arXiv - CS - Computer Science and Game Theory最新文献

MALADY: Multiclass Active Learning with Auction Dynamics on Graphs MALADY：利用图形上的拍卖动态进行多类主动学习

arXiv - CS - Computer Science and Game Theory Pub Date : 2024-09-14 DOI: arxiv-2409.09475

Gokul Bhusal, Kevin Miller, Ekaterina Merkurjev

引用次数: 0

On Robustness to $k$-wise Independence of Optimal Bayesian Mechanisms 论最优贝叶斯机制的 $k$-wise 独立性的鲁棒性

arXiv - CS - Computer Science and Game Theory Pub Date : 2024-09-13 DOI: arxiv-2409.08547

Nick Gravin, Zhiqi Wang

{"title":"On Robustness to $k$-wise Independence of Optimal Bayesian Mechanisms","authors":"Nick Gravin, Zhiqi Wang","doi":"arxiv-2409.08547","DOIUrl":"https://doi.org/arxiv-2409.08547","url":null,"abstract":"This paper reexamines the classic problem of revenue maximization in\u0000single-item auctions with $n$ buyers under the lens of the robust optimization\u0000framework. The celebrated Myerson's mechanism is the format that maximizes the\u0000seller's revenue under the prior distribution, which is mutually independent\u0000across all $n$ buyers. As argued in a recent line of work (Caragiannis et al.\u000022), (Dughmi et al. 24), mutual independence is a strong assumption that is\u0000extremely hard to verify statistically, thus it is important to relax the\u0000assumption. While optimal under mutual independent prior, we find that Myerson's\u0000mechanism may lose almost all of its revenue when the independence assumption\u0000is relaxed to pairwise independence, i.e., Myerson's mechanism is not\u0000pairwise-robust. The mechanism regains robustness when the prior is assumed to\u0000be 3-wise independent. In contrast, we show that second-price auctions with\u0000anonymous reserve, including optimal auctions under i.i.d. priors, lose at most\u0000a constant fraction of their revenues on any regular pairwise independent\u0000prior. Our findings draw a comprehensive picture of robustness to $k$-wise\u0000independence in single-item auction settings.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269510","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}

引用次数: 0

The common revenue allocation based on modified Shapley value and DEA cross-efficiency 基于修正的夏普利值和 DEA 交叉效率的共同收益分配

arXiv - CS - Computer Science and Game Theory Pub Date : 2024-09-13 DOI: arxiv-2409.08491

Xinyu Wanga, Qianwei Zhanga, Binwei Guib, Yingdi Zhaoa

引用次数: 0

Mechanism Design for Extending the Accessibility of Facilities 扩大无障碍设施的机制设计

arXiv - CS - Computer Science and Game Theory Pub Date : 2024-09-13 DOI: arxiv-2409.08993

Hau Chan, Jianan Lin, Chenhao Wang, Yanxi Xie

{"title":"Mechanism Design for Extending the Accessibility of Facilities","authors":"Hau Chan, Jianan Lin, Chenhao Wang, Yanxi Xie","doi":"arxiv-2409.08993","DOIUrl":"https://doi.org/arxiv-2409.08993","url":null,"abstract":"We study a variation of facility location problems (FLPs) that aims to\u0000improve the accessibility of agents to the facility within the context of\u0000mechanism design without money. In such a variation, agents have preferences on\u0000the ideal locations of the facility on a real line, and the facility's location\u0000is fixed in advance where (re)locating the facility is not possible due to\u0000various constraints (e.g., limited space and construction costs). To improve\u0000the accessibility of agents to facilities, existing mechanism design literature\u0000in FLPs has proposed to structurally modify the real line (e.g., by adding a\u0000new interval) or provide shuttle services between two points when structural\u0000modifications are not possible. In this paper, we focus on the latter approach\u0000and propose to construct an accessibility range to extend the accessibility of\u0000the facility. In the range, agents can receive accommodations (e.g., school\u0000buses, campus shuttles, or pickup services) to help reach the facility.\u0000Therefore, the cost of each agent is the distance from their ideal location to\u0000the facility (possibility) through the range. We focus on designing\u0000strategyproof mechanisms that elicit true ideal locations from the agents and\u0000construct accessibility ranges (intervals) to approximately minimize the social\u0000cost or the maximum cost of agents. For both social and maximum costs, we\u0000design group strategyproof mechanisms with asymptotically tight bounds on the\u0000approximation ratios.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142265126","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}

引用次数: 0

Common revenue allocation in DMUs with two stages based on DEA cross-efficiency and cooperative game 基于 DEA 交叉效率和合作博弈的两阶段 DMU 共同收入分配

arXiv - CS - Computer Science and Game Theory Pub Date : 2024-09-13 DOI: arxiv-2409.08502

Xinyu Wang, Qianwei Zhang, Yilun Lu, Yingdi Zhao

{"title":"Common revenue allocation in DMUs with two stages based on DEA cross-efficiency and cooperative game","authors":"Xinyu Wang, Qianwei Zhang, Yilun Lu, Yingdi Zhao","doi":"arxiv-2409.08502","DOIUrl":"https://doi.org/arxiv-2409.08502","url":null,"abstract":"In this paper, we examine two-stage production organizations as\u0000decision-making units (DMUs) that can collaborate to form alliances. We present\u0000a novel approach to transform a grand coalition of n DMUs with a two-stage\u0000structure into 2n single-stage sub-DMUs by extending the vectors of the initial\u0000input, intermediate product, and final output, thus creating a 2n*2n DEA\u0000cross-efficiency (CREE) matrix. By combining cooperative game theory with CREE\u0000and utilizing three cooperative game solution concepts, namely, the nucleolus,\u0000the least core and the Shapley value, a characteristic function is developed to\u0000account for two types of allocation, i.e., direct allocation and secondary\u0000allocation. Moreover, the super-additivity and the core non-emptiness\u0000properties are explored. It is found that the sum of the revenue allocated to\u0000all DMUs will remain constant at each stage regardless of the allocation manner\u0000and the cooperative solution concept selected. To illustrate the efficiency and\u0000practicality of the proposed approach, both a numerical example and an\u0000empirical application are provided.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142265127","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}

引用次数: 0

Distributed Learning Dynamics Converging to the Core of $B$-Matchings 向$B$匹配核心靠拢的分布式学习动力

arXiv - CS - Computer Science and Game Theory Pub Date : 2024-09-12 DOI: arxiv-2409.07754

Aya Hamed, Jeff S. Shamma

{"title":"Distributed Learning Dynamics Converging to the Core of $B$-Matchings","authors":"Aya Hamed, Jeff S. Shamma","doi":"arxiv-2409.07754","DOIUrl":"https://doi.org/arxiv-2409.07754","url":null,"abstract":"$B$-matching is a special case of matching problems where nodes can join\u0000multiple matchings with the degree of each node constrained by an upper bound,\u0000the node's $B$-value. The core solution of a bipartite $B$-matching is both a\u0000matching between the agents respecting the upper bound constraint and an\u0000allocation of the value of the edge among its nodes such that no group of\u0000agents can deviate and collectively gain higher allocation. We present two\u0000learning dynamics that converge to the core of the bipartite $B$-matching\u0000problems. The first dynamics are centralized dynamics in the nature of the\u0000Hungarian method, which converge to the core in a polynomial time. The second\u0000dynamics are distributed dynamics, which converge to the core with probability\u0000one. For the distributed dynamics, a node maintains only a state consisting of\u0000(i) its aspiration levels for all of its possible matches and (ii) the matches,\u0000if any, to which it belongs. The node does not keep track of its history nor is\u0000it aware of the environment state. In each stage, a randomly activated node\u0000proposes to form a new match and changes its aspiration based on the success or\u0000failure of its proposal. At this stage, the proposing node inquires about the\u0000aspiration of the agent it wants to match with to calculate the feasibility of\u0000the match. The environment matching structure changes whenever a proposal\u0000succeeds. A state is absorbing for the distributed dynamics if and only if it\u0000is in the core of the $B$-matching.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"98 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197671","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}

引用次数: 0

Communication Separations for Truthful Auctions: Breaking the Two-Player Barrier 真实拍卖的通信分离：打破双人障碍

arXiv - CS - Computer Science and Game Theory Pub Date : 2024-09-12 DOI: arxiv-2409.08241

Shiri Ron, Clayton Thomas, S. Matthew Weinberg, Qianfan Zhang

{"title":"Communication Separations for Truthful Auctions: Breaking the Two-Player Barrier","authors":"Shiri Ron, Clayton Thomas, S. Matthew Weinberg, Qianfan Zhang","doi":"arxiv-2409.08241","DOIUrl":"https://doi.org/arxiv-2409.08241","url":null,"abstract":"We study the communication complexity of truthful combinatorial auctions, and\u0000in particular the case where valuations are either subadditive or\u0000single-minded, which we denote with $mathsf{SubAdd}cupmathsf{SingleM}$. We\u0000show that for three bidders with valuations in\u0000$mathsf{SubAdd}cupmathsf{SingleM}$, any deterministic truthful mechanism\u0000that achieves at least a $0.366$-approximation requires $exp(m)$\u0000communication. In contrast, a natural extension of [Fei09] yields a\u0000non-truthful $mathrm{poly}(m)$-communication protocol that achieves a\u0000$frac{1}{2}$-approximation, demonstrating a gap between the power of truthful\u0000mechanisms and non-truthful protocols for this problem. Our approach follows the taxation complexity framework laid out in [Dob16b],\u0000but applies this framework in a setting not encompassed by the techniques used\u0000in past work. In particular, the only successful prior application of this\u0000framework uses a reduction to simultaneous protocols which only applies for two\u0000bidders [AKSW20], whereas our three-player lower bounds are stronger than what\u0000can possibly arise from a two-player construction (since a trivial truthful\u0000auction guarantees a $frac{1}{2}$-approximation for two players).","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"65 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197666","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}

引用次数: 0

Selling Joint Ads: A Regret Minimization Perspective 销售联合广告：后悔最小化视角

arXiv - CS - Computer Science and Game Theory Pub Date : 2024-09-12 DOI: arxiv-2409.07819

Gagan Aggarwal, Ashwinkumar Badanidiyuru, Paul Dütting, Federico Fusco

{"title":"Selling Joint Ads: A Regret Minimization Perspective","authors":"Gagan Aggarwal, Ashwinkumar Badanidiyuru, Paul Dütting, Federico Fusco","doi":"arxiv-2409.07819","DOIUrl":"https://doi.org/arxiv-2409.07819","url":null,"abstract":"Motivated by online retail, we consider the problem of selling one item\u0000(e.g., an ad slot) to two non-excludable buyers (say, a merchant and a brand).\u0000This problem captures, for example, situations where a merchant and a brand\u0000cooperatively bid in an auction to advertise a product, and both benefit from\u0000the ad being shown. A mechanism collects bids from the two and decides whether\u0000to allocate and which payments the two parties should make. This gives rise to\u0000intricate incentive compatibility constraints, e.g., on how to split payments\u0000between the two parties. We approach the problem of finding a\u0000revenue-maximizing incentive-compatible mechanism from an online learning\u0000perspective; this poses significant technical challenges. First, the action\u0000space (the class of all possible mechanisms) is huge; second, the function that\u0000maps mechanisms to revenue is highly irregular, ruling out standard\u0000discretization-based approaches. In the stochastic setting, we design an efficient learning algorithm\u0000achieving a regret bound of $O(T^{3/4})$. Our approach is based on an adaptive\u0000discretization scheme of the space of mechanisms, as any non-adaptive\u0000discretization fails to achieve sublinear regret. In the adversarial setting,\u0000we exploit the non-Lipschitzness of the problem to prove a strong negative\u0000result, namely that no learning algorithm can achieve more than half of the\u0000revenue of the best fixed mechanism in hindsight. We then consider the\u0000$sigma$-smooth adversary; we construct an efficient learning algorithm that\u0000achieves a regret bound of $O(T^{2/3})$ and builds on a succinct encoding of\u0000exponentially many experts. Finally, we prove that no learning algorithm can\u0000achieve less than $Omega(sqrt T)$ regret in both the stochastic and the\u0000smooth setting, thus narrowing the range where the minimax regret rates for\u0000these two problems lie.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197669","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}

引用次数: 0

The Complexity of Two-Team Polymatrix Games with Independent Adversaries 有独立对手的两队多矩阵游戏的复杂性

arXiv - CS - Computer Science and Game Theory Pub Date : 2024-09-11 DOI: arxiv-2409.07398

Alexandros Hollender, Gilbert Maystre, Sai Ganesh Nagarajan

{"title":"The Complexity of Two-Team Polymatrix Games with Independent Adversaries","authors":"Alexandros Hollender, Gilbert Maystre, Sai Ganesh Nagarajan","doi":"arxiv-2409.07398","DOIUrl":"https://doi.org/arxiv-2409.07398","url":null,"abstract":"Adversarial multiplayer games are an important object of study in multiagent\u0000learning. In particular, polymatrix zero-sum games are a multiplayer setting\u0000where Nash equilibria are known to be efficiently computable. Towards\u0000understanding the limits of tractability in polymatrix games, we study the\u0000computation of Nash equilibria in such games where each pair of players plays\u0000either a zero-sum or a coordination game. We are particularly interested in the\u0000setting where players can be grouped into a small number of teams of identical\u0000interest. While the three-team version of the problem is known to be\u0000PPAD-complete, the complexity for two teams has remained open. Our main\u0000contribution is to prove that the two-team version remains hard, namely it is\u0000CLS-hard. Furthermore, we show that this lower bound is tight for the setting\u0000where one of the teams consists of multiple independent adversaries. On the way\u0000to obtaining our main result, we prove hardness of finding any stationary point\u0000in the simplest type of non-convex-concave min-max constrained optimization\u0000problem, namely for a class of bilinear polynomial objective functions.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"171 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197667","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}

引用次数: 0

Randomized Strategic Facility Location with Predictions 带有预测的随机战略设施选址

arXiv - CS - Computer Science and Game Theory Pub Date : 2024-09-11 DOI: arxiv-2409.07142

Eric Balkanski, Vasilis Gkatzelis, Golnoosh Shahkarami

{"title":"Randomized Strategic Facility Location with Predictions","authors":"Eric Balkanski, Vasilis Gkatzelis, Golnoosh Shahkarami","doi":"arxiv-2409.07142","DOIUrl":"https://doi.org/arxiv-2409.07142","url":null,"abstract":"We revisit the canonical problem of strategic facility location and study the\u0000power and limitations of randomization in the design of truthful mechanisms\u0000augmented with machine-learned predictions. In the strategic facility location\u0000problem, a set of agents are asked to report their locations in some metric\u0000space and the goal is to use these reported locations to determine where to\u0000open a new facility, aiming to optimize some aggregate measure of distance of\u0000the agents from that facility. However, the agents are strategic and can\u0000misreport their locations if this may lead to a facility location choice that\u0000they prefer. The goal is to design truthful mechanisms, which ensure the agents\u0000cannot benefit by misreporting. A lot of prior work has studied this problem\u0000from a worst-case perspective, but a recent line of work proposed a framework\u0000to refine these results when the designer is provided with some, possible\u0000incorrect, predictions regarding the agents' true locations. The goal is to\u0000simultaneously provide strong consistency guarantees (i.e., guarantees when the\u0000predictions provided to the mechanism are correct) and near-optimal robustness\u0000guarantees (i.e., guarantees that hold irrespective of how inaccurate the\u0000predictions may be). In this work we focus on the power of randomization in\u0000this problem and analyze the best approximation guarantees achievable with\u0000respect to the egalitarian social cost measure for one- and two-dimensional\u0000Euclidean spaces.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197517","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}

引用次数: 0