The problem of finding stable matches that meet distributional concerns is usually formulated by imposing various side constraints. Prior work has focused on constraints whose "right hand sides" are absolute numbers specified before the preferences or number of agents on the "proposing" side are known. In many cases it is more natural to express the relevant constraints as proportions. We treat such constraints as soft, but provide ex-post guarantees on how well the constraints are satisfied while preserving stability. We violate the proportions by an amount proportional to the reciprocal of the number of students assigned to the school. For example, if a school is assigned 100 students, then the actual proportion will differ from the desired proportion by at most 2%. Our technique requires an extension of Scarf's lemma, which is of independent interest.
{"title":"Stable Matching with Proportionality Constraints","authors":"Thành Nguyen, R. Vohra","doi":"10.1145/3033274.3084091","DOIUrl":"https://doi.org/10.1145/3033274.3084091","url":null,"abstract":"The problem of finding stable matches that meet distributional concerns is usually formulated by imposing various side constraints. Prior work has focused on constraints whose \"right hand sides\" are absolute numbers specified before the preferences or number of agents on the \"proposing\" side are known. In many cases it is more natural to express the relevant constraints as proportions. We treat such constraints as soft, but provide ex-post guarantees on how well the constraints are satisfied while preserving stability. We violate the proportions by an amount proportional to the reciprocal of the number of students assigned to the school. For example, if a school is assigned 100 students, then the actual proportion will differ from the desired proportion by at most 2%. Our technique requires an extension of Scarf's lemma, which is of independent interest.","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121797606","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 inefficiency and computation of pure Nash equilibria in unweighted congestion games, where the strategies of each player i are given implicitly by the binary vectors of a polytope $P_i$. Given these polytopes, a strategy profile naturally corresponds to an integral vector in the aggregation polytope PN = ∑i Pi. We identify two general properties of the aggregation polytope $P_N$ that are sufficient for our results to go through, namely the integer decomposition property (IDP) and the box-totally dual integrality property (box-TDI). Intuitively, the IDP is needed to decompose a load profile in PN into a respective strategy profile of the players, and box-TDI ensures that the intersection of a polytope with an arbitrary integer box is an integral polytope. Examples of polytopal congestion games which satisfy IDP and box-TDI include common source network congestion games, symmetric totally unimodular congestion games, non-symmetric matroid congestion games and symmetric matroid intersection congestion games (in particular, r-arborescences and strongly base-orderable matroids). Our main contributions for polytopal congestion games satisfying IDP and box-TDI are as follows: We derive tight bounds on the price of stability for these games. This extends a result of Fotakis (2010) on the price of stability for symmetric network congestion games to the larger class of polytopal congestion games. Our bounds improve upon the ones for general polynomial congestion games obtained by Christodoulou and Gairing (2016). We show that pure Nash equilibria can be computed in strongly polynomial time for these games. To this aim, we generalize a recent aggregation/decomposition framework by Del Pia et al. (2017) for symmetric totally unimodular and non-symmetric matroid congestion games, both being a special case of our polytopal congestion games. Finally, we generalize and extend results on the computation of strong equilibria in bottleneck congestion games studied by Harks, Hoefer, Klimm and Skopalik (2013). In particular, we show that strong equilibria can be computed efficiently for symmetric totally unimodular bottleneck congestion games. In general, our results reveal that the combination of IDP and box-TDI gives rise to an efficient approach to compute a pure Nash equilibrium whose inefficiency is better than in general congestion games.
{"title":"Potential Function Minimizers of Combinatorial Congestion Games: Efficiency and Computation","authors":"P. Kleer, G. Schäfer","doi":"10.1145/3033274.3085149","DOIUrl":"https://doi.org/10.1145/3033274.3085149","url":null,"abstract":"We study the inefficiency and computation of pure Nash equilibria in unweighted congestion games, where the strategies of each player i are given implicitly by the binary vectors of a polytope $P_i$. Given these polytopes, a strategy profile naturally corresponds to an integral vector in the aggregation polytope PN = ∑i Pi. We identify two general properties of the aggregation polytope $P_N$ that are sufficient for our results to go through, namely the integer decomposition property (IDP) and the box-totally dual integrality property (box-TDI). Intuitively, the IDP is needed to decompose a load profile in PN into a respective strategy profile of the players, and box-TDI ensures that the intersection of a polytope with an arbitrary integer box is an integral polytope. Examples of polytopal congestion games which satisfy IDP and box-TDI include common source network congestion games, symmetric totally unimodular congestion games, non-symmetric matroid congestion games and symmetric matroid intersection congestion games (in particular, r-arborescences and strongly base-orderable matroids). Our main contributions for polytopal congestion games satisfying IDP and box-TDI are as follows: We derive tight bounds on the price of stability for these games. This extends a result of Fotakis (2010) on the price of stability for symmetric network congestion games to the larger class of polytopal congestion games. Our bounds improve upon the ones for general polynomial congestion games obtained by Christodoulou and Gairing (2016). We show that pure Nash equilibria can be computed in strongly polynomial time for these games. To this aim, we generalize a recent aggregation/decomposition framework by Del Pia et al. (2017) for symmetric totally unimodular and non-symmetric matroid congestion games, both being a special case of our polytopal congestion games. Finally, we generalize and extend results on the computation of strong equilibria in bottleneck congestion games studied by Harks, Hoefer, Klimm and Skopalik (2013). In particular, we show that strong equilibria can be computed efficiently for symmetric totally unimodular bottleneck congestion games. In general, our results reveal that the combination of IDP and box-TDI gives rise to an efficient approach to compute a pure Nash equilibrium whose inefficiency is better than in general congestion games.","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115069010","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 are interested in the problem of dividing a cake -- a heterogeneous divisible good -- among n players, in a way that is ε-equitable: every pair of players must have the same value for their own allocated pieces, up to a difference of at most ε. It is known that such allocations can be computed using O(n ln(1/ε)) operations in the standard Robertson-Webb Model. We establish a lower bound of Ω(ln(1/ε)/lnln(1/ε)) on the complexity of this problem, which is almost tight for a constant number of players. Importantly, our result implies that allocations that are exactly equitable cannot be computed.
{"title":"A Lower Bound for Equitable Cake Cutting","authors":"A. Procaccia, Junxing Wang","doi":"10.1145/3033274.3085107","DOIUrl":"https://doi.org/10.1145/3033274.3085107","url":null,"abstract":"We are interested in the problem of dividing a cake -- a heterogeneous divisible good -- among n players, in a way that is ε-equitable: every pair of players must have the same value for their own allocated pieces, up to a difference of at most ε. It is known that such allocations can be computed using O(n ln(1/ε)) operations in the standard Robertson-Webb Model. We establish a lower bound of Ω(ln(1/ε)/lnln(1/ε)) on the complexity of this problem, which is almost tight for a constant number of players. Importantly, our result implies that allocations that are exactly equitable cannot be computed.","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126611969","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}
J. Correa, Patricio Foncea, R. Hoeksma, Tim Oosterwijk, T. Vredeveld
Posted price mechanisms constitute a widely used way of selling items to strategic consumers. Although suboptimal, the attractiveness of these mechanisms comes from their simplicity and easy implementation. In this paper, we investigate the performance of posted price mechanisms when customers arrive in an unknown random order. We compare the expected revenue of these mechanisms to the expected revenue of the optimal auction in two different settings. Namely, the nonadaptive setting in which all offers are sent to the customers beforehand, and the adaptive setting in which an offer is made when a consumer arrives. For the nonadaptive case, we obtain a strategy achieving an expected revenue within at least a 1-1/e fraction of that of the optimal auction. We also show that this bound is tight, even if the customers have i.i.d. valuations for the item. For the adaptive case, we exhibit a posted price mechanism that achieves a factor 0.745 of the optimal revenue, when the customers have i.i.d. valuations for the item. Furthermore, we prove that our results extend to the prophet inequality setting and in particular our result for i.i.d. random valuations resolves a problem posed by Hill and Kertz. [13]
{"title":"Posted Price Mechanisms for a Random Stream of Customers","authors":"J. Correa, Patricio Foncea, R. Hoeksma, Tim Oosterwijk, T. Vredeveld","doi":"10.1145/3033274.3085137","DOIUrl":"https://doi.org/10.1145/3033274.3085137","url":null,"abstract":"Posted price mechanisms constitute a widely used way of selling items to strategic consumers. Although suboptimal, the attractiveness of these mechanisms comes from their simplicity and easy implementation. In this paper, we investigate the performance of posted price mechanisms when customers arrive in an unknown random order. We compare the expected revenue of these mechanisms to the expected revenue of the optimal auction in two different settings. Namely, the nonadaptive setting in which all offers are sent to the customers beforehand, and the adaptive setting in which an offer is made when a consumer arrives. For the nonadaptive case, we obtain a strategy achieving an expected revenue within at least a 1-1/e fraction of that of the optimal auction. We also show that this bound is tight, even if the customers have i.i.d. valuations for the item. For the adaptive case, we exhibit a posted price mechanism that achieves a factor 0.745 of the optimal revenue, when the customers have i.i.d. valuations for the item. Furthermore, we prove that our results extend to the prophet inequality setting and in particular our result for i.i.d. random valuations resolves a problem posed by Hill and Kertz. [13]","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127741437","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 a model of large trading networks with bilateral contracts. Contracts capture exchange, production, and prices, as well as frictions such as complex taxes and the absence of transfers. In our setting, under standard continuity and convexity conditions, a stable outcome exists in any acyclic network, as long as all firms regard sales as substitutes and the market is large. Thus, complementarities between inputs do not preclude the existence of stable outcomes in large markets, unlike in discrete markets. Even when sales are not substitutable, tree stable outcomes exist in our setting. The model presented in this paper generalizes and unifies versions of general equilibrium models with divisible and indivisible goods, matching models with continuously divisible contracts, models of large (two-sided) matching with complementarities, and club formation models. Additional results provide intuition for the role of uni-directional substitutability conditions and acyclicity in the main existence results, and explain what kinds of equilibria are guaranteed to exist even when these conditions are relaxed. Unlike in two-sided large-market settings, the sufficient conditions described in this paper pin down maximal domains for the existence of equilibria.
{"title":"Complementary Inputs and the Existence of Stable Outcomes in Large Trading Networks","authors":"Ravi Jagadeesan","doi":"10.1145/3033274.3085113","DOIUrl":"https://doi.org/10.1145/3033274.3085113","url":null,"abstract":"This paper studies a model of large trading networks with bilateral contracts. Contracts capture exchange, production, and prices, as well as frictions such as complex taxes and the absence of transfers. In our setting, under standard continuity and convexity conditions, a stable outcome exists in any acyclic network, as long as all firms regard sales as substitutes and the market is large. Thus, complementarities between inputs do not preclude the existence of stable outcomes in large markets, unlike in discrete markets. Even when sales are not substitutable, tree stable outcomes exist in our setting. The model presented in this paper generalizes and unifies versions of general equilibrium models with divisible and indivisible goods, matching models with continuously divisible contracts, models of large (two-sided) matching with complementarities, and club formation models. Additional results provide intuition for the role of uni-directional substitutability conditions and acyclicity in the main existence results, and explain what kinds of equilibria are guaranteed to exist even when these conditions are relaxed. Unlike in two-sided large-market settings, the sufficient conditions described in this paper pin down maximal domains for the existence of equilibria.","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126390361","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 online advertising markets, advertisers often purchase ad placements through bidding in repeated auctions based on realized viewer information. We study how budget-constrained advertisers may bid in the presence of competition, when there is uncertainty about future bidding opportunities as well as competitors' heterogenous preferences and budgets. We formulate this problem as a sequential game of incomplete information, where bidders know neither their own valuation distribution, nor the budgets and valuation distributions of their competitors. We introduce a family of dynamic bidding strategies we refer to as "adaptive pacing" strategies, in which advertisers adjust their bids throughout the campaign according to the sample path of observed expenditures. We analyze the performance of this class of strategies under different assumptions on competitors' behavior. Under arbitrary competitors' bids, we establish through matching lower and upper bounds the asymptotic optimality of this class of strategies as the number of auctions grows large. When adopted by all the bidders, the dynamics converge to a tractable and meaningful steady state. Moreover, we show that these strategies constitute an approximate Nash equilibrium in dynamic strategies: The benefit of unilaterally deviating to other strategies, including ones with access to complete information, becomes negligible as the number of auctions and competitors grows large. This establishes a connection between regret minimization and market stability, by which advertisers can essentially follow equilibrium bidding strategies that also ensure the best performance that can be guaranteed off-equilibrium.
{"title":"Learning in Repeated Auctions with Budgets: Regret Minimization and Equilibrium","authors":"S. Balseiro, Y. Gur","doi":"10.2139/ssrn.2921446","DOIUrl":"https://doi.org/10.2139/ssrn.2921446","url":null,"abstract":"In online advertising markets, advertisers often purchase ad placements through bidding in repeated auctions based on realized viewer information. We study how budget-constrained advertisers may bid in the presence of competition, when there is uncertainty about future bidding opportunities as well as competitors' heterogenous preferences and budgets. We formulate this problem as a sequential game of incomplete information, where bidders know neither their own valuation distribution, nor the budgets and valuation distributions of their competitors. We introduce a family of dynamic bidding strategies we refer to as \"adaptive pacing\" strategies, in which advertisers adjust their bids throughout the campaign according to the sample path of observed expenditures. We analyze the performance of this class of strategies under different assumptions on competitors' behavior. Under arbitrary competitors' bids, we establish through matching lower and upper bounds the asymptotic optimality of this class of strategies as the number of auctions grows large. When adopted by all the bidders, the dynamics converge to a tractable and meaningful steady state. Moreover, we show that these strategies constitute an approximate Nash equilibrium in dynamic strategies: The benefit of unilaterally deviating to other strategies, including ones with access to complete information, becomes negligible as the number of auctions and competitors grows large. This establishes a connection between regret minimization and market stability, by which advertisers can essentially follow equilibrium bidding strategies that also ensure the best performance that can be guaranteed off-equilibrium.","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"102 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122494453","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}
Deferred-acceptance (DA) auctions} are mechanisms that are based on backward-greedy algorithms and possess a number of remarkable incentive properties, including implementation as an obviously-strategyproof ascending auction. All existing work on DA auctions considers only binary single-parameter problems, where each bidder either ``wins'' or ``loses.'' This paper generalizes the DA auction framework to non-binary settings, and applies this generalized framework to obtain approximately welfare-maximizing DA auctions for a number of basic mechanism design problems: multiunit auctions, problems with polymatroid constraints or multiple knapsack constraints, and the problem of scheduling jobs to minimize their total weighted completion time. Our results require the design of novel backward-greedy algorithms with good approximation guarantees.
{"title":"Deferred-Acceptance Auctions for Multiple Levels of Service","authors":"Vasilis Gkatzelis, E. Markakis, T. Roughgarden","doi":"10.1145/3033274.3085142","DOIUrl":"https://doi.org/10.1145/3033274.3085142","url":null,"abstract":"Deferred-acceptance (DA) auctions} are mechanisms that are based on backward-greedy algorithms and possess a number of remarkable incentive properties, including implementation as an obviously-strategyproof ascending auction. All existing work on DA auctions considers only binary single-parameter problems, where each bidder either ``wins'' or ``loses.'' This paper generalizes the DA auction framework to non-binary settings, and applies this generalized framework to obtain approximately welfare-maximizing DA auctions for a number of basic mechanism design problems: multiunit auctions, problems with polymatroid constraints or multiple knapsack constraints, and the problem of scheduling jobs to minimize their total weighted completion time. Our results require the design of novel backward-greedy algorithms with good approximation guarantees.","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116774265","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 setting in which agents and items match dynamically over time. We show that repeated independent lotteries with unlimited entry (which are commonly used in practice) encourage agents to enter many lotteries, and may result in low match value. We consider three alternate mechanisms: allowing agents to save unused tickets, limiting agents to entering at most one lottery, and allocating developments using a waiting list. We show that these three mechanisms are equivalent: for each agent, the probability of matching and expected value conditioned on matching are identical. Compared to a repeated lottery, these mechanisms result in higher-quality matches for matched agents. However, in some cases, a repeated lottery is more likely to match agents with the worst outside options, and thus may outperform the other mechanisms in terms of utilitarian welfare. We discuss the implications of these findings for two systems in New York City that currently use a repeated lottery: the allocation of affordable housing and of discounted tickets to broadway shows.
{"title":"How (Not) to Allocate Affordable Housing","authors":"N. Arnosti, Peng Shi","doi":"10.1145/3033274.3085157","DOIUrl":"https://doi.org/10.1145/3033274.3085157","url":null,"abstract":"We consider a setting in which agents and items match dynamically over time. We show that repeated independent lotteries with unlimited entry (which are commonly used in practice) encourage agents to enter many lotteries, and may result in low match value. We consider three alternate mechanisms: allowing agents to save unused tickets, limiting agents to entering at most one lottery, and allocating developments using a waiting list. We show that these three mechanisms are equivalent: for each agent, the probability of matching and expected value conditioned on matching are identical. Compared to a repeated lottery, these mechanisms result in higher-quality matches for matched agents. However, in some cases, a repeated lottery is more likely to match agents with the worst outside options, and thus may outperform the other mechanisms in terms of utilitarian welfare. We discuss the implications of these findings for two systems in New York City that currently use a repeated lottery: the allocation of affordable housing and of discounted tickets to broadway shows.","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"11 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126124335","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}
Due to complex interactions in financial markets, financial regulations can sometimes produce unexpected outcomes, and fail to achieve their macroeconomic goals. We replicate a previous agent-based simulation study which showed that the Basel banking regulations may increase financial instability, counter to their intended purpose. Our replication confirms that this is the case, following the original study's assumption that the financial firms' behaviors are fixed. We then extend the model to account for a possible strategic response, where financial firms adapt to the regulatory regime. Using empirical game-theoretic analysis, we derive equilibria with and without regulation. We find that in the new Basel-regulated equilibria, more funds stay out of default and banks lose less capital. The overall effect of regulation on financial stability becomes benign on most measures when accounting for the strategic adaptation of agents.
{"title":"Accounting for Strategic Response in an Agent-Based Model of Financial Regulation","authors":"F. Cheng, Michael P. Wellman","doi":"10.1145/3033274.3085114","DOIUrl":"https://doi.org/10.1145/3033274.3085114","url":null,"abstract":"Due to complex interactions in financial markets, financial regulations can sometimes produce unexpected outcomes, and fail to achieve their macroeconomic goals. We replicate a previous agent-based simulation study which showed that the Basel banking regulations may increase financial instability, counter to their intended purpose. Our replication confirms that this is the case, following the original study's assumption that the financial firms' behaviors are fixed. We then extend the model to account for a possible strategic response, where financial firms adapt to the regulatory regime. Using empirical game-theoretic analysis, we derive equilibria with and without regulation. We find that in the new Basel-regulated equilibria, more funds stay out of default and banks lose less capital. The overall effect of regulation on financial stability becomes benign on most measures when accounting for the strategic adaptation of agents.","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122669052","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 dynamic mechanism design problem of a seller who repeatedly sells independent items to a buyer with private values. In this setting, the seller could potentially extract the entire buyer surplus by running efficient auctions and charging an upfront participation fee at the beginning of the horizon. In some markets, such as internet advertising, participation fees are not practical since buyers expect to inspect items before purchasing them. This motivates us to study the design of dynamic mechanisms under successively more stringent requirements that capture the implicit business constraints of these markets. We first consider a periodic individual rationality constraint, which limits the mechanism to charge at most the buyer's value in each period. While this prevents large upfront participation fees, the seller can still design mechanisms that spread a participation fee across the first few auctions. These mechanisms have the unappealing feature that they provide close-to-zero buyer utility in earlier auctions in exchange for higher utility in later auctions. To address this problem, we introduce a {martingale utility constraint, which imposes the requirement that from the perspective of the buyer, the next item's expected utility is equal to the present one's. Our main result is providing a dynamic auction satisfying martingale utility and periodic individual rationality whose loss in profit with respect to first-best (full extraction of buyer surplus) is optimal up to polylogarithmic factors. The proposed mechanism is a dynamic two-tier auction with a hard floor and a soft floor that allocates the item whenever the buyer's bid is above the hard floor and charges the minimum of the bid and the soft floor.
{"title":"Dynamic Mechanisms with Martingale Utilities","authors":"S. Balseiro, V. Mirrokni, R. Leme","doi":"10.2139/ssrn.2821261","DOIUrl":"https://doi.org/10.2139/ssrn.2821261","url":null,"abstract":"We study the dynamic mechanism design problem of a seller who repeatedly sells independent items to a buyer with private values. In this setting, the seller could potentially extract the entire buyer surplus by running efficient auctions and charging an upfront participation fee at the beginning of the horizon. In some markets, such as internet advertising, participation fees are not practical since buyers expect to inspect items before purchasing them. This motivates us to study the design of dynamic mechanisms under successively more stringent requirements that capture the implicit business constraints of these markets. We first consider a periodic individual rationality constraint, which limits the mechanism to charge at most the buyer's value in each period. While this prevents large upfront participation fees, the seller can still design mechanisms that spread a participation fee across the first few auctions. These mechanisms have the unappealing feature that they provide close-to-zero buyer utility in earlier auctions in exchange for higher utility in later auctions. To address this problem, we introduce a {martingale utility constraint, which imposes the requirement that from the perspective of the buyer, the next item's expected utility is equal to the present one's. Our main result is providing a dynamic auction satisfying martingale utility and periodic individual rationality whose loss in profit with respect to first-best (full extraction of buyer surplus) is optimal up to polylogarithmic factors. The proposed mechanism is a dynamic two-tier auction with a hard floor and a soft floor that allocates the item whenever the buyer's bid is above the hard floor and charges the minimum of the bid and the soft floor.","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123133703","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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