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Markov Decision Processes with Sure Parity and Multiple Reachability Objectives 具有确定奇偶性和多重可达性目标的马尔可夫决策过程
arXiv - CS - Computer Science and Game Theory Pub Date : 2024-08-02 DOI: arxiv-2408.01212
Raphaël Berthon, Joost-Pieter Katoen, Tobias Winkler
{"title":"Markov Decision Processes with Sure Parity and Multiple Reachability Objectives","authors":"Raphaël Berthon, Joost-Pieter Katoen, Tobias Winkler","doi":"arxiv-2408.01212","DOIUrl":"https://doi.org/arxiv-2408.01212","url":null,"abstract":"This paper considers the problem of finding strategies that satisfy a mixture\u0000of sure and threshold objectives in Markov decision processes. We focus on a\u0000single $omega$-regular objective expressed as parity that must be surely met\u0000while satisfying $n$ reachability objectives towards sink states with some\u0000probability thresholds too. We consider three variants of the problem: (a)\u0000strict and (b) non-strict thresholds on all reachability objectives, and (c)\u0000maximizing the thresholds with respect to a lexicographic order. We show that\u0000(a) and (c) can be reduced to solving parity games, and (b) can be solved in\u0000$sf{EXPTIME}$. Strategy complexities as well as algorithms are provided for\u0000all cases.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"86 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141934942","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
Distribution Aggregation via Continuous Thiele's Rules 通过连续蒂勒规则进行分布聚合
arXiv - CS - Computer Science and Game Theory Pub Date : 2024-08-02 DOI: arxiv-2408.01054
Jonathan Wagner, Reshef Meir
{"title":"Distribution Aggregation via Continuous Thiele's Rules","authors":"Jonathan Wagner, Reshef Meir","doi":"arxiv-2408.01054","DOIUrl":"https://doi.org/arxiv-2408.01054","url":null,"abstract":"We introduce the class of textit{Continuous Thiele's Rules} that generalize\u0000the familiar textbf{Thiele's rules} cite{janson2018phragmens} of multi-winner\u0000voting to distribution aggregation problems. Each rule in that class maximizes\u0000$sum_if(pi^i)$ where $pi^i$ is an agent $i$'s satisfaction and $f$ could be\u0000any twice differentiable, increasing and concave real function. Based on a\u0000single quantity we call the textit{'Inequality Aversion'} of $f$ (elsewhere\u0000known as \"Relative Risk Aversion\"), we derive bounds on the Egalitarian loss,\u0000welfare loss and the approximation of textit{Average Fair Share}, leading to a\u0000quantifiable, continuous presentation of their inevitable trade-offs. In\u0000particular, we show that the Nash Product Rule satisfiestextit{ Average Fair\u0000Share} in our setting.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141934939","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
Explaining a probabilistic prediction on the simplex with Shapley compositions 用夏普利合成解释单纯形上的概率预测
arXiv - CS - Computer Science and Game Theory Pub Date : 2024-08-02 DOI: arxiv-2408.01382
Paul-Gauthier Noé, Miquel Perelló-Nieto, Jean-François Bonastre, Peter Flach
{"title":"Explaining a probabilistic prediction on the simplex with Shapley compositions","authors":"Paul-Gauthier Noé, Miquel Perelló-Nieto, Jean-François Bonastre, Peter Flach","doi":"arxiv-2408.01382","DOIUrl":"https://doi.org/arxiv-2408.01382","url":null,"abstract":"Originating in game theory, Shapley values are widely used for explaining a\u0000machine learning model's prediction by quantifying the contribution of each\u0000feature's value to the prediction. This requires a scalar prediction as in\u0000binary classification, whereas a multiclass probabilistic prediction is a\u0000discrete probability distribution, living on a multidimensional simplex. In\u0000such a multiclass setting the Shapley values are typically computed separately\u0000on each class in a one-vs-rest manner, ignoring the compositional nature of the\u0000output distribution. In this paper, we introduce Shapley compositions as a\u0000well-founded way to properly explain a multiclass probabilistic prediction,\u0000using the Aitchison geometry from compositional data analysis. We prove that\u0000the Shapley composition is the unique quantity satisfying linearity, symmetry\u0000and efficiency on the Aitchison simplex, extending the corresponding axiomatic\u0000properties of the standard Shapley value. We demonstrate this proper multiclass\u0000treatment in a range of scenarios.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141934940","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
Games in Public Announcement: How to Reduce System Losses in Optimistic Blockchain Mechanisms 公告中的游戏：如何在乐观的区块链机制中减少系统损失
arXiv - CS - Computer Science and Game Theory Pub Date : 2024-07-31 DOI: arxiv-2407.21413
Siyuan Liu, Yulong Zeng
{"title":"Games in Public Announcement: How to Reduce System Losses in Optimistic Blockchain Mechanisms","authors":"Siyuan Liu, Yulong Zeng","doi":"arxiv-2407.21413","DOIUrl":"https://doi.org/arxiv-2407.21413","url":null,"abstract":"Announcement games, where information is disseminated by announcers and\u0000challenged by validators, are prevalent in real-world scenarios. Validators\u0000take effort to verify the validity of the announcements, gaining rewards for\u0000successfully challenging invalid ones, while receiving nothing for valid ones.\u0000Optimistic Rollup, a Layer 2 blockchain scaling solution, exemplifies such\u0000games, offering significant improvements in transaction throughput and cost\u0000efficiency. We present a game-theoretic model of announcement games to analyze\u0000the potential behaviors of announcers and validators. We identify all Nash\u0000equilibria and study the corresponding system losses for different Nash\u0000equilibria. Additionally, we analyze the impact of various system parameters on\u0000system loss under the Nash equilibrium. Finally, we provide suggestions for\u0000mechanism optimization to reduce system losses.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872063","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
Escape Sensing Games: Detection-vs-Evasion in Security Applications 逃生感应游戏：安全应用中的检测与入侵
arXiv - CS - Computer Science and Game Theory Pub Date : 2024-07-30 DOI: arxiv-2407.20981
Niclas Boehmer, Minbiao Han, Haifeng Xu, Milind Tambe
{"title":"Escape Sensing Games: Detection-vs-Evasion in Security Applications","authors":"Niclas Boehmer, Minbiao Han, Haifeng Xu, Milind Tambe","doi":"arxiv-2407.20981","DOIUrl":"https://doi.org/arxiv-2407.20981","url":null,"abstract":"Traditional game-theoretic research for security applications primarily\u0000focuses on the allocation of external protection resources to defend targets.\u0000This work puts forward the study of a new class of games centered around\u0000strategically arranging targets to protect them against a constrained\u0000adversary, with motivations from varied domains such as peacekeeping resource\u0000transit and cybersecurity. Specifically, we introduce Escape Sensing Games\u0000(ESGs). In ESGs, a blue player manages the order in which targets pass through\u0000a channel, while her opponent tries to capture the targets using a set of\u0000sensors that need some time to recharge after each activation. We present a\u0000thorough computational study of ESGs. Among others, we show that it is NP-hard\u0000to compute best responses and equilibria. Nevertheless, we propose a variety of\u0000effective (heuristic) algorithms whose quality we demonstrate in extensive\u0000computational experiments.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872073","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
Diffusion Mechanism Design in Tree-Structured Social Network 树状结构社交网络中的扩散机制设计
arXiv - CS - Computer Science and Game Theory Pub Date : 2024-07-30 DOI: arxiv-2407.21143
Feiyang Yu
{"title":"Diffusion Mechanism Design in Tree-Structured Social Network","authors":"Feiyang Yu","doi":"arxiv-2407.21143","DOIUrl":"https://doi.org/arxiv-2407.21143","url":null,"abstract":"We design a fixed-price auction mechanism for a seller to sell multiple items\u0000in a tree-structured market. The buyers have independently drawn valuation from\u0000a uniform distribution, and the seller would like to incentivize buyers to\u0000invite more people to the auction. We prove that our mechanism is individual\u0000rational, and incentivize compatible with regard to the buyers' action.\u0000Furthermore, we show the approximation ratio of our mechanism to the optimal\u0000fixed-price auction in two ways, theoretically and via Monte-Carlo simulation,\u0000and show a high practical ratio. Finally, we discuss several factors affecting\u0000the behavior of our mechanism and its feasibility in reality.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141873347","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
A Stackelberg Game Model of Flocking 成群结队的斯塔克尔伯格博弈模型
arXiv - CS - Computer Science and Game Theory Pub Date : 2024-07-29 DOI: arxiv-2407.19678
Chenlan Wang, Mehrdad Moharrami, Mingyan Liu
{"title":"A Stackelberg Game Model of Flocking","authors":"Chenlan Wang, Mehrdad Moharrami, Mingyan Liu","doi":"arxiv-2407.19678","DOIUrl":"https://doi.org/arxiv-2407.19678","url":null,"abstract":"We study a Stackelberg game to examine how two agents determine to cooperate\u0000while competing with each other. Each selects an arrival time to a destination,\u0000the earlier one fetching a higher reward. There is, however, an inherent\u0000penalty in arriving too early as well as a risk in traveling alone. This gives\u0000rise to the possibility of the agents cooperating by traveling together while\u0000competing for the reward. In our prior work [1] we studied this problem as a\u0000sequential game among a set of $N$ competing agents in continuous time, and\u0000defined the formation of a group traveling together as arriving at exactly the\u0000same time. In the present study, we relax this definition to allow arrival\u0000times within a small window, and study a 2-agent game in both continuous and\u0000discrete time, referred to as the flock formation game. We derive and examine\u0000the properties of the subgame perfect equilibrium (SPE) of this game.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872074","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
LiteEFG: An Efficient Python Library for Solving Extensive-form Games LiteEFG：用于求解广式博弈的高效 Python 库
arXiv - CS - Computer Science and Game Theory Pub Date : 2024-07-29 DOI: arxiv-2407.20351
Mingyang Liu, Gabriele Farina, Asuman Ozdaglar
{"title":"LiteEFG: An Efficient Python Library for Solving Extensive-form Games","authors":"Mingyang Liu, Gabriele Farina, Asuman Ozdaglar","doi":"arxiv-2407.20351","DOIUrl":"https://doi.org/arxiv-2407.20351","url":null,"abstract":"LiteEFG is an efficient library with easy-to-use Python bindings, which can\u0000solve multiplayer extensive-form games (EFGs). LiteEFG enables the user to\u0000express computation graphs in Python to define updates on the game tree\u0000structure. The graph is then executed by the C++ backend, leading to\u0000significant speedups compared to running the algorithm in Python. Moreover, in\u0000LiteEFG, the user needs to only specify the computation graph of the update\u0000rule in a decision node of the game, and LiteEFG will automatically distribute\u0000the update rule to each decision node and handle the structure of the\u0000imperfect-information game.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872075","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
Approval-Based Committee Voting under Uncertainty 不确定性条件下以批准为基础的委员会表决
arXiv - CS - Computer Science and Game Theory Pub Date : 2024-07-28 DOI: arxiv-2407.19391
Hariz Aziz, Venkateswara Rao Kagita, Baharak Rastegari, Mashbat Suzuki
{"title":"Approval-Based Committee Voting under Uncertainty","authors":"Hariz Aziz, Venkateswara Rao Kagita, Baharak Rastegari, Mashbat Suzuki","doi":"arxiv-2407.19391","DOIUrl":"https://doi.org/arxiv-2407.19391","url":null,"abstract":"We study approval-based committee voting in which a target number of\u0000candidates are selected based on voters' approval preferences over candidates.\u0000In contrast to most of the work, we consider the setting where voters express\u0000uncertain approval preferences and explore four different types of uncertain\u0000approval preference models. For each model, we study the problems such as\u0000computing a committee with the highest probability of satisfying axioms such as\u0000justified representation.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872076","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
Discovering Consistent Subelections 发现一致的子选择
arXiv - CS - Computer Science and Game Theory Pub Date : 2024-07-26 DOI: arxiv-2407.18767
Łukasz Janeczko, Jérôme Lang, Grzegorz Lisowski, Stanisław Szufa
{"title":"Discovering Consistent Subelections","authors":"Łukasz Janeczko, Jérôme Lang, Grzegorz Lisowski, Stanisław Szufa","doi":"arxiv-2407.18767","DOIUrl":"https://doi.org/arxiv-2407.18767","url":null,"abstract":"We show how hidden interesting subelections can be discovered in ordinal\u0000elections. An interesting subelection consists of a reasonably large set of\u0000voters and a reasonably large set of candidates such that the former have a\u0000consistent opinion about the latter. Consistency may take various forms but we\u0000focus on three: Identity (all selected voters rank all selected candidates the\u0000same way), antagonism (half of the selected voters rank candidates in some\u0000order and the other half in the reverse order), and clones (all selected voters\u0000rank all selected candidates contiguously in the original election). We first\u0000study the computation of such hidden subelections. Second, we analyze synthetic\u0000and real-life data, and find that identifying hidden consistent subelections\u0000allows us to uncover some relevant concepts.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871863","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
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