We consider a model of Bayesian persuasion with one informed sender and several uninformed receivers. The sender can affect receivers' beliefs via private signals and the sender's objective depends on the combination of induced beliefs. We reduce the persuasion problem to the Monge-Kantorovich problem of optimal transportation. Using insights from optimal transportation theory, we identify several classes of multi-receiver problems that admit explicit solutions, get general structural results, derive a dual representation for the value, and generalize the celebrated concavification formula for the value to multi-receiver problems. The full paper is available at https://fedors.info/papers/2022persuasion/persuasion_as_transport.pdf
{"title":"Persuasion as Transportation","authors":"Itai Arieli, Y. Babichenko, Fedor Sandomirskiy","doi":"10.1145/3490486.3538345","DOIUrl":"https://doi.org/10.1145/3490486.3538345","url":null,"abstract":"We consider a model of Bayesian persuasion with one informed sender and several uninformed receivers. The sender can affect receivers' beliefs via private signals and the sender's objective depends on the combination of induced beliefs. We reduce the persuasion problem to the Monge-Kantorovich problem of optimal transportation. Using insights from optimal transportation theory, we identify several classes of multi-receiver problems that admit explicit solutions, get general structural results, derive a dual representation for the value, and generalize the celebrated concavification formula for the value to multi-receiver problems. The full paper is available at https://fedors.info/papers/2022persuasion/persuasion_as_transport.pdf","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126885228","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}
Correlated equilibrium is an established solution concept in game theory describing a situation when players condition their strategies on external signals produced by a correlation device. In recent years, the concept has begun gaining traction also in general artificial intelligence because of its suitability for studying coordinated multi-agent systems. Yet the original formulation of correlated equilibrium assumes entirely rational players and hence fails to capture the subrational behavior of human decision-makers. We investigate the analogue of quantal response for correlated equilibrium, which is among the most commonly used models of bounded rationality. We coin the solution concept the quantal correlated equilibrium and study its relation to quantal response and correlated equilibria. The definition corroborates with prior conception as every quantal response equilibrium is a quantal correlated equilibrium, and correlated equilibrium is its limit as quantal responses approach the best response. We prove the concept remains PPAD-hard but searching for an optimal correlation device is beneficial for the signaler. To this end, we introduce a homotopic algorithm that simultaneously traces the equilibrium and optimizes the signaling distribution. Empirical results on one structured and one random domain show that our approach is sufficiently precise and several orders of magnitude faster than a state-of-the-art non-convex optimization solver.
{"title":"Quantal Correlated Equilibrium in Normal Form Games","authors":"Jakub Černý, Bo An, A. N. Zhang","doi":"10.1145/3490486.3538350","DOIUrl":"https://doi.org/10.1145/3490486.3538350","url":null,"abstract":"Correlated equilibrium is an established solution concept in game theory describing a situation when players condition their strategies on external signals produced by a correlation device. In recent years, the concept has begun gaining traction also in general artificial intelligence because of its suitability for studying coordinated multi-agent systems. Yet the original formulation of correlated equilibrium assumes entirely rational players and hence fails to capture the subrational behavior of human decision-makers. We investigate the analogue of quantal response for correlated equilibrium, which is among the most commonly used models of bounded rationality. We coin the solution concept the quantal correlated equilibrium and study its relation to quantal response and correlated equilibria. The definition corroborates with prior conception as every quantal response equilibrium is a quantal correlated equilibrium, and correlated equilibrium is its limit as quantal responses approach the best response. We prove the concept remains PPAD-hard but searching for an optimal correlation device is beneficial for the signaler. To this end, we introduce a homotopic algorithm that simultaneously traces the equilibrium and optimizes the signaling distribution. Empirical results on one structured and one random domain show that our approach is sufficiently precise and several orders of magnitude faster than a state-of-the-art non-convex optimization solver.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124739195","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 theory of repeated games offers a compelling rationale for cooperation in a variety of environments. Yet, its consequences for collective decision-making have been largely unexplored. In this paper, we propose a general model of repeated voting and study equilibrium behavior under alternative majority rules. Our main characterization reveals a complex, non-monotonic, relationship between the majority threshold, the preference distribution, and the optimal equilibrium outcome. In contrast with the stage-game equilibrium, the optimal equilibrium of the repeated game involves a form of implicit logroll, individuals sometimes voting against their preference to achieve the efficient decision. In turn, this affects the optimal voting rule, which may significantly differ from the optimal rule under sincere voting. The model provides a rationale for the use of unanimity rule, while accounting for the prevalence of consensus in committees which use a lower majority threshold. The full version of the paper is available at: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4114079
{"title":"A Model of Repeated Collective Decisions","authors":"Antonin Macé, Rafael Treibich","doi":"10.2139/ssrn.4114079","DOIUrl":"https://doi.org/10.2139/ssrn.4114079","url":null,"abstract":"The theory of repeated games offers a compelling rationale for cooperation in a variety of environments. Yet, its consequences for collective decision-making have been largely unexplored. In this paper, we propose a general model of repeated voting and study equilibrium behavior under alternative majority rules. Our main characterization reveals a complex, non-monotonic, relationship between the majority threshold, the preference distribution, and the optimal equilibrium outcome. In contrast with the stage-game equilibrium, the optimal equilibrium of the repeated game involves a form of implicit logroll, individuals sometimes voting against their preference to achieve the efficient decision. In turn, this affects the optimal voting rule, which may significantly differ from the optimal rule under sincere voting. The model provides a rationale for the use of unanimity rule, while accounting for the prevalence of consensus in committees which use a lower majority threshold. The full version of the paper is available at: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4114079","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128587129","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 two linear pricing mechanisms for quasilinear economies in which market-clearing prices may not exist. Electricity markets, fisheries markets, and many others include producers with start-up costs, ramping costs, or other fixed costs that fail the convexity assumptions traditionally used to prove that clearing prices exist. Each mechanism relaxes a condition of Walrasian equilibrium. While the Walrasian mechanism determines payments among buyers and sellers using a single price vector, our markup mechanism allows one more parameter -- a multiplier -- that marks up the prices paid by buyers above those paid to sellers. These markups allow the mechanism to avoid budget deficits even when non-convexities lead to failures of market-clearing. And while the Walrasian mechanism assigns each producer its preferred production plan, our rationing mechanism carefully rations some buyers. Both mechanisms always produce feasible allocations, avoid budget deficits, and are computationally tractable. The proportion of efficient surplus lost in the markup mechanism is O(1/N), where N is the number of buyers and sellers. When agents on the buyer side have convex preferences and strongly monotone demand, the rationing mechanism suffers a smaller welfare loss, namely O(1/N2-ε) for all ε>0. Importantly, both mechanisms have good large-market incentive properties similar to those of the Walrasian mechanism. Key to our construction of these mechanisms and of some independent interest is our new Bound-Form First Welfare Theorem for quasilinear economies, which gives an upper bound on the deadweight loss of any feasible allocation ω in terms of any positive price vector p. It asserts that the welfare loss is bounded above by B+R, where B is the budget deficit from ω at prices p, which is non-zero when supply strictly exceeds demand, and R is the sum of the rationing losses suffered by each individual agent n when its allocated bundle ωn is different from its preferred bundle at price vector p. The Bound Form First Welfare Theorem takes its name from its implication that the welfare loss is zero when (p,ω) is a competitive equilibrium. The full paper is available at https://mitchwatt.github.io/files/PricingMechanismsNonConvex.pdf.
{"title":"Linear Pricing Mechanisms for Markets without Convexity","authors":"Paul R. Milgrom, Mitchell Watt","doi":"10.1145/3490486.3538310","DOIUrl":"https://doi.org/10.1145/3490486.3538310","url":null,"abstract":"We introduce two linear pricing mechanisms for quasilinear economies in which market-clearing prices may not exist. Electricity markets, fisheries markets, and many others include producers with start-up costs, ramping costs, or other fixed costs that fail the convexity assumptions traditionally used to prove that clearing prices exist. Each mechanism relaxes a condition of Walrasian equilibrium. While the Walrasian mechanism determines payments among buyers and sellers using a single price vector, our markup mechanism allows one more parameter -- a multiplier -- that marks up the prices paid by buyers above those paid to sellers. These markups allow the mechanism to avoid budget deficits even when non-convexities lead to failures of market-clearing. And while the Walrasian mechanism assigns each producer its preferred production plan, our rationing mechanism carefully rations some buyers. Both mechanisms always produce feasible allocations, avoid budget deficits, and are computationally tractable. The proportion of efficient surplus lost in the markup mechanism is O(1/N), where N is the number of buyers and sellers. When agents on the buyer side have convex preferences and strongly monotone demand, the rationing mechanism suffers a smaller welfare loss, namely O(1/N2-ε) for all ε>0. Importantly, both mechanisms have good large-market incentive properties similar to those of the Walrasian mechanism. Key to our construction of these mechanisms and of some independent interest is our new Bound-Form First Welfare Theorem for quasilinear economies, which gives an upper bound on the deadweight loss of any feasible allocation ω in terms of any positive price vector p. It asserts that the welfare loss is bounded above by B+R, where B is the budget deficit from ω at prices p, which is non-zero when supply strictly exceeds demand, and R is the sum of the rationing losses suffered by each individual agent n when its allocated bundle ωn is different from its preferred bundle at price vector p. The Bound Form First Welfare Theorem takes its name from its implication that the welfare loss is zero when (p,ω) is a competitive equilibrium. The full paper is available at https://mitchwatt.github.io/files/PricingMechanismsNonConvex.pdf.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116681698","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}
Nika Haghtalab, Thodoris Lykouris, Sloan Nietert, Alexander Wei
Stackelberg games are a canonical model for strategic principal-agent interactions. Consider, for instance, a defense system that distributes its security resources across high-risk targets prior to attacks being executed; or a tax policymaker who sets rules on when audits are triggered prior to seeing filed tax reports; or a seller who chooses a price prior to knowing a customer's proclivity to buy. In each of these scenarios, a principal first selects an action x∈X and then an agent reacts with an action y∈Y, where X and Y are the principal's and agent's action spaces, respectively. In the examples above, agent actions correspond to which target to attack, how much tax to pay to evade an audit, and how much to purchase, respectively. Typically, the principal wants an x that maximizes their payoff when the agent plays a best response y = br(x); such a pair (x, y) is a Stackelberg equilibrium. By committing to a strategy, the principal can guarantee they achieve a higher payoff than in the fixed point equilibrium of the corresponding simultaneous-play game. However, finding such a strategy requires knowledge of the agent's payoff function. When faced with unknown agent payoffs, the principal can attempt to learn a best response via repeated interactions with the agent. If a (naïve) agent is unaware that such learning occurs and always plays a best response, the principal can use classical online learning approaches to optimize their own payoff in the stage game. Learning from myopic agents has been extensively studied in multiple Stackelberg games, including security games[2,6,7], demand learning[1,5], and strategic classification[3,4]. However, long-lived agents will generally not volunteer information that can be used against them in the future. This is especially the case in online environments where a learner seeks to exploit recently learned patterns of behavior as soon as possible, and the agent can see a tangible advantage for deviating from its instantaneous best response and leading the learner astray. This trade-off between the (statistical) efficiency of learning algorithms and the perverse incentives they may create over the long-term brings us to the main questions of this work: What are principled approaches to learning against non-myopic agents in general Stackelberg games? How can insights from learning against myopic agents be applied to learning in the non-myopic case?
{"title":"Learning in Stackelberg Games with Non-myopic Agents","authors":"Nika Haghtalab, Thodoris Lykouris, Sloan Nietert, Alexander Wei","doi":"10.1145/3490486.3538308","DOIUrl":"https://doi.org/10.1145/3490486.3538308","url":null,"abstract":"Stackelberg games are a canonical model for strategic principal-agent interactions. Consider, for instance, a defense system that distributes its security resources across high-risk targets prior to attacks being executed; or a tax policymaker who sets rules on when audits are triggered prior to seeing filed tax reports; or a seller who chooses a price prior to knowing a customer's proclivity to buy. In each of these scenarios, a principal first selects an action x∈X and then an agent reacts with an action y∈Y, where X and Y are the principal's and agent's action spaces, respectively. In the examples above, agent actions correspond to which target to attack, how much tax to pay to evade an audit, and how much to purchase, respectively. Typically, the principal wants an x that maximizes their payoff when the agent plays a best response y = br(x); such a pair (x, y) is a Stackelberg equilibrium. By committing to a strategy, the principal can guarantee they achieve a higher payoff than in the fixed point equilibrium of the corresponding simultaneous-play game. However, finding such a strategy requires knowledge of the agent's payoff function. When faced with unknown agent payoffs, the principal can attempt to learn a best response via repeated interactions with the agent. If a (naïve) agent is unaware that such learning occurs and always plays a best response, the principal can use classical online learning approaches to optimize their own payoff in the stage game. Learning from myopic agents has been extensively studied in multiple Stackelberg games, including security games[2,6,7], demand learning[1,5], and strategic classification[3,4]. However, long-lived agents will generally not volunteer information that can be used against them in the future. This is especially the case in online environments where a learner seeks to exploit recently learned patterns of behavior as soon as possible, and the agent can see a tangible advantage for deviating from its instantaneous best response and leading the learner astray. This trade-off between the (statistical) efficiency of learning algorithms and the perverse incentives they may create over the long-term brings us to the main questions of this work: What are principled approaches to learning against non-myopic agents in general Stackelberg games? How can insights from learning against myopic agents be applied to learning in the non-myopic case?","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130518702","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}
Quantal Response Equilibrium (QRE) generalizes Nash equilibrium (NE) by allowing players to make probabilistic mistakes in best responding to others' behavior while maintaining fixed-point consistency. QRE has had considerable success in explaining empirically observed deviations from NE ([3]) and so has become a standard benchmark for analyzing experimental data. QRE is nothing more than equilibrium with noisy players, and the only modelling consideration is how to model this noise: one must select the admissable family of noise structures. The literature has proposed a number of such families, ranging from the very precise to the very flexible. At one extreme, noise is governed by a specific parametric family, whereas on the other, there are so many degrees of freedom that the model is difficult to reject.
{"title":"Quantal Response Equilibrium with Symmetry: Representation and Applications","authors":"Evan Friedman, Felix Mauersberger","doi":"10.1145/3490486.3538351","DOIUrl":"https://doi.org/10.1145/3490486.3538351","url":null,"abstract":"Quantal Response Equilibrium (QRE) generalizes Nash equilibrium (NE) by allowing players to make probabilistic mistakes in best responding to others' behavior while maintaining fixed-point consistency. QRE has had considerable success in explaining empirically observed deviations from NE ([3]) and so has become a standard benchmark for analyzing experimental data. QRE is nothing more than equilibrium with noisy players, and the only modelling consideration is how to model this noise: one must select the admissable family of noise structures. The literature has proposed a number of such families, ranging from the very precise to the very flexible. At one extreme, noise is governed by a specific parametric family, whereas on the other, there are so many degrees of freedom that the model is difficult to reject.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132553169","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}
Simon Jantschgi, H. H. Nax, Bary S. R. Pradelski, M. Pycia
Transaction costs are omnipresent in markets but are often omitted in economic models. We show that the presence of transaction costs can fundamentally alter incentive and welfare properties of Double Auctions, a canonical market organization. We further show that transaction costs can be categorized into two types. Double Auctions with homogeneous transaction costs---a category that includes fixed fees and price based fees---preserve the key advantages of Double Auctions without transaction costs: markets with homogeneous transaction costs are asymptotically strategyproof, and there is no efficiency-loss due to strategic behavior. In contrast, double auctions with heterogeneous transaction costs---such as spread fees---lead to complex strategic behavior (price guessing) and may result in severe market failures. Allowing for aggregate uncertainty, we extend these insights to market organizations other than Double Auctions.
{"title":"Double Auctions and Transaction Costs","authors":"Simon Jantschgi, H. H. Nax, Bary S. R. Pradelski, M. Pycia","doi":"10.1145/3490486.3538276","DOIUrl":"https://doi.org/10.1145/3490486.3538276","url":null,"abstract":"Transaction costs are omnipresent in markets but are often omitted in economic models. We show that the presence of transaction costs can fundamentally alter incentive and welfare properties of Double Auctions, a canonical market organization. We further show that transaction costs can be categorized into two types. Double Auctions with homogeneous transaction costs---a category that includes fixed fees and price based fees---preserve the key advantages of Double Auctions without transaction costs: markets with homogeneous transaction costs are asymptotically strategyproof, and there is no efficiency-loss due to strategic behavior. In contrast, double auctions with heterogeneous transaction costs---such as spread fees---lead to complex strategic behavior (price guessing) and may result in severe market failures. Allowing for aggregate uncertainty, we extend these insights to market organizations other than Double Auctions.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121675970","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}
Online platforms increasingly act as gatekeepers that enable producers to access downstream markets, while also competing with producers in these downstream markets. A prominent example is Amazon, which sells e-commerce and distribution services to producers in an upstream market, while also selling AmazonBasics and other private-label products downstream. Should platforms be allowed to control whom they compete with in downstream markets through their upstream market interactions? In this paper, we study the antitrust implications of a platform acting both as a producer in a downstream market and an upstream supplier to rival producers. We find that banning a monopolist platform from producing in downstream markets can only harm consumers because platforms that produce positive output in equilibrium always reduce downstream prices. Consequently, the claimed "conflict of interest," or tradeoff between the platform's upstream and downstream profits, always benefits the consumer, at the expense of producers. Intuitively, any output produced by the competitive fringe of producers is associated with a vertical externality that resembles double marginalization, while any output produced by the platform is only associated with a single marginalization effect. If the platform's own production costs are reduced, the corresponding substitution towards output produced by the platform results in higher overall production in the downstream market, which benefits consumers. However, when the platform is not a monopolist, meaning that producers can access downstream markets through alternative distribution channels, platforms may have an incentive to undermine this upstream market competition. For example, the platform may profitably engage in "killer" horizontal acquisitions (acquire and then shuttering smaller upstream competitors) or exclusive dealing (offer contracts that preclude producers from accessing alternative distribution channels). These practices harm consumers by reducing overall output in the downstream market and would therefore warrant the scrutiny of antitrust authorities. Our analysis introduces a general mechanism design framework for studying vertical market structures involving a dominant platform. In particular, we consider a model in which a platform sells a productive input to producers in an upstream market before competing with these producers in a downstream market. We characterize the optimal menu of contracts offered by the platform in the upstream market, assuming the platform seeks to maximize its total upstream and downstream profits. In our formulation, producers have private information about their costs, which gives rise to incentive and participation constraints. We first consider the case in which the platform monopolizes the upstream market and then add the possibility that producers have access to alternative distribution channels. In each case the optimal menu of upstream contracts involves a nonlinear pricing schedule
{"title":"Contracting and Vertical Control by a Dominant Platform","authors":"Zi Yang Kang, Ellen V. Muir","doi":"10.1145/3490486.3538260","DOIUrl":"https://doi.org/10.1145/3490486.3538260","url":null,"abstract":"Online platforms increasingly act as gatekeepers that enable producers to access downstream markets, while also competing with producers in these downstream markets. A prominent example is Amazon, which sells e-commerce and distribution services to producers in an upstream market, while also selling AmazonBasics and other private-label products downstream. Should platforms be allowed to control whom they compete with in downstream markets through their upstream market interactions? In this paper, we study the antitrust implications of a platform acting both as a producer in a downstream market and an upstream supplier to rival producers. We find that banning a monopolist platform from producing in downstream markets can only harm consumers because platforms that produce positive output in equilibrium always reduce downstream prices. Consequently, the claimed \"conflict of interest,\" or tradeoff between the platform's upstream and downstream profits, always benefits the consumer, at the expense of producers. Intuitively, any output produced by the competitive fringe of producers is associated with a vertical externality that resembles double marginalization, while any output produced by the platform is only associated with a single marginalization effect. If the platform's own production costs are reduced, the corresponding substitution towards output produced by the platform results in higher overall production in the downstream market, which benefits consumers. However, when the platform is not a monopolist, meaning that producers can access downstream markets through alternative distribution channels, platforms may have an incentive to undermine this upstream market competition. For example, the platform may profitably engage in \"killer\" horizontal acquisitions (acquire and then shuttering smaller upstream competitors) or exclusive dealing (offer contracts that preclude producers from accessing alternative distribution channels). These practices harm consumers by reducing overall output in the downstream market and would therefore warrant the scrutiny of antitrust authorities. Our analysis introduces a general mechanism design framework for studying vertical market structures involving a dominant platform. In particular, we consider a model in which a platform sells a productive input to producers in an upstream market before competing with these producers in a downstream market. We characterize the optimal menu of contracts offered by the platform in the upstream market, assuming the platform seeks to maximize its total upstream and downstream profits. In our formulation, producers have private information about their costs, which gives rise to incentive and participation constraints. We first consider the case in which the platform monopolizes the upstream market and then add the possibility that producers have access to alternative distribution channels. In each case the optimal menu of upstream contracts involves a nonlinear pricing schedule","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129318515","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 role of information structures in mechanism design problems with limited commitment. In each period, a principal offers a ''spot'' contract to a privately informed agent without committing to future spot contracts, and the agent responds to the contract. In contrast to the classical approach in which the information structure is fixed, we allow for all admissible information structures. We represent the information structure as a fictitious mediator and re-interpret the model as a mechanism design problem by the mediator with commitment. The mediator collects the agent's private information and then, in each period, privately recommends the principal's spot contract and the agent's response in an incentive-compatible manner (both in truth-telling and obedience). We construct several examples to clarify why new equilibrium outcomes can arise once we allow for general information structures. We next develop a durable-good monopoly application. We show that trading outcomes and welfare consequences can substantially differ from those in the classical model with a fixed information structure. In the seller-optimal mechanism, the seller offers a discounted price to the high-valuation buyer only in the initial period, followed by the high, surplus-extracting price until some endogenous deadline, when the buyer's information is revealed and hence fully extracted. As a result, the Coase conjecture fails: even in the limiting case of perfect patience, the seller makes a positive surplus, and the trading outcome is not the first best. We also characterize mediated and unmediated implementation of the seller-optimal outcome. Full paper available at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4116543.
{"title":"A Mediator Approach to Mechanism Design with Limited Commitment","authors":"Niccolò Lomys, Takuro Yamashita","doi":"10.1145/3490486.3538232","DOIUrl":"https://doi.org/10.1145/3490486.3538232","url":null,"abstract":"We study the role of information structures in mechanism design problems with limited commitment. In each period, a principal offers a ''spot'' contract to a privately informed agent without committing to future spot contracts, and the agent responds to the contract. In contrast to the classical approach in which the information structure is fixed, we allow for all admissible information structures. We represent the information structure as a fictitious mediator and re-interpret the model as a mechanism design problem by the mediator with commitment. The mediator collects the agent's private information and then, in each period, privately recommends the principal's spot contract and the agent's response in an incentive-compatible manner (both in truth-telling and obedience). We construct several examples to clarify why new equilibrium outcomes can arise once we allow for general information structures. We next develop a durable-good monopoly application. We show that trading outcomes and welfare consequences can substantially differ from those in the classical model with a fixed information structure. In the seller-optimal mechanism, the seller offers a discounted price to the high-valuation buyer only in the initial period, followed by the high, surplus-extracting price until some endogenous deadline, when the buyer's information is revealed and hence fully extracted. As a result, the Coase conjecture fails: even in the limiting case of perfect patience, the seller makes a positive surplus, and the trading outcome is not the first best. We also characterize mediated and unmediated implementation of the seller-optimal outcome. Full paper available at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4116543.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127571529","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}
S. Balseiro, Yuan Deng, Jieming Mao, V. Mirrokni, Song Zuo
We study the design of revenue-maximizing mechanisms for value-maximizing agents with budget constraints. Agents have return-on-spend constraints requiring a minimum amount of value per unit of payment made and budget constraints limiting their total payments. The agents' only private information are the minimum admissible ratios on the return-on-spend constraint, referred to as the target ratios. Our work is motivated by internet advertising platforms, where advertisers are increasingly adopting automated bidders to purchase advertising opportunities on their behalf. Instead of specifying bids for each keyword, advertisers set high-level goals, such as maximizing clicks, and targets on cost-per-clicks or return-on-spend. The platform then automatically purchases opportunities by bidding in different auctions. We present a model that abstracts away the complexities of the auto-bidding procurement process that is general enough to accommodate many allocation mechanisms such as auctions, matchings, etc. We reduce the mechanism design problem when agents have private target ratios to a challenging non-linear optimization problem with monotonicity constraints. We provide a novel decomposition approach to tackle this problem that yields insights into the structure of optimal mechanisms and show that surprising features stem from the interaction between budget and return-on-spend constraints. Our optimal mechanism, which we dub the target-clipping mechanism, has an appealing structure: it sets a threshold on the target ratio of each agent, targets above the threshold are allocated efficiently, and targets below are clipped to the threshold.
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