We study the problem of fairly allocating indivisible goods among a set of agents. Our focus is on the existence of allocations that give each agent their maximin fair share--the value they are guaranteed if they divide the goods into as many bundles as there are agents, and receive their lowest valued bundle. An MMS allocation is one where every agent receives at least their maximin fair share. We examine the existence of such allocations when agents have cost utilities. In this setting, each item has an associated cost, and an agent's valuation for an item is the cost of the item if it is useful to them, and zero otherwise. Our main results indicate that cost utilities are a promising restriction for achieving MMS. We show that for the case of three agents with cost utilities, an MMS allocation always exists. We also show that when preferences are restricted slightly further--to what we call laminar set approvals--we can guarantee MMS allocations for any number of agents. Finally, we explore if it is possible to guarantee each agent their maximin fair share while using a strategyproof mechanism.
{"title":"Maximin Fair Allocation of Indivisible Items under Cost Utilities","authors":"Sirin Botan, Angus Ritossa, Mashbat Suzuki, Toby Walsh","doi":"arxiv-2407.13171","DOIUrl":"https://doi.org/arxiv-2407.13171","url":null,"abstract":"We study the problem of fairly allocating indivisible goods among a set of\u0000agents. Our focus is on the existence of allocations that give each agent their\u0000maximin fair share--the value they are guaranteed if they divide the goods into\u0000as many bundles as there are agents, and receive their lowest valued bundle. An\u0000MMS allocation is one where every agent receives at least their maximin fair\u0000share. We examine the existence of such allocations when agents have cost\u0000utilities. In this setting, each item has an associated cost, and an agent's\u0000valuation for an item is the cost of the item if it is useful to them, and zero\u0000otherwise. Our main results indicate that cost utilities are a promising restriction for\u0000achieving MMS. We show that for the case of three agents with cost utilities,\u0000an MMS allocation always exists. We also show that when preferences are\u0000restricted slightly further--to what we call laminar set approvals--we can\u0000guarantee MMS allocations for any number of agents. Finally, we explore if it\u0000is possible to guarantee each agent their maximin fair share while using a\u0000strategyproof mechanism.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745269","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 establish a compatibility between fairness and efficiency, captured via Nash Social Welfare (NSW), under the broad class of subadditive valuations. We prove that, for subadditive valuations, there always exists a partial allocation that is envy-free up to the removal of any good (EFx) and has NSW at least half of the optimal; here, optimality is considered across all allocations, fair or otherwise. We also prove, for subadditive valuations, the universal existence of complete allocations that are envy-free up to one good (EF1) and also achieve a factor $1/2$ approximation to the optimal NSW. Our EF1 result resolves an open question posed by Garg et al. (STOC 2023). In addition, we develop a polynomial-time algorithm which, given an arbitrary allocation ~A as input, returns an EF1 allocation with NSW at least $1/3$ times that of ~A. Therefore, our results imply that the EF1 criterion can be attained simultaneously with a constant-factor approximation to optimal NSW in polynomial time (with demand queries), for subadditive valuations. The previously best-known approximation factor for optimal NSW, under EF1 and among $n$ agents, was $O(n)$ - we improve this bound to $O(1)$. It is known that EF1 and exact Pareto efficiency (PO) are incompatible with subadditive valuations. Complementary to this negative result, the current work shows that we regain compatibility by just considering a factor $1/2$ approximation: EF1 can be achieved in conjunction with $frac{1}{2}$-PO under subadditive valuations. As such, our results serve as a general tool that can be used as a black box to convert any efficient outcome into a fair one, with only a marginal decrease in efficiency.
{"title":"Compatibility of Fairness and Nash Welfare under Subadditive Valuations","authors":"Siddharth Barman, Mashbat Suzuki","doi":"arxiv-2407.12461","DOIUrl":"https://doi.org/arxiv-2407.12461","url":null,"abstract":"We establish a compatibility between fairness and efficiency, captured via\u0000Nash Social Welfare (NSW), under the broad class of subadditive valuations. We\u0000prove that, for subadditive valuations, there always exists a partial\u0000allocation that is envy-free up to the removal of any good (EFx) and has NSW at\u0000least half of the optimal; here, optimality is considered across all\u0000allocations, fair or otherwise. We also prove, for subadditive valuations, the\u0000universal existence of complete allocations that are envy-free up to one good\u0000(EF1) and also achieve a factor $1/2$ approximation to the optimal NSW. Our EF1\u0000result resolves an open question posed by Garg et al. (STOC 2023). In addition, we develop a polynomial-time algorithm which, given an arbitrary\u0000allocation ~A as input, returns an EF1 allocation with NSW at least $1/3$\u0000times that of ~A. Therefore, our results imply that the EF1 criterion can be\u0000attained simultaneously with a constant-factor approximation to optimal NSW in\u0000polynomial time (with demand queries), for subadditive valuations. The\u0000previously best-known approximation factor for optimal NSW, under EF1 and among\u0000$n$ agents, was $O(n)$ - we improve this bound to $O(1)$. It is known that EF1 and exact Pareto efficiency (PO) are incompatible with\u0000subadditive valuations. Complementary to this negative result, the current work\u0000shows that we regain compatibility by just considering a factor $1/2$\u0000approximation: EF1 can be achieved in conjunction with $frac{1}{2}$-PO under\u0000subadditive valuations. As such, our results serve as a general tool that can\u0000be used as a black box to convert any efficient outcome into a fair one, with\u0000only a marginal decrease in efficiency.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745398","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 revenue maximization for agents with additive preferences, subject to downward-closed constraints on the set of feasible allocations. In seminal work, Alaei~cite{alaei2014bayesian} introduced a powerful multi-to-single agent reduction based on an ex-ante relaxation of the multi-agent problem. This reduction employs a rounding procedure which is an online contention resolution scheme (OCRS) in disguise, a now widely-used method for rounding fractional solutions in online Bayesian and stochastic optimization problems. In this paper, we leverage our vantage point, 10 years after the work of Alaei, with a rich OCRS toolkit and modern approaches to analyzing multi-agent mechanisms; we introduce a general framework for designing non-sequential and sequential multi-agent, revenue-maximizing mechanisms, capturing a wide variety of problems Alaei's framework could not address. Our framework uses an emph{interim} relaxation, that is rounded to a feasible mechanism using what we call a two-level OCRS, which allows for some structured dependence between the activation of its input elements. For a wide family of constraints, we can construct such schemes using existing OCRSs as a black box; for other constraints, such as knapsack, we construct such schemes from scratch. We demonstrate numerous applications of our framework, including a sequential mechanism that guarantees a $frac{2e}{e-1} approx 3.16$ approximation to the optimal revenue for the case of additive agents subject to matroid feasibility constraints. We also show how our framework can be easily extended to multi-parameter procurement auctions, where we provide an OCRS for Stochastic Knapsack that might be of independent interest.
{"title":"Mechanism Design via the Interim Relaxation","authors":"Kshipra Bhawalkar, Marios Mertzanidis, Divyarthi Mohan, Alexandros Psomas","doi":"arxiv-2407.12699","DOIUrl":"https://doi.org/arxiv-2407.12699","url":null,"abstract":"We study revenue maximization for agents with additive preferences, subject\u0000to downward-closed constraints on the set of feasible allocations. In seminal\u0000work, Alaei~cite{alaei2014bayesian} introduced a powerful multi-to-single\u0000agent reduction based on an ex-ante relaxation of the multi-agent problem. This\u0000reduction employs a rounding procedure which is an online contention resolution\u0000scheme (OCRS) in disguise, a now widely-used method for rounding fractional\u0000solutions in online Bayesian and stochastic optimization problems. In this\u0000paper, we leverage our vantage point, 10 years after the work of Alaei, with a\u0000rich OCRS toolkit and modern approaches to analyzing multi-agent mechanisms; we\u0000introduce a general framework for designing non-sequential and sequential\u0000multi-agent, revenue-maximizing mechanisms, capturing a wide variety of\u0000problems Alaei's framework could not address. Our framework uses an\u0000emph{interim} relaxation, that is rounded to a feasible mechanism using what\u0000we call a two-level OCRS, which allows for some structured dependence between\u0000the activation of its input elements. For a wide family of constraints, we can\u0000construct such schemes using existing OCRSs as a black box; for other\u0000constraints, such as knapsack, we construct such schemes from scratch. We\u0000demonstrate numerous applications of our framework, including a sequential\u0000mechanism that guarantees a $frac{2e}{e-1} approx 3.16$ approximation to the\u0000optimal revenue for the case of additive agents subject to matroid feasibility\u0000constraints. We also show how our framework can be easily extended to\u0000multi-parameter procurement auctions, where we provide an OCRS for Stochastic\u0000Knapsack that might be of independent interest.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745270","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}
For decades, Simultaneous Ascending Auction (SAA) has been the most widely used mechanism for spectrum auctions, and it has recently gained popularity for allocating 5G licenses in many countries. Despite its relatively simple rules, SAA introduces a complex strategic game with an unknown optimal bidding strategy. Given the high stakes involved, with billions of euros sometimes on the line, developing an efficient bidding strategy is of utmost importance. In this work, we extend our previous method, a Simultaneous Move Monte-Carlo Tree Search (SM-MCTS) based algorithm named $SMS^{alpha}$ to incomplete information framework. For this purpose, we compare three determinization approaches which allow us to rely on complete information SM-MCTS. This algorithm addresses, in incomplete framework, the four key strategic issues of SAA: the exposure problem, the own price effect, budget constraints, and the eligibility management problem. Through extensive numerical experiments on instances of realistic size with an uncertain framework, we show that $SMS^{alpha}$ largely outperforms state-of-the-art algorithms by achieving higher expected utility while taking less risks, no matter which determinization method is chosen.
几十年来，同步递增拍卖（SAA）一直是最广泛使用的频谱拍卖机制，最近在许多国家的 5G 许可分配中也越来越受欢迎。尽管 SAA 的规则相对简单，但它引入了一个复杂的战略博弈，其最佳竞标策略尚不可知。由于涉及的赌注很大，有时甚至高达数十亿欧元，因此制定有效的竞标策略至关重要。在这项工作中，我们将之前的方法--基于同步移动蒙特卡洛树搜索（SM-MCTS）的算法（名为 $SMS^{alpha}$）扩展到了不完全信息框架。为此，我们比较了三种确定方法，它们允许我们依赖完整信息 SM-MCTS。该算法在不完全框架下解决了 SAA 的四个关键战略问题：风险暴露问题、自有价格效应、预算约束和资格管理问题。通过在不确定框架下对现实大小的实例进行大量数值实验，我们发现，无论选择哪种确定方法，$SMS^{alpha}$ 都能实现更高的预期效用，同时承担更少的风险，在很大程度上优于最先进的算法。
{"title":"Bidding efficiently in Simultaneous Ascending Auctions with incomplete information using Monte Carlo Tree Search and determinization","authors":"Alexandre Pacaud, Aurélien Bechler, Marceau Coupechoux","doi":"arxiv-2407.11715","DOIUrl":"https://doi.org/arxiv-2407.11715","url":null,"abstract":"For decades, Simultaneous Ascending Auction (SAA) has been the most widely\u0000used mechanism for spectrum auctions, and it has recently gained popularity for\u0000allocating 5G licenses in many countries. Despite its relatively simple rules,\u0000SAA introduces a complex strategic game with an unknown optimal bidding\u0000strategy. Given the high stakes involved, with billions of euros sometimes on\u0000the line, developing an efficient bidding strategy is of utmost importance. In\u0000this work, we extend our previous method, a Simultaneous Move Monte-Carlo Tree\u0000Search (SM-MCTS) based algorithm named $SMS^{alpha}$ to incomplete information\u0000framework. For this purpose, we compare three determinization approaches which\u0000allow us to rely on complete information SM-MCTS. This algorithm addresses, in\u0000incomplete framework, the four key strategic issues of SAA: the exposure\u0000problem, the own price effect, budget constraints, and the eligibility\u0000management problem. Through extensive numerical experiments on instances of\u0000realistic size with an uncertain framework, we show that $SMS^{alpha}$ largely\u0000outperforms state-of-the-art algorithms by achieving higher expected utility\u0000while taking less risks, no matter which determinization method is chosen.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"250 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141718534","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}
Linear Fisher market is one of the most fundamental economic models. The market is traditionally examined on the basis of individual's price-taking behavior. However, this assumption breaks in markets such as online advertising and e-commerce, where several oligopolists dominate the market and are able to compete with each other via strategic actions. Motivated by this, we study the price competition among sellers in linear Fisher markets. From an algorithmic game-theoretic perspective, we establish a model to analyze behaviors of buyers and sellers that are driven by utility-maximizing purposes and also constrained by computational tractability. The main economic observation is the role played by personalization: the classic benchmark market outcome, namely competitive equilibrium, remains to be a steady-state if every buyer must be treated "equally"; however, sellers have the incentive to personalize, and as a result the market would become more unpredictable and less efficient. In addition, we build a series of algorithmic and complexity results along the road to justify our modeling choices and reveal market structures. We find interesting connections between our model and other computational problems such as stable matching, network flow, etc. We believe these results and techniques are of independent interest.
{"title":"Price Competition in Linear Fisher Markets: Stability, Equilibrium and Personalization","authors":"Juncheng Li, Pingzhong Tang","doi":"arxiv-2407.11869","DOIUrl":"https://doi.org/arxiv-2407.11869","url":null,"abstract":"Linear Fisher market is one of the most fundamental economic models. The\u0000market is traditionally examined on the basis of individual's price-taking\u0000behavior. However, this assumption breaks in markets such as online advertising\u0000and e-commerce, where several oligopolists dominate the market and are able to\u0000compete with each other via strategic actions. Motivated by this, we study the\u0000price competition among sellers in linear Fisher markets. From an algorithmic\u0000game-theoretic perspective, we establish a model to analyze behaviors of buyers\u0000and sellers that are driven by utility-maximizing purposes and also constrained\u0000by computational tractability. The main economic observation is the role played\u0000by personalization: the classic benchmark market outcome, namely competitive\u0000equilibrium, remains to be a steady-state if every buyer must be treated\u0000\"equally\"; however, sellers have the incentive to personalize, and as a result\u0000the market would become more unpredictable and less efficient. In addition, we\u0000build a series of algorithmic and complexity results along the road to justify\u0000our modeling choices and reveal market structures. We find interesting\u0000connections between our model and other computational problems such as stable\u0000matching, network flow, etc. We believe these results and techniques are of\u0000independent interest.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141718533","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}
Proportional dynamics, originated from peer-to-peer file sharing systems, models a decentralized price-learning process in Fisher markets. Previously, items in the dynamics operate independently of one another, and each is assumed to belong to a different seller. In this paper, we show how it can be generalized to the setting where each seller brings multiple items and buyers allocate budgets at the granularity of sellers rather than individual items. The generalized dynamics consistently converges to the competitive equilibrium, and interestingly relates to the auto-bidding paradigm currently popular in online advertising auction markets. In contrast to peer-to-peer networks, the proportional rule is not imposed as a protocol in auto-bidding markets. Regarding this incentive concern, we show that buyers have a strong tendency to follow the rule, but it is easy for sellers to profitably deviate (given buyers' commitment to the rule). Based on this observation, we further study the seller-side deviation game and show that it admits a unique pure Nash equilibrium. Though it is generally different from the competitive equilibrium, we show that it attains a good fairness guarantee as long as the market is competitive enough and not severely monopolized.
{"title":"Proportional Dynamics in Linear Fisher Markets with Auto-bidding: Convergence, Incentives and Fairness","authors":"Juncheng Li, Pingzhong Tang","doi":"arxiv-2407.11872","DOIUrl":"https://doi.org/arxiv-2407.11872","url":null,"abstract":"Proportional dynamics, originated from peer-to-peer file sharing systems,\u0000models a decentralized price-learning process in Fisher markets. Previously,\u0000items in the dynamics operate independently of one another, and each is assumed\u0000to belong to a different seller. In this paper, we show how it can be\u0000generalized to the setting where each seller brings multiple items and buyers\u0000allocate budgets at the granularity of sellers rather than individual items.\u0000The generalized dynamics consistently converges to the competitive equilibrium,\u0000and interestingly relates to the auto-bidding paradigm currently popular in\u0000online advertising auction markets. In contrast to peer-to-peer networks, the\u0000proportional rule is not imposed as a protocol in auto-bidding markets.\u0000Regarding this incentive concern, we show that buyers have a strong tendency to\u0000follow the rule, but it is easy for sellers to profitably deviate (given\u0000buyers' commitment to the rule). Based on this observation, we further study\u0000the seller-side deviation game and show that it admits a unique pure Nash\u0000equilibrium. Though it is generally different from the competitive equilibrium,\u0000we show that it attains a good fairness guarantee as long as the market is\u0000competitive enough and not severely monopolized.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141718535","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}
Gergely Csáji, Tamás Király, Kenjiro Takazawa, Yu Yokoi
We investigate weighted settings of popular matching problems with matroid constraints. The concept of popularity was originally defined for matchings in bipartite graphs, where vertices have preferences over the incident edges. There are two standard models depending on whether vertices on one or both sides have preferences. A matching $M$ is popular if it does not lose a head-to-head election against any other matching. In our generalized models, one or both sides have matroid constraints, and a weight function is defined on the ground set. Our objective is to find a popular optimal matching, i.e., a maximum-weight matching that is popular among all maximum-weight matchings satisfying the matroid constraints. For both one- and two-sided preferences models, we provide efficient algorithms to find such solutions, combining algorithms for unweighted models with fundamental techniques from combinatorial optimization. The algorithm for the one-sided preferences model is further extended to a model where the weight function is generalized to an M$^natural$-concave utility function. Finally, we complement these tractability results by providing hardness results for the problems of finding a popular near-optimal matching. These hardness results hold even without matroid constraints and with very restricted weight functions.
{"title":"Popular Maximum-Utility Matchings with Matroid Constraints","authors":"Gergely Csáji, Tamás Király, Kenjiro Takazawa, Yu Yokoi","doi":"arxiv-2407.09798","DOIUrl":"https://doi.org/arxiv-2407.09798","url":null,"abstract":"We investigate weighted settings of popular matching problems with matroid\u0000constraints. The concept of popularity was originally defined for matchings in\u0000bipartite graphs, where vertices have preferences over the incident edges.\u0000There are two standard models depending on whether vertices on one or both\u0000sides have preferences. A matching $M$ is popular if it does not lose a\u0000head-to-head election against any other matching. In our generalized models,\u0000one or both sides have matroid constraints, and a weight function is defined on\u0000the ground set. Our objective is to find a popular optimal matching, i.e., a\u0000maximum-weight matching that is popular among all maximum-weight matchings\u0000satisfying the matroid constraints. For both one- and two-sided preferences\u0000models, we provide efficient algorithms to find such solutions, combining\u0000algorithms for unweighted models with fundamental techniques from combinatorial\u0000optimization. The algorithm for the one-sided preferences model is further\u0000extended to a model where the weight function is generalized to an\u0000M$^natural$-concave utility function. Finally, we complement these\u0000tractability results by providing hardness results for the problems of finding\u0000a popular near-optimal matching. These hardness results hold even without\u0000matroid constraints and with very restricted weight functions.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"68 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141718536","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}
Aggelos Kiayias, Elias Koutsoupias, Francisco Marmolejo-Cossio, Aikaterini-Panagiota Stouka
Proof-of-stake blockchain protocols have emerged as a compelling paradigm for organizing distributed ledger systems. In proof-of-stake (PoS), a subset of stakeholders participate in validating a growing ledger of transactions. For the safety and liveness of the underlying system, it is desirable for the set of validators to include multiple independent entities as well as represent a non-negligible percentage of the total stake issued. In this paper, we study a secondary form of participation in the transaction validation process, which takes the form of stake delegation, whereby an agent delegates their stake to an active validator who acts as a stake pool operator. We study payment schemes that reward agents as a function of their collective actions regarding stake pool operation and delegation. Such payment schemes serve as a mechanism to incentivize participation in the validation process while maintaining decentralization. We observe natural trade-offs between these objectives and the total expenditure required to run the relevant payment schemes. Ultimately, we provide a family of payment schemes which can strike different balances between these competing objectives at equilibrium in a Bayesian game theoretic framework.
{"title":"Balancing Participation and Decentralization in Proof-of-Stake Cryptocurrencies","authors":"Aggelos Kiayias, Elias Koutsoupias, Francisco Marmolejo-Cossio, Aikaterini-Panagiota Stouka","doi":"arxiv-2407.08686","DOIUrl":"https://doi.org/arxiv-2407.08686","url":null,"abstract":"Proof-of-stake blockchain protocols have emerged as a compelling paradigm for\u0000organizing distributed ledger systems. In proof-of-stake (PoS), a subset of\u0000stakeholders participate in validating a growing ledger of transactions. For\u0000the safety and liveness of the underlying system, it is desirable for the set\u0000of validators to include multiple independent entities as well as represent a\u0000non-negligible percentage of the total stake issued. In this paper, we study a\u0000secondary form of participation in the transaction validation process, which\u0000takes the form of stake delegation, whereby an agent delegates their stake to\u0000an active validator who acts as a stake pool operator. We study payment schemes\u0000that reward agents as a function of their collective actions regarding stake\u0000pool operation and delegation. Such payment schemes serve as a mechanism to\u0000incentivize participation in the validation process while maintaining\u0000decentralization. We observe natural trade-offs between these objectives and\u0000the total expenditure required to run the relevant payment schemes. Ultimately,\u0000we provide a family of payment schemes which can strike different balances\u0000between these competing objectives at equilibrium in a Bayesian game theoretic\u0000framework.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141609630","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}
Akaki Mamageishvili, Christoph Schlegel, Benny Sudakov, Danning Sui
We study the amount of maximal extractable value (MEV) captured by validators, as a function of searcher competition, in blockchains with competitive block building markets such as Ethereum. We argue that the core is a suitable solution concept in this context that makes robust predictions that are independent of implementation details or specific mechanisms chosen. We characterize how much value validators extract in the core and quantify the surplus share of validators as a function of searcher competition. Searchers can obtain at most the marginal value increase of the winning block relative to the best block that can be built without their bundles. Dually this gives a lower bound on the value extracted by the validator. If arbitrages are easy to find and many searchers find similar bundles, the validator gets paid all value almost surely, while searchers can capture most value if there is little searcher competition per arbitrage. For the case of passive block-proposers we study, moreover, mechanisms that implement core allocations in dominant strategies and find that for submodular value, there is a unique dominant-strategy incentive compatible core-selecting mechanism that gives each searcher exactly their marginal value contribution to the winning block. We validate our theoretical prediction empirically with aggregate bundle data and find a significant positive relation between the number of submitted backruns for the same opportunity and the median value captured by the proposer from the opportunity.
{"title":"Searcher Competition in Block Building","authors":"Akaki Mamageishvili, Christoph Schlegel, Benny Sudakov, Danning Sui","doi":"arxiv-2407.07474","DOIUrl":"https://doi.org/arxiv-2407.07474","url":null,"abstract":"We study the amount of maximal extractable value (MEV) captured by\u0000validators, as a function of searcher competition, in blockchains with\u0000competitive block building markets such as Ethereum. We argue that the core is\u0000a suitable solution concept in this context that makes robust predictions that\u0000are independent of implementation details or specific mechanisms chosen. We\u0000characterize how much value validators extract in the core and quantify the\u0000surplus share of validators as a function of searcher competition. Searchers\u0000can obtain at most the marginal value increase of the winning block relative to\u0000the best block that can be built without their bundles. Dually this gives a\u0000lower bound on the value extracted by the validator. If arbitrages are easy to\u0000find and many searchers find similar bundles, the validator gets paid all value\u0000almost surely, while searchers can capture most value if there is little\u0000searcher competition per arbitrage. For the case of passive block-proposers we\u0000study, moreover, mechanisms that implement core allocations in dominant\u0000strategies and find that for submodular value, there is a unique\u0000dominant-strategy incentive compatible core-selecting mechanism that gives each\u0000searcher exactly their marginal value contribution to the winning block. We\u0000validate our theoretical prediction empirically with aggregate bundle data and\u0000find a significant positive relation between the number of submitted backruns\u0000for the same opportunity and the median value captured by the proposer from the\u0000opportunity.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141585164","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}
Practical mechanisms often limit agent reports to constrained formats like trades or orderings, potentially limiting the information agents can express. We propose a novel class of mechanisms that elicit agent reports in natural language and leverage the world-modeling capabilities of large language models (LLMs) to select outcomes and assign payoffs. We identify sufficient conditions for these mechanisms to be incentive-compatible and efficient as the LLM being a good enough world model and a strong inter-agent information over-determination condition. We show situations where these LM-based mechanisms can successfully aggregate information in signal structures on which prediction markets fail.
{"title":"Natural Language Mechanisms via Self-Resolution with Foundation Models","authors":"Nicolas Della Penna","doi":"arxiv-2407.07845","DOIUrl":"https://doi.org/arxiv-2407.07845","url":null,"abstract":"Practical mechanisms often limit agent reports to constrained formats like\u0000trades or orderings, potentially limiting the information agents can express.\u0000We propose a novel class of mechanisms that elicit agent reports in natural\u0000language and leverage the world-modeling capabilities of large language models\u0000(LLMs) to select outcomes and assign payoffs. We identify sufficient conditions\u0000for these mechanisms to be incentive-compatible and efficient as the LLM being\u0000a good enough world model and a strong inter-agent information\u0000over-determination condition. We show situations where these LM-based\u0000mechanisms can successfully aggregate information in signal structures on which\u0000prediction markets fail.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"168 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141588531","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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