J. Correa, R. Epstein, Juan F. Escobar, Ignacio Rios, Bastián Bahamondes, Carlos Bonet, Natalie Epstein, Nicolas Aramayo, Martin Castillo, Andrés Cristi, Boris Epstein
Centralized school admission mechanisms are an attractive way of improving social welfare and fairness in large educational systems. In this paper we report the design and implementation of the newly established school choice mechanism in Chile, where over 274,000 students applied to more than 6,400 schools. The Chilean system presents unprecedented design challenges that make it unique. On the one hand, it is a simultaneous nationwide system, making it one of the largest school admission problems worldwide. On the other hand, the system runs at all school levels, from Pre-K to 12th grade, raising at least two issues of outmost importance; namely, the system needs to guarantee their current seat to students applying for a school change, and the system has to favor the assignment of siblings to the same school. As in other systems around the world, we develop a model based on the celebrated Deferred Acceptance algorithm. The algorithm deals not only with the aforementioned issues, but also with further practical features such as soft-bounds and overlapping types. In this context we analyze new stability definitions, present the results of its implementation and conduct simulations showing the benefits of the innovations of the implemented system.
{"title":"School Choice in Chile","authors":"J. Correa, R. Epstein, Juan F. Escobar, Ignacio Rios, Bastián Bahamondes, Carlos Bonet, Natalie Epstein, Nicolas Aramayo, Martin Castillo, Andrés Cristi, Boris Epstein","doi":"10.1145/3328526.3329580","DOIUrl":"https://doi.org/10.1145/3328526.3329580","url":null,"abstract":"Centralized school admission mechanisms are an attractive way of improving social welfare and fairness in large educational systems. In this paper we report the design and implementation of the newly established school choice mechanism in Chile, where over 274,000 students applied to more than 6,400 schools. The Chilean system presents unprecedented design challenges that make it unique. On the one hand, it is a simultaneous nationwide system, making it one of the largest school admission problems worldwide. On the other hand, the system runs at all school levels, from Pre-K to 12th grade, raising at least two issues of outmost importance; namely, the system needs to guarantee their current seat to students applying for a school change, and the system has to favor the assignment of siblings to the same school. As in other systems around the world, we develop a model based on the celebrated Deferred Acceptance algorithm. The algorithm deals not only with the aforementioned issues, but also with further practical features such as soft-bounds and overlapping types. In this context we analyze new stability definitions, present the results of its implementation and conduct simulations showing the benefits of the innovations of the implemented system.","PeriodicalId":416173,"journal":{"name":"Proceedings of the 2019 ACM Conference on Economics and Computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132511765","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}
Dynamic network flows, or network flows over time, constitute an important model for real-world situations where steady states are unusual, such as urban traffic and the Internet. These applications immediately raise the issue of analyzing dynamic network flows from a game-theoretic perspective. In this paper we study dynamic equilibria in the deterministic fluid queuing model in single-source single-sink networks, arguably the most basic model for flows over time. In the last decade we have witnessed significant developments in the theoretical understanding of the model. However, several fundamental questions remain open. One of the most prominent ones concerns the Price of Anarchy, measured as the worst case ratio between the minimum time required to route a given amount of flow from the source to the sink, and the time a dynamic equilibrium takes to perform the same task. Our main result states that if we could reduce the inflow of the network in a dynamic equilibrium, then the Price of Anarchy is exactly $e/(e-1)approx 1.582$. This significantly extends a result by Bhaskar, Fleischer, and Anshelevich (SODA 2011). Furthermore, our methods allow to determine that the Price of Anarchy in parallel-link networks is exactly 4/3. Finally, we argue that if a certain very natural monotonicity conjecture holds, the Price of Anarchy in the general case is exactly $e/(e-1)$.
动态网络流，或随时间变化的网络流，构成了稳定状态不寻常的现实世界情况的重要模型，例如城市交通和互联网。这些应用立即提出了从博弈论角度分析动态网络流的问题。本文研究了单源单汇网络中确定性流体排队模型的动态平衡问题，该模型可以说是最基本的随时间流动模型。在过去十年中，我们见证了对该模型的理论理解的重大发展。然而，仍有几个基本问题有待解决。其中最突出的便是无政府状态的价格(Price of Anarchy)，即将一定数量的流从源发送到汇聚所需的最短时间与执行相同任务所需的动态平衡时间之间的最坏情况比率。我们的主要结果表明，如果我们能够在动态均衡中减少网络的流入，那么无政府状态的价格恰好是$e/(e-1)约1.582$。这大大扩展了Bhaskar, Fleischer和Anshelevich (SODA 2011)的结果。此外，我们的方法允许确定并行链路网络的无政府状态的价格正好是4/3。最后，我们论证了如果一个非常自然的单调性猜想成立，在一般情况下，无政府状态的价格恰好是$e/(e-1)$。
{"title":"On the Price of Anarchy for flows over time","authors":"J. Correa, Andrés Cristi, Tim Oosterwijk","doi":"10.1145/3328526.3329593","DOIUrl":"https://doi.org/10.1145/3328526.3329593","url":null,"abstract":"Dynamic network flows, or network flows over time, constitute an important model for real-world situations where steady states are unusual, such as urban traffic and the Internet. These applications immediately raise the issue of analyzing dynamic network flows from a game-theoretic perspective. In this paper we study dynamic equilibria in the deterministic fluid queuing model in single-source single-sink networks, arguably the most basic model for flows over time. In the last decade we have witnessed significant developments in the theoretical understanding of the model. However, several fundamental questions remain open. One of the most prominent ones concerns the Price of Anarchy, measured as the worst case ratio between the minimum time required to route a given amount of flow from the source to the sink, and the time a dynamic equilibrium takes to perform the same task. Our main result states that if we could reduce the inflow of the network in a dynamic equilibrium, then the Price of Anarchy is exactly $e/(e-1)approx 1.582$. This significantly extends a result by Bhaskar, Fleischer, and Anshelevich (SODA 2011). Furthermore, our methods allow to determine that the Price of Anarchy in parallel-link networks is exactly 4/3. Finally, we argue that if a certain very natural monotonicity conjecture holds, the Price of Anarchy in the general case is exactly $e/(e-1)$.","PeriodicalId":416173,"journal":{"name":"Proceedings of the 2019 ACM Conference on Economics and Computation","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133758531","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 a game of complete information with multiple principals and multiple common agents. Each agent takes an action that can affect the payoffs of all principals. Prat and Rustichini (Econometrica, 2003) who introduce this model assume first price contracts: each principal offers monetary transfers to each agent conditional on the action taken by the agent. We define a notion of VCG contracts which are a restricted natural class of contractible contracts and study its effect on the existence of efficient pure subgame perfect equilibrium outcomes. We identify a "unitary balancedness'' condition that is necessary and sufficient for the existence of a pure subgame perfect equilibrium (SPE) with VCG contracts. As a consequence, we show that the class of instances of this game that admit an efficient SPE with VCG contracts strictly contains the class of instances of this game that admit an efficient SPE with first price contracts. Although VCG contracts broaden the existence of pure subgame perfect equilibria, we show that the worst case welfare loss in any SPE outcome with VCG contracts is not worse than the respective worst case loss with first price contracts.
{"title":"Principal-Agent VCG Contracts","authors":"R. Lavi, Elisheva S. Shamash","doi":"10.1145/3328526.3329570","DOIUrl":"https://doi.org/10.1145/3328526.3329570","url":null,"abstract":"We study a game of complete information with multiple principals and multiple common agents. Each agent takes an action that can affect the payoffs of all principals. Prat and Rustichini (Econometrica, 2003) who introduce this model assume first price contracts: each principal offers monetary transfers to each agent conditional on the action taken by the agent. We define a notion of VCG contracts which are a restricted natural class of contractible contracts and study its effect on the existence of efficient pure subgame perfect equilibrium outcomes. We identify a \"unitary balancedness'' condition that is necessary and sufficient for the existence of a pure subgame perfect equilibrium (SPE) with VCG contracts. As a consequence, we show that the class of instances of this game that admit an efficient SPE with VCG contracts strictly contains the class of instances of this game that admit an efficient SPE with first price contracts. Although VCG contracts broaden the existence of pure subgame perfect equilibria, we show that the worst case welfare loss in any SPE outcome with VCG contracts is not worse than the respective worst case loss with first price contracts.","PeriodicalId":416173,"journal":{"name":"Proceedings of the 2019 ACM Conference on Economics and Computation","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129430122","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 introduce a general class of simplicity concepts that vary the foresight abilities required of agents in extensive-form games, and use it to provide characterizations of simple mechanisms in social choice environments with and without transfers. We show that obvious strategy-proofness---an important simplicity concept included in our class---is characterized by clinch-or-pass games we call millipede games. Some millipede games are indeed simple and widely-used, though others may be complex, requiring significant foresight on the part of the agents, and are rarely observed. Weakening the foresight abilities assumed of the agents eliminates these complex millipede games, leaving monotonic games as the only simple games, a class which includes ascending auctions. As an application, we explain the widespread popularity of the well-known Random Priority mechanism by showing it is the unique mechanism that is efficient, fair, and simple to play.
{"title":"Obvious Dominance and Random Priority","authors":"M. Pycia, Peter Troyan","doi":"10.1145/3328526.3329613","DOIUrl":"https://doi.org/10.1145/3328526.3329613","url":null,"abstract":"We introduce a general class of simplicity concepts that vary the foresight abilities required of agents in extensive-form games, and use it to provide characterizations of simple mechanisms in social choice environments with and without transfers. We show that obvious strategy-proofness---an important simplicity concept included in our class---is characterized by clinch-or-pass games we call millipede games. Some millipede games are indeed simple and widely-used, though others may be complex, requiring significant foresight on the part of the agents, and are rarely observed. Weakening the foresight abilities assumed of the agents eliminates these complex millipede games, leaving monotonic games as the only simple games, a class which includes ascending auctions. As an application, we explain the widespread popularity of the well-known Random Priority mechanism by showing it is the unique mechanism that is efficient, fair, and simple to play.","PeriodicalId":416173,"journal":{"name":"Proceedings of the 2019 ACM Conference on Economics and Computation","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126840210","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}
A. Fiat, A. Karlin, E. Koutsoupias, C. Papadimitriou
The Bitcoin protocol induces miners, through monetary rewards, to expend energy in order to add blocks to the chain. We show that, when energy costs are substantial and taken into account, counterintuitive and unintended strategic behavior results: In a simple bounded-horizon setting with two identical miners there is a unique pure symmetric equilibrium in which both miners first "slow down" in order to decrease the crypto complexity and then take advantage of this decrease. If miners have different energy efficiencies and are restricted to choose the same hash rate for many epochs, there is a unique pure equilibrium in which miners either participate at low levels that depend in intricate ways on all the other miners' efficiencies, or choose to abstain from mining if their efficiency is too low. In the general setting in which miners can adapt their hash rates over time, we show that, unless the number of miners is very small, the only possible pure equilibria are rather chaotic, with miners quitting and starting again periodically --- or there is no pure equilibrium at all. We discuss the implications of these results for the stability of proof-of-work protocols.
{"title":"Energy Equilibria in Proof-of-Work Mining","authors":"A. Fiat, A. Karlin, E. Koutsoupias, C. Papadimitriou","doi":"10.1145/3328526.3329630","DOIUrl":"https://doi.org/10.1145/3328526.3329630","url":null,"abstract":"The Bitcoin protocol induces miners, through monetary rewards, to expend energy in order to add blocks to the chain. We show that, when energy costs are substantial and taken into account, counterintuitive and unintended strategic behavior results: In a simple bounded-horizon setting with two identical miners there is a unique pure symmetric equilibrium in which both miners first \"slow down\" in order to decrease the crypto complexity and then take advantage of this decrease. If miners have different energy efficiencies and are restricted to choose the same hash rate for many epochs, there is a unique pure equilibrium in which miners either participate at low levels that depend in intricate ways on all the other miners' efficiencies, or choose to abstain from mining if their efficiency is too low. In the general setting in which miners can adapt their hash rates over time, we show that, unless the number of miners is very small, the only possible pure equilibria are rather chaotic, with miners quitting and starting again periodically --- or there is no pure equilibrium at all. We discuss the implications of these results for the stability of proof-of-work protocols.","PeriodicalId":416173,"journal":{"name":"Proceedings of the 2019 ACM Conference on Economics and Computation","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123192770","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 Multinomial Logit (MNL) model and the axiom it satisfies, the Independence of Irrelevant Alternatives (IIA), are together the most widely used tools of discrete choice. The MNL model serves as the workhorse model for a variety of fields, but is also widely criticized, with a large body of experimental literature claiming to document real-world settings where IIA fails to hold. Statistical tests of IIA as a modelling assumption have been the subject of many practical tests focusing on specific deviations from IIA over the past several decades, but the formal size properties of hypothesis testing IIA are still not well understood. In this work we replace some of the ambiguity in this literature with rigorous pessimism, demonstrating that any general test for IIA with low worst-case error would require a number of samples exponential in the number of alternatives of the choice problem. A major benefit of our analysis over previous work is that it lies entirely in the finite-sample domain, a feature crucial to understanding the behavior of tests in the common data-poor settings of discrete choice. Our lower bounds are structure-dependent, and as a potential cause for optimism, we find that if one restricts the test of IIA to violations that can occur in a specific collection of choice sets (e.g., pairs), one obtains structure-dependent lower bounds that are much less pessimistic. Our analysis of this testing problem is unorthodox in being highly combinatorial, counting Eulerian orientations of cycle decompositions of a particular bipartite graph constructed from a data set of choices. By identifying fundamental relationships between the comparison structure of a given testing problem and its sample efficiency, we hope these relationships will help lay the groundwork for a rigorous rethinking of the IIA testing problem as well as other testing problems in discrete choice.
{"title":"Fundamental Limits of Testing the Independence of Irrelevant Alternatives in Discrete Choice","authors":"Arjun Seshadri, J. Ugander","doi":"10.1145/3328526.3329656","DOIUrl":"https://doi.org/10.1145/3328526.3329656","url":null,"abstract":"The Multinomial Logit (MNL) model and the axiom it satisfies, the Independence of Irrelevant Alternatives (IIA), are together the most widely used tools of discrete choice. The MNL model serves as the workhorse model for a variety of fields, but is also widely criticized, with a large body of experimental literature claiming to document real-world settings where IIA fails to hold. Statistical tests of IIA as a modelling assumption have been the subject of many practical tests focusing on specific deviations from IIA over the past several decades, but the formal size properties of hypothesis testing IIA are still not well understood. In this work we replace some of the ambiguity in this literature with rigorous pessimism, demonstrating that any general test for IIA with low worst-case error would require a number of samples exponential in the number of alternatives of the choice problem. A major benefit of our analysis over previous work is that it lies entirely in the finite-sample domain, a feature crucial to understanding the behavior of tests in the common data-poor settings of discrete choice. Our lower bounds are structure-dependent, and as a potential cause for optimism, we find that if one restricts the test of IIA to violations that can occur in a specific collection of choice sets (e.g., pairs), one obtains structure-dependent lower bounds that are much less pessimistic. Our analysis of this testing problem is unorthodox in being highly combinatorial, counting Eulerian orientations of cycle decompositions of a particular bipartite graph constructed from a data set of choices. By identifying fundamental relationships between the comparison structure of a given testing problem and its sample efficiency, we hope these relationships will help lay the groundwork for a rigorous rethinking of the IIA testing problem as well as other testing problems in discrete choice.","PeriodicalId":416173,"journal":{"name":"Proceedings of the 2019 ACM Conference on Economics and Computation","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121738664","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}
Agents rarely act in isolation -- their behavioral history, in particular, is public to others. We seek a non-asymptotic understanding of how a leader agent should shape this history to its maximal advantage, knowing that follower agent(s) will be learning and responding to it. We study Stackelberg leader-follower games with finite observations of the leader commitment, which commonly models security games and network routing in engineering, and persuasion mechanisms in economics. First, we formally show that when the game is not zero-sum and the vanilla Stackelberg commitment is mixed, it is not robust to observational uncertainty. We propose observation-robust, polynomial-time-computable commitment constructions for leader strategies that approximate the Stackelberg payoff, and also show that these commitment rules approximate the maximum obtainable payoff (which could in general be greater than the Stackelberg payoff). Full paper: https://eecs.berkeley.edu/~sahai/reputation.pdf
{"title":"Robust Commitments and Partial Reputation","authors":"Vidya Muthukumar, A. Sahai","doi":"10.1145/3328526.3329647","DOIUrl":"https://doi.org/10.1145/3328526.3329647","url":null,"abstract":"Agents rarely act in isolation -- their behavioral history, in particular, is public to others. We seek a non-asymptotic understanding of how a leader agent should shape this history to its maximal advantage, knowing that follower agent(s) will be learning and responding to it. We study Stackelberg leader-follower games with finite observations of the leader commitment, which commonly models security games and network routing in engineering, and persuasion mechanisms in economics. First, we formally show that when the game is not zero-sum and the vanilla Stackelberg commitment is mixed, it is not robust to observational uncertainty. We propose observation-robust, polynomial-time-computable commitment constructions for leader strategies that approximate the Stackelberg payoff, and also show that these commitment rules approximate the maximum obtainable payoff (which could in general be greater than the Stackelberg payoff). Full paper: https://eecs.berkeley.edu/~sahai/reputation.pdf","PeriodicalId":416173,"journal":{"name":"Proceedings of the 2019 ACM Conference on Economics and Computation","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133905228","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}
Jason D. Hartline, Aleck C. Johnsen, Denis Nekipelov, O. Zoeter
This paper gives a theoretical model for design and analysis of mechanisms for online marketplaces where a bidding dashboard enables the bid-optimization of long-lived agents. We assume that a good allocation algorithm exists when given the true values of the agents and we develop online winner-pays-bid and all-pay mechanisms that implement the same outcome of the algorithm with the aid of a bidding dashboard. The bidding dashboards that we develop work in conjunction with the mechanism to guarantee that bidding according to the dashboard is strategically equivalent (with vanishing utility difference) to bidding truthfully in the truthful implementation of the allocation algorithm. Our dashboard mechanism makes only a single call to the allocation algorithm in each stage.
{"title":"Dashboard Mechanisms for Online Marketplaces","authors":"Jason D. Hartline, Aleck C. Johnsen, Denis Nekipelov, O. Zoeter","doi":"10.1145/3328526.3329653","DOIUrl":"https://doi.org/10.1145/3328526.3329653","url":null,"abstract":"This paper gives a theoretical model for design and analysis of mechanisms for online marketplaces where a bidding dashboard enables the bid-optimization of long-lived agents. We assume that a good allocation algorithm exists when given the true values of the agents and we develop online winner-pays-bid and all-pay mechanisms that implement the same outcome of the algorithm with the aid of a bidding dashboard. The bidding dashboards that we develop work in conjunction with the mechanism to guarantee that bidding according to the dashboard is strategically equivalent (with vanishing utility difference) to bidding truthfully in the truthful implementation of the allocation algorithm. Our dashboard mechanism makes only a single call to the allocation algorithm in each stage.","PeriodicalId":416173,"journal":{"name":"Proceedings of the 2019 ACM Conference on Economics and Computation","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116604148","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}
Yu Cheng, Zhihao Jiang, Kamesh Munagala, Kangning Wang
In this paper, we study fairness in committee selection problems. We consider a general notion of fairness via stability: A committee is em stable if no coalition of voters can deviate and choose a committee of proportional size, so that all these voters strictly prefer the new committee to the existing one. Our main contribution is to extend this definition to stability of a distribution (or lottery) over committees. We consider two canonical voter preference models: the Approval Set setting where each voter approves a set of candidates and prefers committees with larger intersection with this set; and the Ranking setting where each voter ranks committees based on how much she likes her favorite candidate in a committee. Our main result is to show that stable lotteries always exist for these canonical preference models. Interestingly, given preferences of voters over committees, the procedure for computing an approximately stable lottery is the same for both models and therefore extends to the setting where some voters have the former preference structure and others have the latter. Our existence proof uses the probabilistic method and a new large deviation inequality that may be of independent interest.
{"title":"Group Fairness in Committee Selection","authors":"Yu Cheng, Zhihao Jiang, Kamesh Munagala, Kangning Wang","doi":"10.1145/3328526.3329577","DOIUrl":"https://doi.org/10.1145/3328526.3329577","url":null,"abstract":"In this paper, we study fairness in committee selection problems. We consider a general notion of fairness via stability: A committee is em stable if no coalition of voters can deviate and choose a committee of proportional size, so that all these voters strictly prefer the new committee to the existing one. Our main contribution is to extend this definition to stability of a distribution (or lottery) over committees. We consider two canonical voter preference models: the Approval Set setting where each voter approves a set of candidates and prefers committees with larger intersection with this set; and the Ranking setting where each voter ranks committees based on how much she likes her favorite candidate in a committee. Our main result is to show that stable lotteries always exist for these canonical preference models. Interestingly, given preferences of voters over committees, the procedure for computing an approximately stable lottery is the same for both models and therefore extends to the setting where some voters have the former preference structure and others have the latter. Our existence proof uses the probabilistic method and a new large deviation inequality that may be of independent interest.","PeriodicalId":416173,"journal":{"name":"Proceedings of the 2019 ACM Conference on Economics and Computation","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114896220","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 revenue optimal mechanism for selling a single item to agents with independent but non-identically distributed values is complex for agents with linear utility (Myerson,1981) and has no closed-form characterization for agents with non-linear utility (cf. Alaei et al., 2012). Nonetheless, for linear utility agents satisfying a natural regularity property, Alaei et al. (2018) showed that simply posting an anonymous price is an e-approximation. We give a parameterization of the regularity property that extends to agents with non-linear utility and show that the approximation bound of anonymous pricing for regular agents approximately extends to agents that satisfy this approximate regularity property. We apply this approximation framework to prove that anonymous pricing is a constant approximation to the revenue optimal single-item auction for agents with public-budget utility, private-budget utility, and (a special case of) risk-averse utility.
对于具有线性效用的代理来说，向具有独立但非相同分布值的代理销售单一商品的收益最优机制是复杂的(Myerson,1981)，对于具有非线性效用的代理来说，没有封闭形式的表征(参见Alaei et al.， 2012)。尽管如此，对于满足自然规律性的线性效用代理，Alaei等人(2018)表明，简单地发布匿名价格是一个e逼近。我们给出了扩展到具有非线性效用的智能体的正则性的参数化，并证明了正则智能体匿名定价的近似界近似地扩展到满足这种近似正则性的智能体。我们应用这个近似框架来证明，对于具有公共预算效用、私人预算效用和(一种特殊情况)风险厌恶效用的代理，匿名定价是收益最优单品拍卖的常数近似。
{"title":"Optimal Auctions vs. Anonymous Pricing: Beyond Linear Utility","authors":"Yiding Feng, Jason D. Hartline, Yingkai Li","doi":"10.1145/3328526.3329603","DOIUrl":"https://doi.org/10.1145/3328526.3329603","url":null,"abstract":"The revenue optimal mechanism for selling a single item to agents with independent but non-identically distributed values is complex for agents with linear utility (Myerson,1981) and has no closed-form characterization for agents with non-linear utility (cf. Alaei et al., 2012). Nonetheless, for linear utility agents satisfying a natural regularity property, Alaei et al. (2018) showed that simply posting an anonymous price is an e-approximation. We give a parameterization of the regularity property that extends to agents with non-linear utility and show that the approximation bound of anonymous pricing for regular agents approximately extends to agents that satisfy this approximate regularity property. We apply this approximation framework to prove that anonymous pricing is a constant approximation to the revenue optimal single-item auction for agents with public-budget utility, private-budget utility, and (a special case of) risk-averse utility.","PeriodicalId":416173,"journal":{"name":"Proceedings of the 2019 ACM Conference on Economics and Computation","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114534748","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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