Ocan SankurDEVINE, UR, Thierry JéronDEVINE, UR, Nicolas MarkeyDEVINE, UR, David MentréMERCE-France, Reiya Noguchi
We consider the automatic online synthesis of black-box test cases from functional requirements specified as automata for reactive implementations. The goal of the tester is to reach some given state, so as to satisfy a coverage criterion, while monitoring the violation of the requirements. We develop an approach based on Monte Carlo Tree Search, which is a classical technique in reinforcement learning for efficiently selecting promising inputs. Seeing the automata requirements as a game between the implementation and the tester, we develop a heuristic by biasing the search towards inputs that are promising in this game. We experimentally show that our heuristic accelerates the convergence of the Monte Carlo Tree Search algorithm, thus improving the performance of testing.
{"title":"Online Test Synthesis From Requirements: Enhancing Reinforcement Learning with Game Theory","authors":"Ocan SankurDEVINE, UR, Thierry JéronDEVINE, UR, Nicolas MarkeyDEVINE, UR, David MentréMERCE-France, Reiya Noguchi","doi":"arxiv-2407.18994","DOIUrl":"https://doi.org/arxiv-2407.18994","url":null,"abstract":"We consider the automatic online synthesis of black-box test cases from\u0000functional requirements specified as automata for reactive implementations. The\u0000goal of the tester is to reach some given state, so as to satisfy a coverage\u0000criterion, while monitoring the violation of the requirements. We develop an\u0000approach based on Monte Carlo Tree Search, which is a classical technique in\u0000reinforcement learning for efficiently selecting promising inputs. Seeing the\u0000automata requirements as a game between the implementation and the tester, we\u0000develop a heuristic by biasing the search towards inputs that are promising in\u0000this game. We experimentally show that our heuristic accelerates the\u0000convergence of the Monte Carlo Tree Search algorithm, thus improving the\u0000performance of testing.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871864","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 consider a model of learning and evolution in games whose action sets are endowed with a partition-based similarity structure intended to capture exogenous similarities between strategies. In this model, revising agents have a higher probability of comparing their current strategy with other strategies that they deem similar, and they switch to the observed strategy with probability proportional to its payoff excess. Because of this implicit bias toward similar strategies, the resulting dynamics - which we call the nested replicator dynamics - do not satisfy any of the standard monotonicity postulates for imitative game dynamics; nonetheless, we show that they retain the main long-run rationality properties of the replicator dynamics, albeit at quantitatively different rates. We also show that the induced dynamics can be viewed as a stimulus-response model in the spirit of Erev & Roth (1998), with choice probabilities given by the nested logit choice rule of Ben-Akiva (1973) and McFadden (1978). This result generalizes an existing relation between the replicator dynamics and the exponential weights algorithm in online learning, and provides an additional layer of interpretation to our analysis and results.
{"title":"Nested replicator dynamics, nested logit choice, and similarity-based learning","authors":"Panayotis Mertikopoulos, William H. Sandholm","doi":"arxiv-2407.17815","DOIUrl":"https://doi.org/arxiv-2407.17815","url":null,"abstract":"We consider a model of learning and evolution in games whose action sets are\u0000endowed with a partition-based similarity structure intended to capture\u0000exogenous similarities between strategies. In this model, revising agents have\u0000a higher probability of comparing their current strategy with other strategies\u0000that they deem similar, and they switch to the observed strategy with\u0000probability proportional to its payoff excess. Because of this implicit bias\u0000toward similar strategies, the resulting dynamics - which we call the nested\u0000replicator dynamics - do not satisfy any of the standard monotonicity\u0000postulates for imitative game dynamics; nonetheless, we show that they retain\u0000the main long-run rationality properties of the replicator dynamics, albeit at\u0000quantitatively different rates. We also show that the induced dynamics can be\u0000viewed as a stimulus-response model in the spirit of Erev & Roth (1998), with\u0000choice probabilities given by the nested logit choice rule of Ben-Akiva (1973)\u0000and McFadden (1978). This result generalizes an existing relation between the\u0000replicator dynamics and the exponential weights algorithm in online learning,\u0000and provides an additional layer of interpretation to our analysis and results.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141781627","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 tournament organizer must select one of $n$ possible teams as the winner of a competition after observing all $binom{n}{2}$ matches between them. The organizer would like to find a tournament rule that simultaneously satisfies the following desiderata. It must be Condorcet-consistent (henceforth, CC), meaning it selects as the winner the unique team that beats all other teams (if one exists). It must also be strongly non-manipulable for groups of size $k$ at probability $alpha$ (henceforth, k-SNM-$alpha$), meaning that no subset of $leq k$ teams can fix the matches among themselves in order to increase the chances any of it's members being selected by more than $alpha$. Our contributions are threefold. First, wee consider a natural generalization of the Randomized Single Elimination Bracket rule from [Schneider et al. 2017] to $d$-ary trees and provide upper bounds to its manipulability. Then, we propose a novel tournament rule that is CC and 3-SNM-1/2, a strict improvement upon the concurrent work of [Dinev and Weinberg, 2022] who proposed a CC and 3-SNM-31/60 rule. Finally, we initiate the study of reductions among tournament rules.
比赛组织者必须在观察了 $binom{n}{2}$ 之间的所有比赛后，从 $n$ 可能的队伍中选出一支队伍作为比赛的获胜者。组织者希望找到一种比赛规则，同时满足以下要求。它必须是康德赛特一致的（以下简称 CC），即它能选出击败所有其他队伍（如果存在的话）的唯一一支队伍作为获胜者。对于概率为 $alpha$ 的大小为 $k$ 的小组来说，它还必须是强不可操纵的（以下简称为 k-SNM-$alpha$），也就是说，没有任何一个由 $leq k$ 小组组成的子集可以固定它们之间的匹配，以增加其任何一个成员被选中的概率超过 $alpha$。我们的贡献有三方面。首先，我们考虑将 [Schneider 等人，2017] 中的 "随机单败淘汰赛"（Randomized Single Elimination Bracket）规则自然推广到 $d$-ary 树，并提供其可操作性的上限。然后，我们提出了一个 CC 和 3-SNM-1/2 的新锦标赛规则，这是对 [Dinev and Weinberg, 2022] 目前工作的严格改进，后者提出了一个 CC 和 3-SNM-31/60 规则。最后，我们开始研究锦标赛规则之间的还原。
{"title":"On Approximately Strategy-Proof Tournament Rules for Collusions of Size at Least Three","authors":"David Mikšaník, Ariel Schvartzman, Jan Soukup","doi":"arxiv-2407.17569","DOIUrl":"https://doi.org/arxiv-2407.17569","url":null,"abstract":"A tournament organizer must select one of $n$ possible teams as the winner of\u0000a competition after observing all $binom{n}{2}$ matches between them. The\u0000organizer would like to find a tournament rule that simultaneously satisfies\u0000the following desiderata. It must be Condorcet-consistent (henceforth, CC),\u0000meaning it selects as the winner the unique team that beats all other teams (if\u0000one exists). It must also be strongly non-manipulable for groups of size $k$ at\u0000probability $alpha$ (henceforth, k-SNM-$alpha$), meaning that no subset of\u0000$leq k$ teams can fix the matches among themselves in order to increase the\u0000chances any of it's members being selected by more than $alpha$. Our\u0000contributions are threefold. First, wee consider a natural generalization of\u0000the Randomized Single Elimination Bracket rule from [Schneider et al. 2017] to\u0000$d$-ary trees and provide upper bounds to its manipulability. Then, we propose\u0000a novel tournament rule that is CC and 3-SNM-1/2, a strict improvement upon the\u0000concurrent work of [Dinev and Weinberg, 2022] who proposed a CC and 3-SNM-31/60\u0000rule. Finally, we initiate the study of reductions among tournament rules.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141781623","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}
Alex Clinton, Yiding Chen, Xiaojin Zhu, Kirthevasan Kandasamy
We study a collaborative learning problem where $m$ agents estimate a vector $muinmathbb{R}^d$ by collecting samples from normal distributions, with each agent $i$ incurring a cost $c_{i,k} in (0, infty]$ to sample from the $k^{text{th}}$ distribution $mathcal{N}(mu_k, sigma^2)$. Instead of working on their own, agents can collect data that is cheap to them, and share it with others in exchange for data that is expensive or even inaccessible to them, thereby simultaneously reducing data collection costs and estimation error. However, when agents have different collection costs, we need to first decide how to fairly divide the work of data collection so as to benefit all agents. Moreover, in naive sharing protocols, strategic agents may under-collect and/or fabricate data, leading to socially undesirable outcomes. Our mechanism addresses these challenges by combining ideas from cooperative and non-cooperative game theory. We use ideas from axiomatic bargaining to divide the cost of data collection. Given such a solution, we develop a Nash incentive-compatible (NIC) mechanism to enforce truthful reporting. We achieve a $mathcal{O}(sqrt{m})$ approximation to the minimum social penalty (sum of agent estimation errors and data collection costs) in the worst case, and a $mathcal{O}(1)$ approximation under favorable conditions. We complement this with a hardness result, showing that $Omega(sqrt{m})$ is unavoidable in any NIC mechanism.
{"title":"Data Sharing for Mean Estimation Among Heterogeneous Strategic Agents","authors":"Alex Clinton, Yiding Chen, Xiaojin Zhu, Kirthevasan Kandasamy","doi":"arxiv-2407.15881","DOIUrl":"https://doi.org/arxiv-2407.15881","url":null,"abstract":"We study a collaborative learning problem where $m$ agents estimate a vector\u0000$muinmathbb{R}^d$ by collecting samples from normal distributions, with each\u0000agent $i$ incurring a cost $c_{i,k} in (0, infty]$ to sample from the\u0000$k^{text{th}}$ distribution $mathcal{N}(mu_k, sigma^2)$. Instead of working\u0000on their own, agents can collect data that is cheap to them, and share it with\u0000others in exchange for data that is expensive or even inaccessible to them,\u0000thereby simultaneously reducing data collection costs and estimation error.\u0000However, when agents have different collection costs, we need to first decide\u0000how to fairly divide the work of data collection so as to benefit all agents.\u0000Moreover, in naive sharing protocols, strategic agents may under-collect and/or\u0000fabricate data, leading to socially undesirable outcomes. Our mechanism\u0000addresses these challenges by combining ideas from cooperative and\u0000non-cooperative game theory. We use ideas from axiomatic bargaining to divide\u0000the cost of data collection. Given such a solution, we develop a Nash\u0000incentive-compatible (NIC) mechanism to enforce truthful reporting. We achieve\u0000a $mathcal{O}(sqrt{m})$ approximation to the minimum social penalty (sum of\u0000agent estimation errors and data collection costs) in the worst case, and a\u0000$mathcal{O}(1)$ approximation under favorable conditions. We complement this\u0000with a hardness result, showing that $Omega(sqrt{m})$ is unavoidable in any\u0000NIC mechanism.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141781624","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}
Abhishek N. Kulkarni, Matthew S. Cohen, Charles A. Kamhoua, Jie Fu
Deception plays a crucial role in strategic interactions with incomplete information. Motivated by security applications, we study a class of two-player turn-based deterministic games with one-sided incomplete information, in which player 1 (P1) aims to prevent player 2 (P2) from reaching a set of target states. In addition to actions, P1 can place two kinds of deception resources: "traps" and "fake targets" to disinform P2 about the transition dynamics and payoff of the game. Traps "hide the real" by making trap states appear normal, while fake targets "reveal the fiction" by advertising non-target states as targets. We are interested in jointly synthesizing optimal decoy placement and deceptive defense strategies for P1 that exploits P2's misinformation. We introduce a novel hypergame on graph model and two solution concepts: stealthy deceptive sure winning and stealthy deceptive almost-sure winning. These identify states from which P1 can prevent P2 from reaching the target in a finite number of steps or with probability one without allowing P2 to become aware that it is being deceived. Consequently, determining the optimal decoy placement corresponds to maximizing the size of P1's deceptive winning region. Considering the combinatorial complexity of exploring all decoy allocations, we utilize compositional synthesis concepts to show that the objective function for decoy placement is monotone, non-decreasing, and, in certain cases, sub- or super-modular. This leads to a greedy algorithm for decoy placement, achieving a $(1 - 1/e)$-approximation when the objective function is sub- or super-modular. The proposed hypergame model and solution concepts contribute to understanding the optimal deception resource allocation and deception strategies in various security applications.
{"title":"Integrated Resource Allocation and Strategy Synthesis in Safety Games on Graphs with Deception","authors":"Abhishek N. Kulkarni, Matthew S. Cohen, Charles A. Kamhoua, Jie Fu","doi":"arxiv-2407.14436","DOIUrl":"https://doi.org/arxiv-2407.14436","url":null,"abstract":"Deception plays a crucial role in strategic interactions with incomplete\u0000information. Motivated by security applications, we study a class of two-player\u0000turn-based deterministic games with one-sided incomplete information, in which\u0000player 1 (P1) aims to prevent player 2 (P2) from reaching a set of target\u0000states. In addition to actions, P1 can place two kinds of deception resources:\u0000\"traps\" and \"fake targets\" to disinform P2 about the transition dynamics and\u0000payoff of the game. Traps \"hide the real\" by making trap states appear normal,\u0000while fake targets \"reveal the fiction\" by advertising non-target states as\u0000targets. We are interested in jointly synthesizing optimal decoy placement and\u0000deceptive defense strategies for P1 that exploits P2's misinformation. We\u0000introduce a novel hypergame on graph model and two solution concepts: stealthy\u0000deceptive sure winning and stealthy deceptive almost-sure winning. These\u0000identify states from which P1 can prevent P2 from reaching the target in a\u0000finite number of steps or with probability one without allowing P2 to become\u0000aware that it is being deceived. Consequently, determining the optimal decoy\u0000placement corresponds to maximizing the size of P1's deceptive winning region.\u0000Considering the combinatorial complexity of exploring all decoy allocations, we\u0000utilize compositional synthesis concepts to show that the objective function\u0000for decoy placement is monotone, non-decreasing, and, in certain cases, sub- or\u0000super-modular. This leads to a greedy algorithm for decoy placement, achieving\u0000a $(1 - 1/e)$-approximation when the objective function is sub- or\u0000super-modular. The proposed hypergame model and solution concepts contribute to\u0000understanding the optimal deception resource allocation and deception\u0000strategies in various security applications.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"64 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745265","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}
Aymeric Capitaine, Etienne Boursier, Antoine Scheid, Eric Moulines, Michael I. Jordan, El-Mahdi El-Mhamdi, Alain Durmus
Collaborative learning offers a promising avenue for leveraging decentralized data. However, collaboration in groups of strategic learners is not a given. In this work, we consider strategic agents who wish to train a model together but have sampling distributions of different quality. The collaboration is organized by a benevolent aggregator who gathers samples so as to maximize total welfare, but is unaware of data quality. This setting allows us to shed light on the deleterious effect of adverse selection in collaborative learning. More precisely, we demonstrate that when data quality indices are private, the coalition may undergo a phenomenon known as unravelling, wherein it shrinks up to the point that it becomes empty or solely comprised of the worst agent. We show how this issue can be addressed without making use of external transfers, by proposing a novel method inspired by probabilistic verification. This approach makes the grand coalition a Nash equilibrium with high probability despite information asymmetry, thereby breaking unravelling.
{"title":"Unravelling in Collaborative Learning","authors":"Aymeric Capitaine, Etienne Boursier, Antoine Scheid, Eric Moulines, Michael I. Jordan, El-Mahdi El-Mhamdi, Alain Durmus","doi":"arxiv-2407.14332","DOIUrl":"https://doi.org/arxiv-2407.14332","url":null,"abstract":"Collaborative learning offers a promising avenue for leveraging decentralized\u0000data. However, collaboration in groups of strategic learners is not a given. In\u0000this work, we consider strategic agents who wish to train a model together but\u0000have sampling distributions of different quality. The collaboration is\u0000organized by a benevolent aggregator who gathers samples so as to maximize\u0000total welfare, but is unaware of data quality. This setting allows us to shed\u0000light on the deleterious effect of adverse selection in collaborative learning.\u0000More precisely, we demonstrate that when data quality indices are private, the\u0000coalition may undergo a phenomenon known as unravelling, wherein it shrinks up\u0000to the point that it becomes empty or solely comprised of the worst agent. We\u0000show how this issue can be addressed without making use of external transfers,\u0000by proposing a novel method inspired by probabilistic verification. This\u0000approach makes the grand coalition a Nash equilibrium with high probability\u0000despite information asymmetry, thereby breaking unravelling.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745266","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}
Minghao Pan, Akaki Mamageishvili, Christoph Schlegel
We show that in the single-parameter mechanism design environment, the only non-wasteful, symmetric, incentive compatible and sibyl-proof mechanism is a second price auction with symmetric tie-breaking. Thus, if there is private information, lotteries or other mechanisms that do not always allocate to a highest-value bidder are not sibyl-proof or not incentive compatible.
{"title":"On sibyl-proof mechanisms","authors":"Minghao Pan, Akaki Mamageishvili, Christoph Schlegel","doi":"arxiv-2407.14485","DOIUrl":"https://doi.org/arxiv-2407.14485","url":null,"abstract":"We show that in the single-parameter mechanism design environment, the only\u0000non-wasteful, symmetric, incentive compatible and sibyl-proof mechanism is a\u0000second price auction with symmetric tie-breaking. Thus, if there is private\u0000information, lotteries or other mechanisms that do not always allocate to a\u0000highest-value bidder are not sibyl-proof or not incentive compatible.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745264","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}
Itai Arieli, Yakov Babichenko, Dimitry Shaiderman, Xianwen Shi
We propose a dynamic product adoption persuasion model involving an impatient partially informed sender who gradually learns the state. In this model, the sender gathers information over time, and hence her posteriors' sequence forms a discrete-time martingale. The sender commits to a dynamic revelation policy to persuade the agent to adopt a product. We demonstrate that under the assumption that the sender's martingale possesses Blackwell-preserving kernels, the family of optimal strategies for the sender takes an interval form; namely, in every period the set of martingale realizations in which adoption occurs is an interval. Utilizing this, we prove that if the sender is sufficiently impatient, then under a random walk martingale, the optimal policy is fully transparent up to the moment of adoption; namely, the sender reveals the entire information she privately holds in every period.
{"title":"Persuading while Learning","authors":"Itai Arieli, Yakov Babichenko, Dimitry Shaiderman, Xianwen Shi","doi":"arxiv-2407.13964","DOIUrl":"https://doi.org/arxiv-2407.13964","url":null,"abstract":"We propose a dynamic product adoption persuasion model involving an impatient\u0000partially informed sender who gradually learns the state. In this model, the\u0000sender gathers information over time, and hence her posteriors' sequence forms\u0000a discrete-time martingale. The sender commits to a dynamic revelation policy\u0000to persuade the agent to adopt a product. We demonstrate that under the\u0000assumption that the sender's martingale possesses Blackwell-preserving kernels,\u0000the family of optimal strategies for the sender takes an interval form; namely,\u0000in every period the set of martingale realizations in which adoption occurs is\u0000an interval. Utilizing this, we prove that if the sender is sufficiently\u0000impatient, then under a random walk martingale, the optimal policy is fully\u0000transparent up to the moment of adoption; namely, the sender reveals the entire\u0000information she privately holds in every period.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745267","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}
Ranked Choice Voting (RCV) and Single Transferable Voting (STV) are widely valued; but are complex to understand due to intricate per-round vote transfers. Questions like determining how far a candidate is from winning or identifying effective election strategies are computationally challenging as minor changes in voter rankings can lead to significant ripple effects - for example, lending support to a losing candidate can prevent their votes from transferring to a more competitive opponent. We study optimal strategies - persuading voters to change their ballots or adding new voters - both algorithmically and theoretically. Algorithmically, we develop efficient methods to reduce election instances while maintaining optimization accuracy, effectively circumventing the computational complexity barrier. Theoretically, we analyze the effectiveness of strategies under both perfect and imperfect polling information. Our algorithmic approach applies to the ranked-choice polling data on the US 2024 Republican Primary, finding, for example, that several candidates would have been optimally served by boosting another candidate instead of themselves.
{"title":"Optimal Strategies in Ranked-Choice Voting","authors":"Sanyukta Deshpande, Nikhil Garg, Sheldon Jacobson","doi":"arxiv-2407.13661","DOIUrl":"https://doi.org/arxiv-2407.13661","url":null,"abstract":"Ranked Choice Voting (RCV) and Single Transferable Voting (STV) are widely\u0000valued; but are complex to understand due to intricate per-round vote\u0000transfers. Questions like determining how far a candidate is from winning or\u0000identifying effective election strategies are computationally challenging as\u0000minor changes in voter rankings can lead to significant ripple effects - for\u0000example, lending support to a losing candidate can prevent their votes from\u0000transferring to a more competitive opponent. We study optimal strategies -\u0000persuading voters to change their ballots or adding new voters - both\u0000algorithmically and theoretically. Algorithmically, we develop efficient\u0000methods to reduce election instances while maintaining optimization accuracy,\u0000effectively circumventing the computational complexity barrier. Theoretically,\u0000we analyze the effectiveness of strategies under both perfect and imperfect\u0000polling information. Our algorithmic approach applies to the ranked-choice\u0000polling data on the US 2024 Republican Primary, finding, for example, that\u0000several candidates would have been optimally served by boosting another\u0000candidate instead of themselves.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745268","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 fairly and truthfully allocating $m$ indivisible items to $n$ agents with additive preferences. Specifically, we consider truthful mechanisms outputting allocations that satisfy EF$^{+u}_{-v}$, where, in an EF$^{+u}_{-v}$ allocation, for any pair of agents $i$ and $j$, agent $i$ will not envy agent $j$ if $u$ items were added to $i$'s bundle and $v$ items were removed from $j$'s bundle. Previous work easily indicates that, when restricted to deterministic mechanisms, truthfulness will lead to a poor guarantee of fairness: even with two agents, for any $u$ and $v$, EF$^{+u}_{-v}$ cannot be guaranteed by truthful mechanisms when the number of items is large enough. In this work, we focus on randomized mechanisms, where we consider ex-ante truthfulness and ex-post fairness. For two agents, we present a truthful mechanism that achieves EF$^{+0}_{-1}$ (i.e., the well-studied fairness notion EF$1$). For three agents, we present a truthful mechanism that achieves EF$^{+1}_{-1}$. For $n$ agents in general, we show that there exist truthful mechanisms that achieve EF$^{+u}_{-v}$ for some $u$ and $v$ that depend only on $n$ (not $m$). We further consider fair and truthful mechanisms that also satisfy the standard efficiency guarantee: Pareto-optimality. We provide a mechanism that simultaneously achieves truthfulness, EF$1$, and Pareto-optimality for bi-valued utilities (where agents' valuation on each item is either $p$ or $q$ for some $p>qgeq0$). For tri-valued utilities (where agents' valuations on each item belong to ${p,q,r}$ for some $p>q>rgeq0$) and any $u,v$, we show that truthfulness is incompatible with EF$^{+u}_{-v}$ and Pareto-optimality even for two agents.
{"title":"Truthful and Almost Envy-Free Mechanism of Allocating Indivisible Goods: the Power of Randomness","authors":"Xiaolin Bu, Biaoshuai Tao","doi":"arxiv-2407.13634","DOIUrl":"https://doi.org/arxiv-2407.13634","url":null,"abstract":"We study the problem of fairly and truthfully allocating $m$ indivisible\u0000items to $n$ agents with additive preferences. Specifically, we consider\u0000truthful mechanisms outputting allocations that satisfy EF$^{+u}_{-v}$, where,\u0000in an EF$^{+u}_{-v}$ allocation, for any pair of agents $i$ and $j$, agent $i$\u0000will not envy agent $j$ if $u$ items were added to $i$'s bundle and $v$ items\u0000were removed from $j$'s bundle. Previous work easily indicates that, when\u0000restricted to deterministic mechanisms, truthfulness will lead to a poor\u0000guarantee of fairness: even with two agents, for any $u$ and $v$,\u0000EF$^{+u}_{-v}$ cannot be guaranteed by truthful mechanisms when the number of\u0000items is large enough. In this work, we focus on randomized mechanisms, where\u0000we consider ex-ante truthfulness and ex-post fairness. For two agents, we\u0000present a truthful mechanism that achieves EF$^{+0}_{-1}$ (i.e., the\u0000well-studied fairness notion EF$1$). For three agents, we present a truthful\u0000mechanism that achieves EF$^{+1}_{-1}$. For $n$ agents in general, we show that\u0000there exist truthful mechanisms that achieve EF$^{+u}_{-v}$ for some $u$ and\u0000$v$ that depend only on $n$ (not $m$). We further consider fair and truthful mechanisms that also satisfy the\u0000standard efficiency guarantee: Pareto-optimality. We provide a mechanism that\u0000simultaneously achieves truthfulness, EF$1$, and Pareto-optimality for\u0000bi-valued utilities (where agents' valuation on each item is either $p$ or $q$\u0000for some $p>qgeq0$). For tri-valued utilities (where agents' valuations on\u0000each item belong to ${p,q,r}$ for some $p>q>rgeq0$) and any $u,v$, we show\u0000that truthfulness is incompatible with EF$^{+u}_{-v}$ and Pareto-optimality\u0000even for two agents.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745271","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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