Stefanos Leonardos, Joseph Sakos, C. Courcoubetis, G. Piliouras
In multi-agent environments in which coordination is desirable, the history of play often causes lock-in at sub-optimal outcomes. Notoriously, technologies with significant environmental footprint or high social cost persist despite the successful development of more environmentally friendly and/or socially efficient alternatives. The displacement of the status quo is hindered by entrenched economic interests and network effects. To exacerbate matters, the standard mechanism design approaches based on centralized authorities with the capacity to use preferential subsidies to effectively dictate system outcomes are not always applicable to modern decentralized economies. What other types of mechanisms are feasible? In this article, we develop and analyze a mechanism that induces transitions from inefficient lock-ins to superior alternatives. This mechanism does not exogenously favor one option over another; instead, the phase transition emerges endogenously via a standard evolutionary learning model, Q-learning, where agents trade off exploration and exploitation. Exerting the same transient influence to both the efficient and inefficient technologies encourages exploration and results in irreversible phase transitions and permanent stabilization of the efficient one. On a technical level, our work is based on bifurcation and catastrophe theory, a branch of mathematics that deals with changes in the number and stability properties of equilibria. Critically, our analysis is shown to be structurally robust to significant and even adversarially chosen perturbations to the parameters of both our game and our behavioral model.
{"title":"Catastrophe by Design in Population Games: A Mechanism to Destabilize Inefficient Locked-in Technologies","authors":"Stefanos Leonardos, Joseph Sakos, C. Courcoubetis, G. Piliouras","doi":"10.1145/3583782","DOIUrl":"https://doi.org/10.1145/3583782","url":null,"abstract":"In multi-agent environments in which coordination is desirable, the history of play often causes lock-in at sub-optimal outcomes. Notoriously, technologies with significant environmental footprint or high social cost persist despite the successful development of more environmentally friendly and/or socially efficient alternatives. The displacement of the status quo is hindered by entrenched economic interests and network effects. To exacerbate matters, the standard mechanism design approaches based on centralized authorities with the capacity to use preferential subsidies to effectively dictate system outcomes are not always applicable to modern decentralized economies. What other types of mechanisms are feasible? In this article, we develop and analyze a mechanism that induces transitions from inefficient lock-ins to superior alternatives. This mechanism does not exogenously favor one option over another; instead, the phase transition emerges endogenously via a standard evolutionary learning model, Q-learning, where agents trade off exploration and exploitation. Exerting the same transient influence to both the efficient and inefficient technologies encourages exploration and results in irreversible phase transitions and permanent stabilization of the efficient one. On a technical level, our work is based on bifurcation and catastrophe theory, a branch of mathematics that deals with changes in the number and stability properties of equilibria. Critically, our analysis is shown to be structurally robust to significant and even adversarially chosen perturbations to the parameters of both our game and our behavioral model.","PeriodicalId":42216,"journal":{"name":"ACM Transactions on Economics and Computation","volume":"11 1","pages":"1 - 36"},"PeriodicalIF":1.2,"publicationDate":"2023-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64065901","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 article defines a general class of cooperative games for which the nucleolus is efficiently computable. This class includes new members for which the complexity of computing their nucleolus was not previously known. We show that when the minimum excess coalition problem of a cooperative game can be formulated as a hypergraph dynamic program, its nucleolus is efficiently computable. This gives a general technique for designing efficient algorithms for computing the nucleolus of a cooperative game. This technique is inspired by a recent result of Pashkovich [27] on weighted voting games. However, our technique significantly extends beyond the capabilities of previous work. We demonstrate this by applying it to give an algorithm for computing the nucleolus of b-matching games in polynomial time on graphs of bounded treewidth.
{"title":"A Framework for Computing the Nucleolus via Dynamic Programming","authors":"Jochen Koenemann, J. Toth","doi":"10.1145/3580375","DOIUrl":"https://doi.org/10.1145/3580375","url":null,"abstract":"This article defines a general class of cooperative games for which the nucleolus is efficiently computable. This class includes new members for which the complexity of computing their nucleolus was not previously known. We show that when the minimum excess coalition problem of a cooperative game can be formulated as a hypergraph dynamic program, its nucleolus is efficiently computable. This gives a general technique for designing efficient algorithms for computing the nucleolus of a cooperative game. This technique is inspired by a recent result of Pashkovich [27] on weighted voting games. However, our technique significantly extends beyond the capabilities of previous work. We demonstrate this by applying it to give an algorithm for computing the nucleolus of b-matching games in polynomial time on graphs of bounded treewidth.","PeriodicalId":42216,"journal":{"name":"ACM Transactions on Economics and Computation","volume":"11 1","pages":"1 - 21"},"PeriodicalIF":1.2,"publicationDate":"2023-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45686969","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 the stable marriage (SM) problem, there are two sets of agents—traditionally referred to as men and women—and each agent has a preference list that ranks (a subset of) agents of the opposite sex. The goal is to find a matching between men and women that is stable in the sense that no man-woman pair mutually prefers each other to their assigned partners. In a seminal work, Gale and Shapley [16] showed that stable matchings always exist and described an efficient algorithm for finding one. Irving and Leather [24] defined the rotation poset of an SM instance and showed that it determines the structure of the set of stable matchings of the instance. They further showed that every finite poset can be realized as the rotation poset of some SM instance. Consequently, many problems—such as counting stable matchings and finding certain “fair” stable matchings—are computationally intractable (NP-hard) in general. In this article, we consider SM instances in which certain restrictions are placed on the preference lists. We show that three natural preference models—k-bounded, k-attribute, and (k1, k2)-list—can realize arbitrary rotation posets for constant values of k. Hence, even in these highly restricted preference models, many stable matching problems remain intractable. In contrast, we show that for any fixed constant k, the rotation posets of k-range instances are highly restricted. As a consequence, we show that exactly counting and uniformly sampling stable matchings, finding median, sex-equal, and balanced stable matchings, are fixed-parameter tractable when parameterized by the range of the instance. Thus, these problems can be solved in polynomial time on instances of the k-range model for any fixed constant k.
{"title":"Stable Matchings with Restricted Preferences: Structure and Complexity","authors":"Christine T. Cheng, Will Rosenbaum","doi":"10.1145/3565558","DOIUrl":"https://doi.org/10.1145/3565558","url":null,"abstract":"In the stable marriage (SM) problem, there are two sets of agents—traditionally referred to as men and women—and each agent has a preference list that ranks (a subset of) agents of the opposite sex. The goal is to find a matching between men and women that is stable in the sense that no man-woman pair mutually prefers each other to their assigned partners. In a seminal work, Gale and Shapley [16] showed that stable matchings always exist and described an efficient algorithm for finding one. Irving and Leather [24] defined the rotation poset of an SM instance and showed that it determines the structure of the set of stable matchings of the instance. They further showed that every finite poset can be realized as the rotation poset of some SM instance. Consequently, many problems—such as counting stable matchings and finding certain “fair” stable matchings—are computationally intractable (NP-hard) in general. In this article, we consider SM instances in which certain restrictions are placed on the preference lists. We show that three natural preference models—k-bounded, k-attribute, and (k1, k2)-list—can realize arbitrary rotation posets for constant values of k. Hence, even in these highly restricted preference models, many stable matching problems remain intractable. In contrast, we show that for any fixed constant k, the rotation posets of k-range instances are highly restricted. As a consequence, we show that exactly counting and uniformly sampling stable matchings, finding median, sex-equal, and balanced stable matchings, are fixed-parameter tractable when parameterized by the range of the instance. Thus, these problems can be solved in polynomial time on instances of the k-range model for any fixed constant k.","PeriodicalId":42216,"journal":{"name":"ACM Transactions on Economics and Computation","volume":"10 1","pages":"1 - 45"},"PeriodicalIF":1.2,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44199237","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}
Peer prediction mechanisms incentivize self-interested agents to truthfully report their signals even in the absence of verification by comparing agents’ reports with their peers. We propose two new mechanisms, Source and Target Differential Peer Prediction, and prove very strong guarantees for a very general setting. Our Differential Peer Prediction mechanisms are strongly truthful: Truth-telling is a strict Bayesian Nash equilibrium. Also, truth-telling pays strictly higher than any other equilibria, excluding permutation equilibria, which pays the same amount as truth-telling. The guarantees hold for asymmetric priors among agents, which the mechanisms need not know (detail-free) in the single question setting. Moreover, they only require three agents, each of which submits a single item report: two report their signals (answers), and the other reports her forecast (prediction of one of the other agent’s reports). Our proof technique is straightforward, conceptually motivated, and turns on the logarithmic scoring rule’s special properties. Moreover, we can recast the Bayesian Truth Serum mechanism [20] into our framework. We can also extend our results to the setting of continuous signals with a slightly weaker guarantee on the optimality of the truthful equilibrium.
{"title":"Two Strongly Truthful Mechanisms for Three Heterogeneous Agents Answering One Question","authors":"G. Schoenebeck, Fang-Yi Yu","doi":"10.1145/3565560","DOIUrl":"https://doi.org/10.1145/3565560","url":null,"abstract":"Peer prediction mechanisms incentivize self-interested agents to truthfully report their signals even in the absence of verification by comparing agents’ reports with their peers. We propose two new mechanisms, Source and Target Differential Peer Prediction, and prove very strong guarantees for a very general setting. Our Differential Peer Prediction mechanisms are strongly truthful: Truth-telling is a strict Bayesian Nash equilibrium. Also, truth-telling pays strictly higher than any other equilibria, excluding permutation equilibria, which pays the same amount as truth-telling. The guarantees hold for asymmetric priors among agents, which the mechanisms need not know (detail-free) in the single question setting. Moreover, they only require three agents, each of which submits a single item report: two report their signals (answers), and the other reports her forecast (prediction of one of the other agent’s reports). Our proof technique is straightforward, conceptually motivated, and turns on the logarithmic scoring rule’s special properties. Moreover, we can recast the Bayesian Truth Serum mechanism [20] into our framework. We can also extend our results to the setting of continuous signals with a slightly weaker guarantee on the optimality of the truthful equilibrium.","PeriodicalId":42216,"journal":{"name":"ACM Transactions on Economics and Computation","volume":"10 1","pages":"1 - 26"},"PeriodicalIF":1.2,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43141336","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}
Strictly proper scoring rules (SPSR) are incentive compatible for eliciting information about random variables from strategic agents when the principal can reward agents after the realization of the random variables. They also quantify the quality of elicited information, with more accurate predictions receiving higher scores in expectation. In this article, we extend such scoring rules to settings in which a principal elicits private probabilistic beliefs but only has access to agents’ reports. We name our solution Surrogate Scoring Rules (SSR). SSR is built on a bias correction step and an error rate estimation procedure for a reference answer defined using agents’ reports. We show that, with a little information about the prior distribution of the random variables, SSR in a multi-task setting recover SPSR in expectation, as if having access to the ground truth. Therefore, a salient feature of SSR is that they quantify the quality of information despite the lack of ground truth, just as SPSR do for the setting with ground truth. As a by-product, SSR induce dominant uniform strategy truthfulness in reporting. Our method is verified both theoretically and empirically using data collected from real human forecasters.
{"title":"Surrogate Scoring Rules","authors":"Yang Liu, Juntao Wang, Yiling Chen","doi":"10.1145/3565559","DOIUrl":"https://doi.org/10.1145/3565559","url":null,"abstract":"Strictly proper scoring rules (SPSR) are incentive compatible for eliciting information about random variables from strategic agents when the principal can reward agents after the realization of the random variables. They also quantify the quality of elicited information, with more accurate predictions receiving higher scores in expectation. In this article, we extend such scoring rules to settings in which a principal elicits private probabilistic beliefs but only has access to agents’ reports. We name our solution Surrogate Scoring Rules (SSR). SSR is built on a bias correction step and an error rate estimation procedure for a reference answer defined using agents’ reports. We show that, with a little information about the prior distribution of the random variables, SSR in a multi-task setting recover SPSR in expectation, as if having access to the ground truth. Therefore, a salient feature of SSR is that they quantify the quality of information despite the lack of ground truth, just as SPSR do for the setting with ground truth. As a by-product, SSR induce dominant uniform strategy truthfulness in reporting. Our method is verified both theoretically and empirically using data collected from real human forecasters.","PeriodicalId":42216,"journal":{"name":"ACM Transactions on Economics and Computation","volume":"10 1","pages":"1 - 36"},"PeriodicalIF":1.2,"publicationDate":"2022-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43629020","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 special issue of ACM Transactions on Economics and Computation (TEAC) contains extended versions of selected articles from the 16th Conference on Web and Internet Economics (WINE’20), which was held as an Internet event organized by Peking University from December 7 to 11, 2020. Since 2005, the WINE conference series (named as Workshop on Internet and Network Economics until 2013) represents a platform to exchange ideas and results on problems involving incentives and computations that originate in diverse fields such as theoretical computer science, operations research, applied mathematics, artificial intelligence, and economics. These problems are of particular importance in application areas like the Web and the Internet that involve large and diverse populations. As the guest editors of this special issue of TEAC, from 42 articles presented at WINE’20, we selected five articles that had extremely positive conference reviews. We invited the authors to submit their extended work to TEAC. Each submission went through a rigorous review process according to TEAC’s high standards. The first part of the special issue comprises the following four excellent articles:
{"title":"Introduction to the Special Issue on WINE’20: Part 1","authors":"M. Hoefer, Xujin Chen, Nikolai Gravin, R. Mehta","doi":"10.1145/3555339","DOIUrl":"https://doi.org/10.1145/3555339","url":null,"abstract":"This special issue of ACM Transactions on Economics and Computation (TEAC) contains extended versions of selected articles from the 16th Conference on Web and Internet Economics (WINE’20), which was held as an Internet event organized by Peking University from December 7 to 11, 2020. Since 2005, the WINE conference series (named as Workshop on Internet and Network Economics until 2013) represents a platform to exchange ideas and results on problems involving incentives and computations that originate in diverse fields such as theoretical computer science, operations research, applied mathematics, artificial intelligence, and economics. These problems are of particular importance in application areas like the Web and the Internet that involve large and diverse populations. As the guest editors of this special issue of TEAC, from 42 articles presented at WINE’20, we selected five articles that had extremely positive conference reviews. We invited the authors to submit their extended work to TEAC. Each submission went through a rigorous review process according to TEAC’s high standards. The first part of the special issue comprises the following four excellent articles:","PeriodicalId":42216,"journal":{"name":"ACM Transactions on Economics and Computation","volume":"10 1","pages":"1 - 1"},"PeriodicalIF":1.2,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47610668","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}
Routing games are amongst the most well studied domains of game theory. How relevant are these pen-and-paper calculations to understanding the reality of everyday traffic routing? We focus on a semantically rich dataset that captures detailed information about the daily behavior of thousands of Singaporean commuters and examine the following basic questions: - Does the traffic stabilize? - Is the system behavior consistent with latency-minimizing agents? - Is the resulting system efficient? In order to capture the efficiency of the traffic network in a way that agrees with our everyday intuition we introduce a new metric, the Free-flow Index (FFI), which reflects the inefficiency resulting from system congestion. Along the way, we provide the first model-free computation of an upper bound to the price of anarchy utilizing only real world measurements of traffic data.
{"title":"Routing Games in the Wild: Efficiency, Equilibration, Regret, and a Price of Anarchy Bound via Long Division","authors":"B. Monnot, F. Benita, G. Piliouras","doi":"10.1145/3512747","DOIUrl":"https://doi.org/10.1145/3512747","url":null,"abstract":"Routing games are amongst the most well studied domains of game theory. How relevant are these pen-and-paper calculations to understanding the reality of everyday traffic routing? We focus on a semantically rich dataset that captures detailed information about the daily behavior of thousands of Singaporean commuters and examine the following basic questions: - Does the traffic stabilize? - Is the system behavior consistent with latency-minimizing agents? - Is the resulting system efficient? In order to capture the efficiency of the traffic network in a way that agrees with our everyday intuition we introduce a new metric, the Free-flow Index (FFI), which reflects the inefficiency resulting from system congestion. Along the way, we provide the first model-free computation of an upper bound to the price of anarchy utilizing only real world measurements of traffic data.","PeriodicalId":42216,"journal":{"name":"ACM Transactions on Economics and Computation","volume":" ","pages":"1 - 26"},"PeriodicalIF":1.2,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47004206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A classic result in computational game theory states that there are infinitely repeated games where one player has a computable strategy that has a best response, but no computable best response. For games with discounted payoff, the result is known to hold for a specific class of games—essentially generalizations of Prisoner’s Dilemma—but until now, no necessary and sufficient condition is known. To be of any value, the computable strategy having no computable best response must be part of a subgame-perfect equilibrium, as otherwise a rational, self-interested player would not play the strategy. We give the first necessary and sufficient conditions for a two-player repeated game ( G ) to have such a computable strategy with no computable best response for all discount factors above some threshold. The conditions involve existence of a Nash equilibrium of the repeated game whose discounted payoffs satisfy certain conditions involving the min–max payoffs of the underlying stage game. We show that it is decidable in polynomial time in the size of the payoff matrix of ( G ) whether it satisfies these conditions.
{"title":"Discounted Repeated Games Having Computable Strategies with No Computable Best Response under Subgame-Perfect Equilibria","authors":"Jakub Dargaj, J. Simonsen","doi":"10.1145/3505585","DOIUrl":"https://doi.org/10.1145/3505585","url":null,"abstract":"A classic result in computational game theory states that there are infinitely repeated games where one player has a computable strategy that has a best response, but no computable best response. For games with discounted payoff, the result is known to hold for a specific class of games—essentially generalizations of Prisoner’s Dilemma—but until now, no necessary and sufficient condition is known. To be of any value, the computable strategy having no computable best response must be part of a subgame-perfect equilibrium, as otherwise a rational, self-interested player would not play the strategy. We give the first necessary and sufficient conditions for a two-player repeated game ( G ) to have such a computable strategy with no computable best response for all discount factors above some threshold. The conditions involve existence of a Nash equilibrium of the repeated game whose discounted payoffs satisfy certain conditions involving the min–max payoffs of the underlying stage game. We show that it is decidable in polynomial time in the size of the payoff matrix of ( G ) whether it satisfies these conditions.","PeriodicalId":42216,"journal":{"name":"ACM Transactions on Economics and Computation","volume":"10 1","pages":"1 - 39"},"PeriodicalIF":1.2,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48251364","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 problem of designing cost-sharing mechanisms for combinatorial domains. Suppose that multiple items or services are available to be shared among a set of interested agents. The outcome of a mechanism in this setting consists of an assignment, determining for each item the set of players who are granted service, together with respective payments. Although there are several works studying specialized versions of such problems, there has been almost no progress for general combinatorial cost-sharing domains until recently [9]. Still, many questions about the interplay between strategyproofness, cost recovery, and economic efficiency remain unanswered. The main goal of our work is to further understand this interplay in terms of budget balance and social cost approximation. Towards this, we provide a refinement of cross-monotonicity (which we term trace-monotonicity) that is applicable to iterative mechanisms. The trace here refers to the order in which players become finalized. On top of this, we also provide two parameterizations (complementary to a certain extent) of cost functions, which capture the behavior of their average cost-shares. Based on our trace-monotonicity property, we design an Iterative Ascending Cost-Sharing Mechanism, which is applicable to the combinatorial cost-sharing setting with symmetric submodular valuations. Using our first cost function parameterization, we identify conditions under which our mechanism is weakly group-strategyproof, ( O(1) ) -budget-balanced, and ( O(H_n) ) -approximate with respect to the social cost. Furthermore, we show that our mechanism is budget-balanced and ( H_n ) -approximate if both the valuations and the cost functions are symmetric submodular; given existing impossibility results, this is best possible. Finally, we consider general valuation functions and exploit our second parameterization to derive a more fine-grained analysis of the Sequential Mechanism introduced by Moulin. This mechanism is budget balanced by construction, but in general, only guarantees a poor social cost approximation of ( n ) . We identify conditions under which the mechanism achieves improved social cost approximation guarantees. In particular, we derive improved mechanisms for fundamental cost-sharing problems, including Vertex Cover and Set Cover.
{"title":"Cost Sharing over Combinatorial Domains","authors":"Georgios Birmpas, E. Markakis, G. Schäfer","doi":"10.1145/3505586","DOIUrl":"https://doi.org/10.1145/3505586","url":null,"abstract":"We study the problem of designing cost-sharing mechanisms for combinatorial domains. Suppose that multiple items or services are available to be shared among a set of interested agents. The outcome of a mechanism in this setting consists of an assignment, determining for each item the set of players who are granted service, together with respective payments. Although there are several works studying specialized versions of such problems, there has been almost no progress for general combinatorial cost-sharing domains until recently [9]. Still, many questions about the interplay between strategyproofness, cost recovery, and economic efficiency remain unanswered. The main goal of our work is to further understand this interplay in terms of budget balance and social cost approximation. Towards this, we provide a refinement of cross-monotonicity (which we term trace-monotonicity) that is applicable to iterative mechanisms. The trace here refers to the order in which players become finalized. On top of this, we also provide two parameterizations (complementary to a certain extent) of cost functions, which capture the behavior of their average cost-shares. Based on our trace-monotonicity property, we design an Iterative Ascending Cost-Sharing Mechanism, which is applicable to the combinatorial cost-sharing setting with symmetric submodular valuations. Using our first cost function parameterization, we identify conditions under which our mechanism is weakly group-strategyproof, ( O(1) ) -budget-balanced, and ( O(H_n) ) -approximate with respect to the social cost. Furthermore, we show that our mechanism is budget-balanced and ( H_n ) -approximate if both the valuations and the cost functions are symmetric submodular; given existing impossibility results, this is best possible. Finally, we consider general valuation functions and exploit our second parameterization to derive a more fine-grained analysis of the Sequential Mechanism introduced by Moulin. This mechanism is budget balanced by construction, but in general, only guarantees a poor social cost approximation of ( n ) . We identify conditions under which the mechanism achieves improved social cost approximation guarantees. In particular, we derive improved mechanisms for fundamental cost-sharing problems, including Vertex Cover and Set Cover.","PeriodicalId":42216,"journal":{"name":"ACM Transactions on Economics and Computation","volume":" ","pages":"1 - 26"},"PeriodicalIF":1.2,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46276359","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}
Routing games over time are widely studied due to various applications, e.g., transportation, road and air traffic control, logistic in production systems, communication networks like the internet, and financial flows. In this article, we present a new competitive packet routing game with edge priorities motivated by traffic and transportation. In this model a set of selfishly acting players travels through the network over time. If the number of players who want to enter an edge at the same time exceeds the inflow capacity of this edge, then edge priorities with respect to the preceding edge are used to resolve these conflicts, which is similar to right-of-way rules in traffic. We analyze the efficiency of pure Nash equilibria, present an efficient algorithm for computing equilibria in symmetric games, and show that it is NP-hard to decide whether a Nash equilibrium exists in an asymmetric game. Furthermore, we address the problem of constructing optimal priorities.
{"title":"Routing Games with Edge Priorities","authors":"R. Scheffler, M. Strehler, Laura Vargas Koch","doi":"10.1145/3488268","DOIUrl":"https://doi.org/10.1145/3488268","url":null,"abstract":"Routing games over time are widely studied due to various applications, e.g., transportation, road and air traffic control, logistic in production systems, communication networks like the internet, and financial flows. In this article, we present a new competitive packet routing game with edge priorities motivated by traffic and transportation. In this model a set of selfishly acting players travels through the network over time. If the number of players who want to enter an edge at the same time exceeds the inflow capacity of this edge, then edge priorities with respect to the preceding edge are used to resolve these conflicts, which is similar to right-of-way rules in traffic. We analyze the efficiency of pure Nash equilibria, present an efficient algorithm for computing equilibria in symmetric games, and show that it is NP-hard to decide whether a Nash equilibrium exists in an asymmetric game. Furthermore, we address the problem of constructing optimal priorities.","PeriodicalId":42216,"journal":{"name":"ACM Transactions on Economics and Computation","volume":"10 1","pages":"1 - 27"},"PeriodicalIF":1.2,"publicationDate":"2022-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42048221","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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