Overcoming the impact of selfish behavior of rational players in multiagent systems is a fundamental problem in game theory. Without any intervention from a central agent, strategic users take actions in order to maximize their personal utility, which can lead to extremely inefficient overall system performance, often indicated by a high Price of Anarchy. Recent work (Lin et al. 2021) investigated and formalized yet another undesirable behavior of rational agents, that of avoiding freely available information about the game for selfish reasons, leading to worse social outcomes. A central planner can significantly mitigate these issues by injecting a subsidy to reduce certain costs associated with the system and obtain net gains in the system performance. Crucially, the planner needs to determine how to allocate this subsidy effectively. We formally show that designing subsidies that perfectly optimize the social good, in terms of minimizing the Price of Anarchy or preventing the information avoidance behavior, is computationally hard under standard complexity theoretic assumptions. On the positive side, we show that we can learn provably good values of subsidy in repeated games coming from the same domain. This data-driven subsidy design approach avoids solving computationally hard problems for unseen games by learning over polynomially many games. We also show that optimal subsidy can be learned with no-regret given an online sequence of games, under mild assumptions on the cost matrix. Our study focuses on two distinct games: a Bayesian extension of the well-studied fair cost-sharing game, and a component maintenance game with engineering applications.
{"title":"Subsidy design for better social outcomes","authors":"Maria-Florina Balcan, Matteo Pozzi, Dravyansh Sharma","doi":"arxiv-2409.03129","DOIUrl":"https://doi.org/arxiv-2409.03129","url":null,"abstract":"Overcoming the impact of selfish behavior of rational players in multiagent\u0000systems is a fundamental problem in game theory. Without any intervention from\u0000a central agent, strategic users take actions in order to maximize their\u0000personal utility, which can lead to extremely inefficient overall system\u0000performance, often indicated by a high Price of Anarchy. Recent work (Lin et\u0000al. 2021) investigated and formalized yet another undesirable behavior of\u0000rational agents, that of avoiding freely available information about the game\u0000for selfish reasons, leading to worse social outcomes. A central planner can\u0000significantly mitigate these issues by injecting a subsidy to reduce certain\u0000costs associated with the system and obtain net gains in the system\u0000performance. Crucially, the planner needs to determine how to allocate this\u0000subsidy effectively. We formally show that designing subsidies that perfectly optimize the social\u0000good, in terms of minimizing the Price of Anarchy or preventing the information\u0000avoidance behavior, is computationally hard under standard complexity theoretic\u0000assumptions. On the positive side, we show that we can learn provably good\u0000values of subsidy in repeated games coming from the same domain. This\u0000data-driven subsidy design approach avoids solving computationally hard\u0000problems for unseen games by learning over polynomially many games. We also\u0000show that optimal subsidy can be learned with no-regret given an online\u0000sequence of games, under mild assumptions on the cost matrix. Our study focuses\u0000on two distinct games: a Bayesian extension of the well-studied fair\u0000cost-sharing game, and a component maintenance game with engineering\u0000applications.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"98 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197514","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 situations where a group of voters need to take a collective decision over a number of public issues, with the goal of getting a result that reflects the voters' opinions in a proportional manner. Our focus is on interconnected public decisions, where the decision on one or more issues has repercussions on the acceptance or rejection of other public issues in the agenda. We show that the adaptations of classical justified-representation axioms to this enriched setting are always satisfiable only for restricted classes of public agendas. However, the use of suitably adapted well-known decision rules on a class of quite expressive constraints, yields proportionality guarantees that match these justified-representation properties in an approximate sense. We also identify another path to achieving proportionality via an adaptation of the notion of priceability.
{"title":"Proportionality for Constrained Public Decisions","authors":"Julian Chingoma, Umberto Grandi, Arianna Novaro","doi":"arxiv-2409.02609","DOIUrl":"https://doi.org/arxiv-2409.02609","url":null,"abstract":"We study situations where a group of voters need to take a collective\u0000decision over a number of public issues, with the goal of getting a result that\u0000reflects the voters' opinions in a proportional manner. Our focus is on\u0000interconnected public decisions, where the decision on one or more issues has\u0000repercussions on the acceptance or rejection of other public issues in the\u0000agenda. We show that the adaptations of classical justified-representation\u0000axioms to this enriched setting are always satisfiable only for restricted\u0000classes of public agendas. However, the use of suitably adapted well-known\u0000decision rules on a class of quite expressive constraints, yields\u0000proportionality guarantees that match these justified-representation properties\u0000in an approximate sense. We also identify another path to achieving\u0000proportionality via an adaptation of the notion of priceability.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"69 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197510","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}
Many online marketplaces personalize prices based on consumer attributes. Since these prices are private, consumers will not realize if they spend more on a good than the lowest possible price, and cannot easily take action to get better prices. In this paper we introduce a system that takes advantage of personalized pricing so consumers can profit while improving fairness. Our system matches consumers for trading; the lower-paying consumer buys the good for the higher-paying consumer for some fee. We explore various modeling choices and fairness targets to determine which schema will leave consumers best off, while also earning revenue for the system itself. We show that when consumers individually negotiate the transaction price, they are able to achieve the most fair outcomes. Conversely, when transaction prices are centrally set, consumers are often unwilling to transact. Minimizing the average price paid by an individual or group is most profitable for the system, while achieving a $67%$ reduction in prices. We see that a high dispersion (or range) of original prices is necessary for our system to be viable. Higher dispersion can actually lead to increased consumer welfare, and act as a check against extreme personalization. Our results provide theoretical evidence that such a system could improve fairness for consumers while sustaining itself financially.
{"title":"Designing Fair Systems for Consumers to Exploit Personalized Pricing","authors":"Aditya Karan, Naina Balepur, Hari Sundaram","doi":"arxiv-2409.02777","DOIUrl":"https://doi.org/arxiv-2409.02777","url":null,"abstract":"Many online marketplaces personalize prices based on consumer attributes.\u0000Since these prices are private, consumers will not realize if they spend more\u0000on a good than the lowest possible price, and cannot easily take action to get\u0000better prices. In this paper we introduce a system that takes advantage of\u0000personalized pricing so consumers can profit while improving fairness. Our\u0000system matches consumers for trading; the lower-paying consumer buys the good\u0000for the higher-paying consumer for some fee. We explore various modeling\u0000choices and fairness targets to determine which schema will leave consumers\u0000best off, while also earning revenue for the system itself. We show that when\u0000consumers individually negotiate the transaction price, they are able to\u0000achieve the most fair outcomes. Conversely, when transaction prices are\u0000centrally set, consumers are often unwilling to transact. Minimizing the\u0000average price paid by an individual or group is most profitable for the system,\u0000while achieving a $67%$ reduction in prices. We see that a high dispersion (or\u0000range) of original prices is necessary for our system to be viable. Higher\u0000dispersion can actually lead to increased consumer welfare, and act as a check\u0000against extreme personalization. Our results provide theoretical evidence that\u0000such a system could improve fairness for consumers while sustaining itself\u0000financially.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197507","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 computing emph{fair} divisions of a set of indivisible goods among agents with emph{additive} valuations. For the past many decades, the literature has explored various notions of fairness, that can be primarily seen as either having emph{envy-based} or emph{share-based} lens. For the discrete setting of resource-allocation problems, emph{envy-free up to any good} (EFX) and emph{maximin share} (MMS) are widely considered as the flag-bearers of fairness notions in the above two categories, thereby capturing different aspects of fairness herein. Due to lack of existence results of these notions and the fact that a good approximation of EFX or MMS does not imply particularly strong guarantees of the other, it becomes important to understand the compatibility of EFX and MMS allocations with one another. In this work, we identify a novel way to simultaneously achieve MMS guarantees with EFX/EF1 notions of fairness, while beating the best known approximation factors [Chaudhury et al., 2021, Amanatidis et al., 2020]. Our main contribution is to constructively prove the existence of (i) a partial allocation that is both $2/3$-MMS and EFX, and (ii) a complete allocation that is both $2/3$-MMS and EF1. Our algorithms run in pseudo-polynomial time if the approximation factor for MMS is relaxed to $2/3-varepsilon$ for any constant $varepsilon > 0$ and in polynomial time if, in addition, the EFX (or EF1) guarantee is relaxed to $(1-delta)$-EFX (or $(1-delta)$-EF1) for any constant $delta>0$. In particular, we improve from the best approximation factor known prior to our work, which computes partial allocations that are $1/2$-MMS and EFX in pseudo-polynomial time [Chaudhury et al., 2021].
{"title":"Achieving Maximin Share and EFX/EF1 Guarantees Simultaneously","authors":"Hannaneh Akrami, Nidhi Rathi","doi":"arxiv-2409.01963","DOIUrl":"https://doi.org/arxiv-2409.01963","url":null,"abstract":"We study the problem of computing emph{fair} divisions of a set of\u0000indivisible goods among agents with emph{additive} valuations. For the past\u0000many decades, the literature has explored various notions of fairness, that can\u0000be primarily seen as either having emph{envy-based} or emph{share-based}\u0000lens. For the discrete setting of resource-allocation problems, emph{envy-free\u0000up to any good} (EFX) and emph{maximin share} (MMS) are widely considered as\u0000the flag-bearers of fairness notions in the above two categories, thereby\u0000capturing different aspects of fairness herein. Due to lack of existence\u0000results of these notions and the fact that a good approximation of EFX or MMS\u0000does not imply particularly strong guarantees of the other, it becomes\u0000important to understand the compatibility of EFX and MMS allocations with one\u0000another. In this work, we identify a novel way to simultaneously achieve MMS\u0000guarantees with EFX/EF1 notions of fairness, while beating the best known\u0000approximation factors [Chaudhury et al., 2021, Amanatidis et al., 2020]. Our\u0000main contribution is to constructively prove the existence of (i) a partial\u0000allocation that is both $2/3$-MMS and EFX, and (ii) a complete allocation that\u0000is both $2/3$-MMS and EF1. Our algorithms run in pseudo-polynomial time if the\u0000approximation factor for MMS is relaxed to $2/3-varepsilon$ for any constant\u0000$varepsilon > 0$ and in polynomial time if, in addition, the EFX (or EF1)\u0000guarantee is relaxed to $(1-delta)$-EFX (or $(1-delta)$-EF1) for any constant\u0000$delta>0$. In particular, we improve from the best approximation factor known\u0000prior to our work, which computes partial allocations that are $1/2$-MMS and\u0000EFX in pseudo-polynomial time [Chaudhury et al., 2021].","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study a variant of the single-choice prophet inequality problem where the decision-maker does not know the underlying distribution and has only access to a set of samples from the distributions. Rubinstein et al. [2020] showed that the optimal competitive-ratio of $frac{1}{2}$ can surprisingly be obtained by observing a set of $n$ samples, one from each of the distributions. In this paper, we prove that this competitive-ratio of $frac{1}{2}$ becomes unattainable when the decision-maker is provided with a set of more samples. We then examine the natural class of ordinal static threshold algorithms, where the algorithm selects the $i$-th highest ranked sample, sets this sample as a static threshold, and then chooses the first value that exceeds this threshold. We show that the best possible algorithm within this class achieves a competitive-ratio of $0.433$. Along the way, we utilize the tools developed in the paper and provide an alternative proof of the main result of Rubinstein et al. [2020].
我们研究了单选预言家不等式问题的一个变体，在这个变体中，决策者不知道基本分布，只能从分布中获取一组样本。鲁宾斯坦等人[2020]的研究表明，通过观察一组 $n$ 样本（每种分布都有一个样本），竟然可以得到 $frac{1}{2}$ 的最优竞争比。在本文中，我们将证明当决策者获得一组更多的样本时，$frac{1}{2}$的竞争比率将变得无法实现。我们研究了顺序静态阈值算法的自然类，该算法选择排名最高的第 i 个样本，将该样本设为静态阈值，然后选择超过该阈值的第一个值。我们证明，该类算法中的最佳算法可实现 0.433 美元的竞争比率。在此过程中，我们利用论文中开发的工具，为鲁宾斯坦等人的主要结果提供了另一种证明。[2020].
{"title":"Prophet Inequality from Samples: Is the More the Merrier?","authors":"Tomer Ezra","doi":"arxiv-2409.00559","DOIUrl":"https://doi.org/arxiv-2409.00559","url":null,"abstract":"We study a variant of the single-choice prophet inequality problem where the\u0000decision-maker does not know the underlying distribution and has only access to\u0000a set of samples from the distributions. Rubinstein et al. [2020] showed that\u0000the optimal competitive-ratio of $frac{1}{2}$ can surprisingly be obtained by\u0000observing a set of $n$ samples, one from each of the distributions. In this\u0000paper, we prove that this competitive-ratio of $frac{1}{2}$ becomes\u0000unattainable when the decision-maker is provided with a set of more samples. We\u0000then examine the natural class of ordinal static threshold algorithms, where\u0000the algorithm selects the $i$-th highest ranked sample, sets this sample as a\u0000static threshold, and then chooses the first value that exceeds this threshold.\u0000We show that the best possible algorithm within this class achieves a\u0000competitive-ratio of $0.433$. Along the way, we utilize the tools developed in\u0000the paper and provide an alternative proof of the main result of Rubinstein et\u0000al. [2020].","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197512","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 examines two different variants of the Ludo game, involving multiple dice and a fixed number of total turns. Within each variant, multiple game lengths (total no. of turns) are considered. To compare the two variants, a set of intuitive, rule-based strategies is designed, representing different broad methods of strategic play. Game play is simulated between bots (automated software applications executing repetitive tasks over a network) following these strategies. The expected results are computed using certain game theoretic and probabilistic explanations, helping to understand the performance of the different strategies. The different strategies are further analyzed using win percentage in a large number of simulations, and Nash Equilibrium strategies are computed for both variants for a varying number of total turns. The Nash Equilibrium strategies across different game lengths are compared. A clear distinction between performances of strategies is observed, with more sophisticated strategies beating the naive one. A gradual shift in optimal strategy profiles is observed with changing game length, and certain sophisticated strategies even confound each other's performance while playing against each other.
{"title":"Skill Dominance Analysis of Two(Four) player, Four(Five) dice Variant of the Ludo Game","authors":"Tathagata Banerjee, Diganta Mukherjee","doi":"arxiv-2409.00376","DOIUrl":"https://doi.org/arxiv-2409.00376","url":null,"abstract":"This paper examines two different variants of the Ludo game, involving\u0000multiple dice and a fixed number of total turns. Within each variant, multiple\u0000game lengths (total no. of turns) are considered. To compare the two variants,\u0000a set of intuitive, rule-based strategies is designed, representing different\u0000broad methods of strategic play. Game play is simulated between bots (automated\u0000software applications executing repetitive tasks over a network) following\u0000these strategies. The expected results are computed using certain game\u0000theoretic and probabilistic explanations, helping to understand the performance\u0000of the different strategies. The different strategies are further analyzed\u0000using win percentage in a large number of simulations, and Nash Equilibrium\u0000strategies are computed for both variants for a varying number of total turns.\u0000The Nash Equilibrium strategies across different game lengths are compared. A\u0000clear distinction between performances of strategies is observed, with more\u0000sophisticated strategies beating the naive one. A gradual shift in optimal\u0000strategy profiles is observed with changing game length, and certain\u0000sophisticated strategies even confound each other's performance while playing\u0000against each other.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197513","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}
Leveraging recent advances in wireless communication, IoT, and AI, intelligent transportation systems (ITS) played an important role in reducing traffic congestion and enhancing user experience. Within ITS, navigational recommendation systems (NRS) are essential for helping users simplify route choices in urban environments. However, NRS are vulnerable to information-based attacks that can manipulate both the NRS and users to achieve the objectives of the malicious entities. This study aims to assess the risks of misinformed demand attacks, where attackers use techniques like Sybil-based attacks to manipulate the demands of certain origins and destinations considered by the NRS. We propose a game-theoretic framework for proactive risk assessment of demand attacks (PRADA) and treat the interaction between attackers and the NRS as a Stackelberg game. The attacker is the leader who conveys misinformed demands, while the NRS is the follower responding to the provided information. Specifically, we consider the case of local-targeted attacks, in which the attacker aims to make the NRS recommend the authentic users towards a specific road that favors certain groups. Our analysis unveils the equivalence between users' incentive compatibility and Wardrop equilibrium recommendations and shows that the NRS and its users are at high risk when encountering intelligent attackers who can significantly alter user routes by strategically fabricating non-existent demands. To mitigate these risks, we introduce a trust mechanism that leverages users' confidence in the integrity of the NRS, and show that it can effectively reduce the impact of misinformed demand attacks. Numerical experiments are used to corroborate the results and demonstrate a Resilience Paradox, where locally targeted attacks can sometimes benefit the overall traffic conditions.
{"title":"PRADA: Proactive Risk Assessment and Mitigation of Misinformed Demand Attacks on Navigational Route Recommendations","authors":"Ya-Ting Yang, Haozhe Lei, Quanyan Zhu","doi":"arxiv-2409.00243","DOIUrl":"https://doi.org/arxiv-2409.00243","url":null,"abstract":"Leveraging recent advances in wireless communication, IoT, and AI,\u0000intelligent transportation systems (ITS) played an important role in reducing\u0000traffic congestion and enhancing user experience. Within ITS, navigational\u0000recommendation systems (NRS) are essential for helping users simplify route\u0000choices in urban environments. However, NRS are vulnerable to information-based\u0000attacks that can manipulate both the NRS and users to achieve the objectives of\u0000the malicious entities. This study aims to assess the risks of misinformed\u0000demand attacks, where attackers use techniques like Sybil-based attacks to\u0000manipulate the demands of certain origins and destinations considered by the\u0000NRS. We propose a game-theoretic framework for proactive risk assessment of\u0000demand attacks (PRADA) and treat the interaction between attackers and the NRS\u0000as a Stackelberg game. The attacker is the leader who conveys misinformed\u0000demands, while the NRS is the follower responding to the provided information.\u0000Specifically, we consider the case of local-targeted attacks, in which the\u0000attacker aims to make the NRS recommend the authentic users towards a specific\u0000road that favors certain groups. Our analysis unveils the equivalence between\u0000users' incentive compatibility and Wardrop equilibrium recommendations and\u0000shows that the NRS and its users are at high risk when encountering intelligent\u0000attackers who can significantly alter user routes by strategically fabricating\u0000non-existent demands. To mitigate these risks, we introduce a trust mechanism\u0000that leverages users' confidence in the integrity of the NRS, and show that it\u0000can effectively reduce the impact of misinformed demand attacks. Numerical\u0000experiments are used to corroborate the results and demonstrate a Resilience\u0000Paradox, where locally targeted attacks can sometimes benefit the overall\u0000traffic conditions.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197515","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 urban transportation environments, drivers often encounter various path (route) options when navigating to their destinations. This emphasizes the importance of navigational recommendation systems (NRS), which simplify decision-making and reduce travel time for users while alleviating potential congestion for broader societal benefits. However, recommending the shortest path may cause the flash crowd effect, and system-optimal routes may not always align the preferences of human users, leading to non-compliance issues. It is also worth noting that universal NRS adoption is impractical. Therefore, in this study, we aim to address these challenges by proposing an incentive compatibility recommendation system from a game-theoretic perspective and accounts for non-user drivers with their own path choice behaviors. Additionally, recognizing the dynamic nature of traffic conditions and the unpredictability of accidents, this work introduces a dynamic NRS with parallel and random update schemes, enabling users to safely adapt to changing traffic conditions while ensuring optimal total travel time costs. The numerical studies indicate that the proposed parallel update scheme exhibits greater effectiveness in terms of user compliance, travel time reduction, and adaptability to the environment.
{"title":"Adaptive Incentive-Compatible Navigational Route Recommendations in Urban Transportation Networks","authors":"Ya-Ting Yang, Haozhe Lei, Quanyan Zhu","doi":"arxiv-2409.00236","DOIUrl":"https://doi.org/arxiv-2409.00236","url":null,"abstract":"In urban transportation environments, drivers often encounter various path\u0000(route) options when navigating to their destinations. This emphasizes the\u0000importance of navigational recommendation systems (NRS), which simplify\u0000decision-making and reduce travel time for users while alleviating potential\u0000congestion for broader societal benefits. However, recommending the shortest\u0000path may cause the flash crowd effect, and system-optimal routes may not always\u0000align the preferences of human users, leading to non-compliance issues. It is\u0000also worth noting that universal NRS adoption is impractical. Therefore, in\u0000this study, we aim to address these challenges by proposing an incentive\u0000compatibility recommendation system from a game-theoretic perspective and\u0000accounts for non-user drivers with their own path choice behaviors.\u0000Additionally, recognizing the dynamic nature of traffic conditions and the\u0000unpredictability of accidents, this work introduces a dynamic NRS with parallel\u0000and random update schemes, enabling users to safely adapt to changing traffic\u0000conditions while ensuring optimal total travel time costs. The numerical\u0000studies indicate that the proposed parallel update scheme exhibits greater\u0000effectiveness in terms of user compliance, travel time reduction, and\u0000adaptability to the environment.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197516","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}
Super-stability and strong stability are properties of a matching in the stable matching problem with ties. In this paper, we introduce a common generalization of super-stability and strong stability, which we call non-uniform stability. First, we prove that we can determine the existence of a non-uniformly stable matching in polynomial time. Next, we give a polyhedral characterization of the set of non-uniformly stable matchings. Finally, we prove that the set of non-uniformly stable matchings forms a distributive lattice.
{"title":"Non-uniformly Stable Matchings","authors":"Naoyuki Kamiyama","doi":"arxiv-2408.16271","DOIUrl":"https://doi.org/arxiv-2408.16271","url":null,"abstract":"Super-stability and strong stability are properties of a matching in the\u0000stable matching problem with ties. In this paper, we introduce a common\u0000generalization of super-stability and strong stability, which we call\u0000non-uniform stability. First, we prove that we can determine the existence of a\u0000non-uniformly stable matching in polynomial time. Next, we give a polyhedral\u0000characterization of the set of non-uniformly stable matchings. Finally, we\u0000prove that the set of non-uniformly stable matchings forms a distributive\u0000lattice.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197522","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}
Tommaso Toso, Francesca Parise, Paolo Frasca, Alain Y. Kibangou
We investigate a traffic assignment problem on a transportation network, considering both the demands of individual drivers and of a large fleet controlled by a central operator (minimizing the fleet's average travel time). We formulate this problem as a two-player convex game and we study how the size of the coordinated fleet, measured in terms of share of the total demand, influences the Price of Anarchy (PoA). We show that, for two-terminal networks, there are cases in which the fleet must reach a minimum share before actually affecting the PoA, which otherwise remains unchanged. Moreover, for parallel networks, we prove that the PoA is monotonically non-increasing in the fleet share.
{"title":"On the impact of coordinated fleets size on traffic efficiency","authors":"Tommaso Toso, Francesca Parise, Paolo Frasca, Alain Y. Kibangou","doi":"arxiv-2408.15742","DOIUrl":"https://doi.org/arxiv-2408.15742","url":null,"abstract":"We investigate a traffic assignment problem on a transportation network,\u0000considering both the demands of individual drivers and of a large fleet\u0000controlled by a central operator (minimizing the fleet's average travel time).\u0000We formulate this problem as a two-player convex game and we study how the size\u0000of the coordinated fleet, measured in terms of share of the total demand,\u0000influences the Price of Anarchy (PoA). We show that, for two-terminal networks,\u0000there are cases in which the fleet must reach a minimum share before actually\u0000affecting the PoA, which otherwise remains unchanged. Moreover, for parallel\u0000networks, we prove that the PoA is monotonically non-increasing in the fleet\u0000share.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197518","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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