity O(log⌈(k+1)/2⌉n). This is based on a novel decomposition theorem about a weaker variant of the Tarski fixed point problem, where the input consists of a monotone function f:[n]k→[n]k and a monotone sign function b:[n]k→ {-1,0,1} and the goal is to find a point x ∈ [n]k that satisfies either f(x) ≼ x and b(x) ≤ 0 or f(x) ≽ x and b(x) ≥ 0.
{"title":"Improved Upper Bounds for Finding Tarski Fixed Points","authors":"X. Chen, Yuhao Li","doi":"10.1145/3490486.3538297","DOIUrl":"https://doi.org/10.1145/3490486.3538297","url":null,"abstract":"We study the query complexity of finding a Tarski fixed point over the k-dimensional grid {1,...,n}k. Improving on the previous best upper bound of O(log⌈2k/3⌉n)[7], we give a new algorithm with query complexity O(log⌈(k+1)/2⌉n). This is based on a novel decomposition theorem about a weaker variant of the Tarski fixed point problem, where the input consists of a monotone function f:[n]k→[n]k and a monotone sign function b:[n]k→ {-1,0,1} and the goal is to find a point x ∈ [n]k that satisfies either f(x) ≼ x and b(x) ≤ 0 or f(x) ≽ x and b(x) ≥ 0.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116464714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the complexity of closure operators, with applications to machine learning and decision theory. In machine learning, closure operators emerge naturally in data classification and clustering. In decision theory, they can model equivalence of choice menus, and therefore situations with a preference for flexibility. Our contribution is to formulate a notion of complexity of closure operators, which translate into the complexity of a classifier in ML, or of a utility function in decision theory.
{"title":"Closure Operators: Complexity and Applications to Classification and Decision-making","authors":"Hamed Hamze Bajgiran, F. Echenique","doi":"10.1145/3490486.3538253","DOIUrl":"https://doi.org/10.1145/3490486.3538253","url":null,"abstract":"We study the complexity of closure operators, with applications to machine learning and decision theory. In machine learning, closure operators emerge naturally in data classification and clustering. In decision theory, they can model equivalence of choice menus, and therefore situations with a preference for flexibility. Our contribution is to formulate a notion of complexity of closure operators, which translate into the complexity of a classifier in ML, or of a utility function in decision theory.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115969275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study sequential bargaining between a proposer and a veto player. Both have single-peaked preferences, but the proposer is uncertain about the veto player's ideal point. The proposer cannot commit to future proposals. When players are patient, there can be equilibria with Coasian dynamics: the veto player's private information can largely nullify proposer's bargaining power. Our main result, however, is that there are also equilibria in which the proposer obtains the high payoff that he would with commitment power. The driving force is that the veto player's single-peaked preferences give the proposer an option to "leapfrog", i.e., to secure agreement from only low-surplus types early on to credibly extract surplus from high types later. Methodologically, we exploit the connection between sequential bargaining and static mechanism design. Full paper available at: https://personal.psu.edu/sma29/papers/AliKartikKleiner.pdf
{"title":"Sequential Veto Bargaining with Incomplete Information","authors":"S. N. Ali, Navin Kartik, Andreas Kleiner","doi":"10.1145/3490486.3538362","DOIUrl":"https://doi.org/10.1145/3490486.3538362","url":null,"abstract":"We study sequential bargaining between a proposer and a veto player. Both have single-peaked preferences, but the proposer is uncertain about the veto player's ideal point. The proposer cannot commit to future proposals. When players are patient, there can be equilibria with Coasian dynamics: the veto player's private information can largely nullify proposer's bargaining power. Our main result, however, is that there are also equilibria in which the proposer obtains the high payoff that he would with commitment power. The driving force is that the veto player's single-peaked preferences give the proposer an option to \"leapfrog\", i.e., to secure agreement from only low-surplus types early on to credibly extract surplus from high types later. Methodologically, we exploit the connection between sequential bargaining and static mechanism design. Full paper available at: https://personal.psu.edu/sma29/papers/AliKartikKleiner.pdf","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129504012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a population of Bayesian agents who share a common prior over some finite state space and each agent is exposed to some information about the state. We ask which distributions over empirical distributions of posteriors beliefs in the population are feasible. We provide a necessary and sufficient condition for feasibility. We apply this result in several domains. First, we study the problem of maximizing the polarization of beliefs in a population. Second, we provide a characterization of the feasible agent-symmetric product distributions of posteriors. Finally, we study an instance of a private Bayesian persuasion problem and provide a clean formula for the sender's optimal value.
{"title":"A Population's Feasible Posterior Beliefs","authors":"Itai Arieli, Y. Babichenko","doi":"10.1145/3490486.3538234","DOIUrl":"https://doi.org/10.1145/3490486.3538234","url":null,"abstract":"We consider a population of Bayesian agents who share a common prior over some finite state space and each agent is exposed to some information about the state. We ask which distributions over empirical distributions of posteriors beliefs in the population are feasible. We provide a necessary and sufficient condition for feasibility. We apply this result in several domains. First, we study the problem of maximizing the polarization of beliefs in a population. Second, we provide a characterization of the feasible agent-symmetric product distributions of posteriors. Finally, we study an instance of a private Bayesian persuasion problem and provide a clean formula for the sender's optimal value.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129531517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The quality of learning generally improves with the scale and diversity of data. Companies and institutions can therefore benefit from building models over shared data. Many cloud and blockchain platforms, as well as government initiatives, are interested in providing this type of service. These cooperative efforts face a challenge, which we call "exclusivity attacks". A firm can share distorted data, so that it learns the best model fit, but is also able to mislead others. We study protocols for long-term interactions and their vulnerability to these attacks, in particular for regression and clustering tasks. We find that the choice of communication protocol is essential for vulnerability: The protocol is much more vulnerable if firms can continuously initiate communication, instead of periodically asked for their inputs. Vulnerability may also depend on the number of Sybil identities a firm can control.
{"title":"Long-term Data Sharing under Exclusivity Attacks","authors":"Yotam gafni, Moshe Tennenholtz","doi":"10.1145/3490486.3538311","DOIUrl":"https://doi.org/10.1145/3490486.3538311","url":null,"abstract":"The quality of learning generally improves with the scale and diversity of data. Companies and institutions can therefore benefit from building models over shared data. Many cloud and blockchain platforms, as well as government initiatives, are interested in providing this type of service. These cooperative efforts face a challenge, which we call \"exclusivity attacks\". A firm can share distorted data, so that it learns the best model fit, but is also able to mislead others. We study protocols for long-term interactions and their vulnerability to these attacks, in particular for regression and clustering tasks. We find that the choice of communication protocol is essential for vulnerability: The protocol is much more vulnerable if firms can continuously initiate communication, instead of periodically asked for their inputs. Vulnerability may also depend on the number of Sybil identities a firm can control.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133382336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alireza Fallah, A. Makhdoumi, Azarakhsh Malekian, A. Ozdaglar
We consider a platform's problem of collecting data from privacy sensitive users to estimate an underlying parameter of interest. We formulate this question as a Bayesian-optimal mechanism design problem, in which an individual can share her (verifiable) data in exchange for a monetary reward or services, but at the same time has a (private) heterogeneous privacy cost which we quantify using differential privacy. We consider two popular differential privacy settings for providing privacy guarantees for the users: central and local. In both settings, we establish minimax lower bounds for the estimation error and derive (near) optimal estimators for given heterogeneous privacy loss levels for users. Building on this characterization, we pose the mechanism design problem as the optimal selection of an estimator and payments that will elicit truthful reporting of users' privacy sensitivities. Under a regularity condition on the distribution of privacy sensitivities we develop efficient algorithmic mechanisms to solve this problem in both privacy settings. Our mechanism in the central setting can be implemented in time O (n log n) where n is the number of users and our mechanism in the local setting admits a Polynomial Time Approximation Scheme (PTAS). The full paper is available at: https://arxiv.org/abs/2201.03968
{"title":"Optimal and Differentially Private Data Acquisition: Central and Local Mechanisms","authors":"Alireza Fallah, A. Makhdoumi, Azarakhsh Malekian, A. Ozdaglar","doi":"10.1145/3490486.3538329","DOIUrl":"https://doi.org/10.1145/3490486.3538329","url":null,"abstract":"We consider a platform's problem of collecting data from privacy sensitive users to estimate an underlying parameter of interest. We formulate this question as a Bayesian-optimal mechanism design problem, in which an individual can share her (verifiable) data in exchange for a monetary reward or services, but at the same time has a (private) heterogeneous privacy cost which we quantify using differential privacy. We consider two popular differential privacy settings for providing privacy guarantees for the users: central and local. In both settings, we establish minimax lower bounds for the estimation error and derive (near) optimal estimators for given heterogeneous privacy loss levels for users. Building on this characterization, we pose the mechanism design problem as the optimal selection of an estimator and payments that will elicit truthful reporting of users' privacy sensitivities. Under a regularity condition on the distribution of privacy sensitivities we develop efficient algorithmic mechanisms to solve this problem in both privacy settings. Our mechanism in the central setting can be implemented in time O (n log n) where n is the number of users and our mechanism in the local setting admits a Polynomial Time Approximation Scheme (PTAS). The full paper is available at: https://arxiv.org/abs/2201.03968","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115957811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Causally identifying the effect of digital advertising is challenging, because experimentation is expensive, and observational data lacks random variation. This paper identifies a pervasive source of naturally occurring, quasi-experimental variation in user-level ad-exposure in digital advertising campaigns. It shows how this variation can be utilized by ad-publishers to identify the causal effect of advertising campaigns. The variation pertains to auction throttling, a probabilistic method of budget pacing that is widely used to spread an ad-campaign's budget over its deployed duration, so that the campaign's budget is not exceeded or overly concentrated in any one period. The throttling mechanism is implemented by computing a participation probability based on the campaign's budget spending rate and then including the campaign in a random subset of available ad-auctions each period according to this probability. We show that access to logged-participation probabilities enables identifying the local average treatment effect (LATE) in the ad-campaign. We present a new estimator that leverages this identification strategy and outline a bootstrap procedure for quantifying its variability. We apply our method to real-world ad-campaign data from an e-commerce advertising platform, which uses such throttling for budget pacing. We show our estimate is statistically different from estimates derived using other standard observational methods such as OLS and two-stage least squares estimators. Our estimated conversion lift is 110%, a more plausible number than 600%, the conversion lifts estimated using naive observational methods. The full version of the paper : https://arxiv.org/abs/2112.15155
{"title":"Auction Throttling and Causal Inference of Online Advertising Effects","authors":"George Gui, Harikesh S. Nair, Fengshi Niu","doi":"10.1145/3490486.3538246","DOIUrl":"https://doi.org/10.1145/3490486.3538246","url":null,"abstract":"Causally identifying the effect of digital advertising is challenging, because experimentation is expensive, and observational data lacks random variation. This paper identifies a pervasive source of naturally occurring, quasi-experimental variation in user-level ad-exposure in digital advertising campaigns. It shows how this variation can be utilized by ad-publishers to identify the causal effect of advertising campaigns. The variation pertains to auction throttling, a probabilistic method of budget pacing that is widely used to spread an ad-campaign's budget over its deployed duration, so that the campaign's budget is not exceeded or overly concentrated in any one period. The throttling mechanism is implemented by computing a participation probability based on the campaign's budget spending rate and then including the campaign in a random subset of available ad-auctions each period according to this probability. We show that access to logged-participation probabilities enables identifying the local average treatment effect (LATE) in the ad-campaign. We present a new estimator that leverages this identification strategy and outline a bootstrap procedure for quantifying its variability. We apply our method to real-world ad-campaign data from an e-commerce advertising platform, which uses such throttling for budget pacing. We show our estimate is statistically different from estimates derived using other standard observational methods such as OLS and two-stage least squares estimators. Our estimated conversion lift is 110%, a more plausible number than 600%, the conversion lifts estimated using naive observational methods. The full version of the paper : https://arxiv.org/abs/2112.15155","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129843298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In a private private information structure, agents' signals contain no information about the signals of their peers. We study how informative such structures can be, and characterize those that are on the Pareto frontier, in the sense that it is impossible to give more information to any agent without violating privacy. In our main application, we show how to optimally disclose information about an unknown state under the constraint of not revealing anything about a correlated variable that contains sensitive information. The full paper is available at https://arxiv.org/abs/2112.14356.
{"title":"Private Private Information","authors":"Kevin He, Fedor Sandomirskiy, O. Tamuz","doi":"10.1145/3490486.3538348","DOIUrl":"https://doi.org/10.1145/3490486.3538348","url":null,"abstract":"In a private private information structure, agents' signals contain no information about the signals of their peers. We study how informative such structures can be, and characterize those that are on the Pareto frontier, in the sense that it is impossible to give more information to any agent without violating privacy. In our main application, we show how to optimally disclose information about an unknown state under the constraint of not revealing anything about a correlated variable that contains sensitive information. The full paper is available at https://arxiv.org/abs/2112.14356.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132682107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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