We develop a model of search by imperfectly informed consumers with unit demand. The innovation is that consumers learn spatially: sampling the payoff to one product causes them to update their payoffs about all products that are nearby in some attribute space. Search is costly, and so consumers face a trade-off between "exploring" far apart regions of the attribute space and "exploiting'' the areas they already know they like. Learning gives rise to path dependence, as each new search decision depends on past experiences through the updating process. We present evidence of these phenomena in data on online camera purchases, showing that the search paths and eventual purchase decisions depend substantially on whether the past items searched were surprisingly good or bad. We argue that search intermediaries can affect purchase decisions not only by highly ranking products that they would like purchased, but also by highlighting bad products in regions of the attribute space that they would like to push the consumer away from.
{"title":"You Can Lead a Horse to Water: Spatial Learning and Path Dependence in Consumer Search","authors":"C. Hodgson, Gregory Lewis","doi":"10.1145/3328526.3329595","DOIUrl":"https://doi.org/10.1145/3328526.3329595","url":null,"abstract":"We develop a model of search by imperfectly informed consumers with unit demand. The innovation is that consumers learn spatially: sampling the payoff to one product causes them to update their payoffs about all products that are nearby in some attribute space. Search is costly, and so consumers face a trade-off between \"exploring\" far apart regions of the attribute space and \"exploiting'' the areas they already know they like. Learning gives rise to path dependence, as each new search decision depends on past experiences through the updating process. We present evidence of these phenomena in data on online camera purchases, showing that the search paths and eventual purchase decisions depend substantially on whether the past items searched were surprisingly good or bad. We argue that search intermediaries can affect purchase decisions not only by highly ranking products that they would like purchased, but also by highlighting bad products in regions of the attribute space that they would like to push the consumer away from.","PeriodicalId":416173,"journal":{"name":"Proceedings of the 2019 ACM Conference on Economics and Computation","volume":"8 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":"126637468","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}
Surender Baswana, P. Chakrabarti, S. Chandran, Yashodhan Kanoria, Utkarsh Patange
The centrally funded technical institutes (CFTIs) for undergraduate studies in India consist of the prestigious Indian Institutes of Technology (IITs) as well as several non-IITs (the National Institutes of Technology, the Indian Institutes of Information Technology, and others). The IITs use the candidate rankings obtained from performance on the JEE Advanced exam for their admissions, whereas the non-IITs use a different set of rankings (obtained from the JEE Main exam) for their admissions. Until 2014, the IITs and the non-IITs used two separate processes to allocate seats to candidates. Every year, several individual candidates would get two seats, one from each of these processes. As a result, at least one of those two seats would go vacant. This would especially be a problem for the IITs as their allocation process would complete before that of the non-IITs. In 2015, we designed and implemented a new joint (centralized) seat allocation process for undergraduate admissions to over 500 programs spread across 80 CFTIs in India, bringing the IIT and the non-IIT processes together under a single umbrella. Our process asks each candidate to submit a single preference list over all these programs, and allots each candidate at most one seat. Our process is based on the well known Deferred Acceptance algorithm, which produces a fair allocation that respects the candidate rankings. However, complex affirmative action seat reservations led us to make a number of algorithmic innovations, including (i) a carefully constructed heuristic for incorporating non-nested common quotas that span multiple programs, (ii) a method to utilize unfilled reserved seats with no modifications to the core software, and (iii) a robust approach to reduce variability in the number of reserved category candidates admitted, while retaining fairness. Because candidates also have outside options (e.g., attending a privately funded institute, or retaking the entrance exams the following year), and we were not allowed, in anticipation of attrition, to speculatively admit more candidates than the capacity permitted, we resorted to a multi-round seat allocation process. After every round, we ask the candidates to accept their allotted seat (if any) by paying a seat acceptance fee by a deadline. Those who don't vacate their seats, and these seats are subsequently allotted to other candidates in future rounds. We implemented a number of process innovations to make the multi-round process smoother and more efficient. These innovations are described in our full paper citejournalPaper Our new seat allocation process went live in 2015, and has remained in successful use since, with continuing improvements. The vacancies at the IITs have reduced by nearly 70% (e.g., there were only 198 vacancies in 10,988 seats in 2017, relative to 587 vacancies in 9,784 seats in 2014 under the legacy process). Meanwhile, vacancies in the non-IITs have reduced only slightly, and concern us, though reducin
{"title":"Centralized Admissions for Engineering Colleges in India","authors":"Surender Baswana, P. Chakrabarti, S. Chandran, Yashodhan Kanoria, Utkarsh Patange","doi":"10.1145/3328526.3329610","DOIUrl":"https://doi.org/10.1145/3328526.3329610","url":null,"abstract":"The centrally funded technical institutes (CFTIs) for undergraduate studies in India consist of the prestigious Indian Institutes of Technology (IITs) as well as several non-IITs (the National Institutes of Technology, the Indian Institutes of Information Technology, and others). The IITs use the candidate rankings obtained from performance on the JEE Advanced exam for their admissions, whereas the non-IITs use a different set of rankings (obtained from the JEE Main exam) for their admissions. Until 2014, the IITs and the non-IITs used two separate processes to allocate seats to candidates. Every year, several individual candidates would get two seats, one from each of these processes. As a result, at least one of those two seats would go vacant. This would especially be a problem for the IITs as their allocation process would complete before that of the non-IITs. In 2015, we designed and implemented a new joint (centralized) seat allocation process for undergraduate admissions to over 500 programs spread across 80 CFTIs in India, bringing the IIT and the non-IIT processes together under a single umbrella. Our process asks each candidate to submit a single preference list over all these programs, and allots each candidate at most one seat. Our process is based on the well known Deferred Acceptance algorithm, which produces a fair allocation that respects the candidate rankings. However, complex affirmative action seat reservations led us to make a number of algorithmic innovations, including (i) a carefully constructed heuristic for incorporating non-nested common quotas that span multiple programs, (ii) a method to utilize unfilled reserved seats with no modifications to the core software, and (iii) a robust approach to reduce variability in the number of reserved category candidates admitted, while retaining fairness. Because candidates also have outside options (e.g., attending a privately funded institute, or retaking the entrance exams the following year), and we were not allowed, in anticipation of attrition, to speculatively admit more candidates than the capacity permitted, we resorted to a multi-round seat allocation process. After every round, we ask the candidates to accept their allotted seat (if any) by paying a seat acceptance fee by a deadline. Those who don't vacate their seats, and these seats are subsequently allotted to other candidates in future rounds. We implemented a number of process innovations to make the multi-round process smoother and more efficient. These innovations are described in our full paper citejournalPaper Our new seat allocation process went live in 2015, and has remained in successful use since, with continuing improvements. The vacancies at the IITs have reduced by nearly 70% (e.g., there were only 198 vacancies in 10,988 seats in 2017, relative to 587 vacancies in 9,784 seats in 2014 under the legacy process). Meanwhile, vacancies in the non-IITs have reduced only slightly, and concern us, though reducin","PeriodicalId":416173,"journal":{"name":"Proceedings of the 2019 ACM Conference on Economics and Computation","volume":"38 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":"126792118","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}
I. Ashlagi, Maximilien Burq, Chinmoy Dutta, Patrick Jaillet, A. Saberi, C. Sholley
Motivated by applications from ride-sharing and kidney exchange, we study the problem of matching agents who arrive at a marketplace over time and leave after d time periods. Agents can only be matched while they are present in the marketplace. Each pair of agents can yield a different match value, and the planner's goal is to maximize the total value over a finite time horizon. First we study the case in which vertices arrive in an adversarial order. We provide a randomized 1/4-competitive algorithm building on a result by Feldman et al. [14] and Lehmann et al. [23]. We extend the model to the case in which departure times are drawn independently from a distribution with non-decreasing hazard rate, for which we establish a 1/8-competitive algorithm. When the arrival order is chosen uniformly at random, we show that a batching algorithm, which computes a maximum-weighted matching every (d+1) periods, is $0.279$-competitive.
{"title":"Edge Weighted Online Windowed Matching","authors":"I. Ashlagi, Maximilien Burq, Chinmoy Dutta, Patrick Jaillet, A. Saberi, C. Sholley","doi":"10.1145/3328526.3329573","DOIUrl":"https://doi.org/10.1145/3328526.3329573","url":null,"abstract":"Motivated by applications from ride-sharing and kidney exchange, we study the problem of matching agents who arrive at a marketplace over time and leave after d time periods. Agents can only be matched while they are present in the marketplace. Each pair of agents can yield a different match value, and the planner's goal is to maximize the total value over a finite time horizon. First we study the case in which vertices arrive in an adversarial order. We provide a randomized 1/4-competitive algorithm building on a result by Feldman et al. [14] and Lehmann et al. [23]. We extend the model to the case in which departure times are drawn independently from a distribution with non-decreasing hazard rate, for which we establish a 1/8-competitive algorithm. When the arrival order is chosen uniformly at random, we show that a batching algorithm, which computes a maximum-weighted matching every (d+1) periods, is $0.279$-competitive.","PeriodicalId":416173,"journal":{"name":"Proceedings of the 2019 ACM Conference on Economics and Computation","volume":"120 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":"124693886","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}
Technological evolution, so central to the progress of humanity in recent decades, is the process of constantly introducing new technologies to replace old ones. A new technology does not necessarily mean a better technology and so should not always be embraced. How can society learn which novelties present actual improvements over the existing technology? Whereas the quality of status-quo technology is well known, the new one is a pig in a poke. With sufficiently many individuals willing to explore the new technology society can learn whether it is indeed an improvement. However, self motivated agents, often, do not agree to explore. This is true, in particular, if agents observed some predecessors that were disappointed from the new technology. Inspired by the classical multi-armed bandit model we study a setting where agents arrive sequentially and must pull one of two arms in order to receive a reward - a risky arm (representing the new technology) and a safe arm (representing the existing one). A central planner must induce sufficiently many agents to experiment with the risky arm. The central planner observes the actions and rewards of all agents while the agents themselves have partial observation. For the setting where each agent observes his predecessor we provide the central planner with a recommendation algorithm that is (almost) incentive compatible and facilitates social learning.
{"title":"Social Learning and the Innkeeper's Challenge","authors":"Gal Bahar, Rann Smorodinsky, Moshe Tennenholtz","doi":"10.1145/3328526.3329569","DOIUrl":"https://doi.org/10.1145/3328526.3329569","url":null,"abstract":"Technological evolution, so central to the progress of humanity in recent decades, is the process of constantly introducing new technologies to replace old ones. A new technology does not necessarily mean a better technology and so should not always be embraced. How can society learn which novelties present actual improvements over the existing technology? Whereas the quality of status-quo technology is well known, the new one is a pig in a poke. With sufficiently many individuals willing to explore the new technology society can learn whether it is indeed an improvement. However, self motivated agents, often, do not agree to explore. This is true, in particular, if agents observed some predecessors that were disappointed from the new technology. Inspired by the classical multi-armed bandit model we study a setting where agents arrive sequentially and must pull one of two arms in order to receive a reward - a risky arm (representing the new technology) and a safe arm (representing the existing one). A central planner must induce sufficiently many agents to experiment with the risky arm. The central planner observes the actions and rewards of all agents while the agents themselves have partial observation. For the setting where each agent observes his predecessor we provide the central planner with a recommendation algorithm that is (almost) incentive compatible and facilitates social learning.","PeriodicalId":416173,"journal":{"name":"Proceedings of the 2019 ACM Conference on Economics and Computation","volume":"15 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":"128802467","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 posted pricing, one defines prices for items (or other outcomes), buyers arrive in some order and take their most preferred bundle among the remaining items. Over the last years, our understanding of such mechanisms has improved considerably. The standard assumption is that the mechanism has exact knowledge of probability distribution the buyers' valuations are drawn from. The prices are then set based on this knowledge. We examine to what extent existing results and techniques are robust to inaccurate prior beliefs. That is, the prices are chosen with respect to similar but different probability distributions. We focus on the question of welfare maximization. We consider all standard distance measures on probability distributions, and derive tight bounds on the welfare guarantees that can be derived for all standard techniques in the various metrics.
{"title":"Posted Pricing and Prophet Inequalities with Inaccurate Priors","authors":"Paul Dütting, Thomas Kesselheim","doi":"10.1145/3328526.3329576","DOIUrl":"https://doi.org/10.1145/3328526.3329576","url":null,"abstract":"In posted pricing, one defines prices for items (or other outcomes), buyers arrive in some order and take their most preferred bundle among the remaining items. Over the last years, our understanding of such mechanisms has improved considerably. The standard assumption is that the mechanism has exact knowledge of probability distribution the buyers' valuations are drawn from. The prices are then set based on this knowledge. We examine to what extent existing results and techniques are robust to inaccurate prior beliefs. That is, the prices are chosen with respect to similar but different probability distributions. We focus on the question of welfare maximization. We consider all standard distance measures on probability distributions, and derive tight bounds on the welfare guarantees that can be derived for all standard techniques in the various metrics.","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":"133657831","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}
Robert Bredereck, A. Kaczmarczyk, D. Knop, R. Niedermeier
We study the (parameterized) computational complexity of problems in the context of fair allocations of indivisible goods. More specifically, we show fixed-parameter tractability results for a broad set of problems concerned with envy-free, Pareto-efficient allocations of items (with agent-specific utility functions) to agents. In principle, this implies efficient exact algorithms for these in general computationally intractable problems whenever we face instances with few agents and low maximum (absolute) utility values. This holds true also in high-multiplicity settings where we may have high numbers of identical items. On the technical side, our approach provides algorithmic meta-theorems covering a rich set of fair allocation problems in the additive preferences model. To achieve this, our main technical contribution is to make an elaborate use of tools from integer linear programming. More specifically, we exploit results originally going back to a famous theorem of Lenstra [Math. Oper. Res. 1983] concerning (the fixed-parameter tractability of) Integer Linear Programs (ILPs) with bounded dimension (that is, the dimension shall be considered as a (small) parameter) and the more recent framework of (combinatorial) N-fold ILPs. We reveal and exploit a fruitful interaction between these two cornerstones in the theory of integer linear programming, which may be of independent interest in applications going beyond fair allocations.
{"title":"High-Multiplicity Fair Allocation: Lenstra Empowered by N-fold Integer Programming","authors":"Robert Bredereck, A. Kaczmarczyk, D. Knop, R. Niedermeier","doi":"10.1145/3328526.3329649","DOIUrl":"https://doi.org/10.1145/3328526.3329649","url":null,"abstract":"We study the (parameterized) computational complexity of problems in the context of fair allocations of indivisible goods. More specifically, we show fixed-parameter tractability results for a broad set of problems concerned with envy-free, Pareto-efficient allocations of items (with agent-specific utility functions) to agents. In principle, this implies efficient exact algorithms for these in general computationally intractable problems whenever we face instances with few agents and low maximum (absolute) utility values. This holds true also in high-multiplicity settings where we may have high numbers of identical items. On the technical side, our approach provides algorithmic meta-theorems covering a rich set of fair allocation problems in the additive preferences model. To achieve this, our main technical contribution is to make an elaborate use of tools from integer linear programming. More specifically, we exploit results originally going back to a famous theorem of Lenstra [Math. Oper. Res. 1983] concerning (the fixed-parameter tractability of) Integer Linear Programs (ILPs) with bounded dimension (that is, the dimension shall be considered as a (small) parameter) and the more recent framework of (combinatorial) N-fold ILPs. We reveal and exploit a fruitful interaction between these two cornerstones in the theory of integer linear programming, which may be of independent interest in applications going beyond fair allocations.","PeriodicalId":416173,"journal":{"name":"Proceedings of the 2019 ACM Conference on Economics and Computation","volume":"11 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120817268","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}
This paper studies the implications of leakage of information through prices for the efficient operation of markets with heterogeneous agents. Focusing on uniform-price double auctions, we first characterize how the presence of heterogeneity (e.g., in terms of agents' trading costs, information precision, or risk attitudes) can shape the information content of prices and hence the market's informational efficiency. We find that price informativeness decreases with the extent of heterogeneity in the market. We then establish that such reductions in price informativeness can in turn manifest themselves as an informational externality: in the presence of heterogeneity, agents do not internalize the impact of their trading decisions on the information revealed to others via prices. We also show that the welfare implications of this heterogeneity-induced informational externality depends on the intricate details of the market. Our results thus indicate that accounting for the possibility of information leakage should be an important consideration in designing markets with asymmetric information. We conclude the paper by exploring the welfare implications of market segmentation in the presence of heterogeneous agents and information leakage.
{"title":"Information and Learning in Heterogeneous Markets","authors":"Yaarit Even, A. Tahbaz-Salehi, X. Vives","doi":"10.1145/3328526.3329631","DOIUrl":"https://doi.org/10.1145/3328526.3329631","url":null,"abstract":"This paper studies the implications of leakage of information through prices for the efficient operation of markets with heterogeneous agents. Focusing on uniform-price double auctions, we first characterize how the presence of heterogeneity (e.g., in terms of agents' trading costs, information precision, or risk attitudes) can shape the information content of prices and hence the market's informational efficiency. We find that price informativeness decreases with the extent of heterogeneity in the market. We then establish that such reductions in price informativeness can in turn manifest themselves as an informational externality: in the presence of heterogeneity, agents do not internalize the impact of their trading decisions on the information revealed to others via prices. We also show that the welfare implications of this heterogeneity-induced informational externality depends on the intricate details of the market. Our results thus indicate that accounting for the possibility of information leakage should be an important consideration in designing markets with asymmetric information. We conclude the paper by exploring the welfare implications of market segmentation in the presence of heterogeneous agents and information leakage.","PeriodicalId":416173,"journal":{"name":"Proceedings of the 2019 ACM Conference on Economics and Computation","volume":"3 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":"133658598","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}
Zhuoshu Li, Kelsey Lieberman, William Macke, Sofia Carrillo, Chien-Ju Ho, J. Wellen, Sanmay Das
Kidney exchange has been studied extensively from the perspective of market design, and a significant focus has been on better algorithms for finding chains and cycles to increase the number of possible matches. A more dramatic benefit could come from incorporating compatible pairs into the mechanism, but this possibility has been relatively understudied. In order to incentivize a compatible pair to participate in exchange, they must be offered a higher quality match for the recipient that can be performed without adding extra waiting time. In this paper, we make two main contributions to the study of incorporating compatible pairs in exchanges. First, we leverage the recently proposed Living Donor Kidney Profile Index (LKDPI) to measure match quality, and develop a novel simulator (based on data from a major transplant center) for the joint distribution of compatibility and quality across pairs. This simulator allows us to study the benefits of including compatible pairs under different models and assumptions. Second, we introduce a hybrid online/batch matching model with impatient (compatible) and patient (incompatible) pairs to capture the need for immediacy. We introduce new algorithms for matching in this model, including one based on online primal-dual techniques. Overall, our results indicate great potential in terms of both increased numbers of transplants of incompatible pairs (almost doubling the number transplanted) as well as improved match quality for recipients in compatible pairs (increasing expected graft survival by between 1 and 2 years). The results are also promising for hard-to-match subpopulations, including blood group O recipients.
{"title":"Incorporating Compatible Pairs in Kidney Exchange: A Dynamic Weighted Matching Model","authors":"Zhuoshu Li, Kelsey Lieberman, William Macke, Sofia Carrillo, Chien-Ju Ho, J. Wellen, Sanmay Das","doi":"10.1145/3328526.3329619","DOIUrl":"https://doi.org/10.1145/3328526.3329619","url":null,"abstract":"Kidney exchange has been studied extensively from the perspective of market design, and a significant focus has been on better algorithms for finding chains and cycles to increase the number of possible matches. A more dramatic benefit could come from incorporating compatible pairs into the mechanism, but this possibility has been relatively understudied. In order to incentivize a compatible pair to participate in exchange, they must be offered a higher quality match for the recipient that can be performed without adding extra waiting time. In this paper, we make two main contributions to the study of incorporating compatible pairs in exchanges. First, we leverage the recently proposed Living Donor Kidney Profile Index (LKDPI) to measure match quality, and develop a novel simulator (based on data from a major transplant center) for the joint distribution of compatibility and quality across pairs. This simulator allows us to study the benefits of including compatible pairs under different models and assumptions. Second, we introduce a hybrid online/batch matching model with impatient (compatible) and patient (incompatible) pairs to capture the need for immediacy. We introduce new algorithms for matching in this model, including one based on online primal-dual techniques. Overall, our results indicate great potential in terms of both increased numbers of transplants of incompatible pairs (almost doubling the number transplanted) as well as improved match quality for recipients in compatible pairs (increasing expected graft survival by between 1 and 2 years). The results are also promising for hard-to-match subpopulations, including blood group O recipients.","PeriodicalId":416173,"journal":{"name":"Proceedings of the 2019 ACM Conference on Economics and Computation","volume":"16 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":"116905344","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 analyze Approval Voting in Poisson games endowing voters with private values over three candidates. We first show that any stable equilibrium is discriminatory: one candidate is commonly regarded as out of contention. We fully characterize stable equilibria and divide them into two classes. In direct equilibria, best responses depend only on ordinal preferences. In indirect equilibria, preference intensities matter. Counterintuitively, any stable equilibrium violates the ordering conditions, a set of belief restrictions used to derive early results in the literature. We finally use Monte-Carlo simulations to estimate the prevalence of the different sorts of equilibria and their likelihood to elect a Condorcet winner.
{"title":"Analysis of Approval Voting in Poisson Games","authors":"F. Durand, Antonin Macé, Matías Núñez","doi":"10.1145/3328526.3329643","DOIUrl":"https://doi.org/10.1145/3328526.3329643","url":null,"abstract":"We analyze Approval Voting in Poisson games endowing voters with private values over three candidates. We first show that any stable equilibrium is discriminatory: one candidate is commonly regarded as out of contention. We fully characterize stable equilibria and divide them into two classes. In direct equilibria, best responses depend only on ordinal preferences. In indirect equilibria, preference intensities matter. Counterintuitively, any stable equilibrium violates the ordering conditions, a set of belief restrictions used to derive early results in the literature. We finally use Monte-Carlo simulations to estimate the prevalence of the different sorts of equilibria and their likelihood to elect a Condorcet winner.","PeriodicalId":416173,"journal":{"name":"Proceedings of the 2019 ACM Conference on Economics and Computation","volume":"32 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":"125456005","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 the general problem of selling a limited inventory of items to heterogeneous customers who arrive sequentially, and analyze the competitive ratio under adversarial arrivals. Previous work in this area, motivated by online matching, advertising, and assortment problems, has considered the case where each item can be sold at only a single price. This work has culminated in two classes of algorithms: "balance'' algorithms, which achieve the best-possible competitive ratio of 1-1/e in an asymptotic large-inventory ("small bids") regime; and "ranking'' algorithms, which achieve the best-possible competitive ratio of 1-1/e in the deterministic case of online matching. In this paper, we extend both of these classes of results to allow for items to have multiple feasible prices. Our algorithms introduce the idea of "booking limits'' from revenue management and integrate them into the multiplicative penalty functions used for online matching and allocation problems. Our algorithms achieve the best-possible weight-dependent competitive ratios, which depend on the sets of feasible prices given in advance. To establish this tightness, we show that by optimizing our additive "value function'' used to make allocation decisions, the resulting objective value is the same as that of an adversary's optimization problem for designing a weighted upper-triangular graph. Our "balance'' algorithm and its analysis further use a randomly-perturbed version of this value function; aside from being asymptotically optimal, they improve the best-known dependence of the competitive ratio on the starting inventory amounts.
{"title":"Tight Weight-dependent Competitive Ratios for Online Edge-weighted Bipartite Matching and Beyond","authors":"Will Ma, D. Simchi-Levi","doi":"10.1145/3328526.3329636","DOIUrl":"https://doi.org/10.1145/3328526.3329636","url":null,"abstract":"We consider the general problem of selling a limited inventory of items to heterogeneous customers who arrive sequentially, and analyze the competitive ratio under adversarial arrivals. Previous work in this area, motivated by online matching, advertising, and assortment problems, has considered the case where each item can be sold at only a single price. This work has culminated in two classes of algorithms: \"balance'' algorithms, which achieve the best-possible competitive ratio of 1-1/e in an asymptotic large-inventory (\"small bids\") regime; and \"ranking'' algorithms, which achieve the best-possible competitive ratio of 1-1/e in the deterministic case of online matching. In this paper, we extend both of these classes of results to allow for items to have multiple feasible prices. Our algorithms introduce the idea of \"booking limits'' from revenue management and integrate them into the multiplicative penalty functions used for online matching and allocation problems. Our algorithms achieve the best-possible weight-dependent competitive ratios, which depend on the sets of feasible prices given in advance. To establish this tightness, we show that by optimizing our additive \"value function'' used to make allocation decisions, the resulting objective value is the same as that of an adversary's optimization problem for designing a weighted upper-triangular graph. Our \"balance'' algorithm and its analysis further use a randomly-perturbed version of this value function; aside from being asymptotically optimal, they improve the best-known dependence of the competitive ratio on the starting inventory amounts.","PeriodicalId":416173,"journal":{"name":"Proceedings of the 2019 ACM Conference on Economics and Computation","volume":"43 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":"123118012","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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