Gregory Z. Gutin, Daniel Karapetyan, Philip R. Neary, Alexander Vicker, Anders Yeo
A run of the deferred acceptance (DA) algorithm may contain proposals that are sure to be rejected. We introduce the accelerated deferred acceptance algorithm that proceeds in a similar manner to DA but with sure-to-be rejected proposals ruled out. Accelerated deferred acceptance outputs the same stable matching as DA but does so more efficiently: it terminates in weakly fewer rounds, requires weakly fewer proposals, and final pairs match no later. Computational experiments show that these efficiency savings can be strict.
延迟接受（DA）算法的运行可能包含一些肯定会被拒绝的建议。我们引入了加速延迟接受算法，它的运行方式与 DA 算法类似，但排除了肯定会被拒绝的提议。加速延迟接受算法能输出与 DA 算法相同的稳定匹配结果，但效率更高：它能在极少数回合内终止，所需的提议数量也极少，而且最终配对匹配的时间不会晚于 DA 算法。
{"title":"Speeding up deferred acceptance","authors":"Gregory Z. Gutin, Daniel Karapetyan, Philip R. Neary, Alexander Vicker, Anders Yeo","doi":"arxiv-2409.06865","DOIUrl":"https://doi.org/arxiv-2409.06865","url":null,"abstract":"A run of the deferred acceptance (DA) algorithm may contain proposals that\u0000are sure to be rejected. We introduce the accelerated deferred acceptance\u0000algorithm that proceeds in a similar manner to DA but with sure-to-be rejected\u0000proposals ruled out. Accelerated deferred acceptance outputs the same stable\u0000matching as DA but does so more efficiently: it terminates in weakly fewer\u0000rounds, requires weakly fewer proposals, and final pairs match no later.\u0000Computational experiments show that these efficiency savings can be strict.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"96 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142225108","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 where an agent is must choose between alternatives that each provide only an imprecise description of the world (e.g. linguistic expressions). The set of alternatives is closed under logical conjunction and disjunction, but not necessarily negation. (Formally: it is a distributive lattice, but not necessarily a Boolean algebra). In our main result, each alternative is identified with a subset of an (endogenously defined) state space, and two axioms characterize maximin decision making. This means: from the agent's preferences over alternatives, we derive a preference order on the endogenous state space, such that alternatives are ranked in terms of their worst outcomes.
{"title":"Coarse Descriptions and Cautious Preferences","authors":"Evan Piermont, Marcus Pivato","doi":"arxiv-2409.06054","DOIUrl":"https://doi.org/arxiv-2409.06054","url":null,"abstract":"We consider a model where an agent is must choose between alternatives that\u0000each provide only an imprecise description of the world (e.g. linguistic\u0000expressions). The set of alternatives is closed under logical conjunction and\u0000disjunction, but not necessarily negation. (Formally: it is a distributive\u0000lattice, but not necessarily a Boolean algebra). In our main result, each\u0000alternative is identified with a subset of an (endogenously defined) state\u0000space, and two axioms characterize maximin decision making. This means: from\u0000the agent's preferences over alternatives, we derive a preference order on the\u0000endogenous state space, such that alternatives are ranked in terms of their\u0000worst outcomes.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197097","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 define and study obvious strategy-proofness with respect to a partition of the set of agents. It encompasses strategy-proofness as a special case when the partition is the coarsest one and obvious strategy-proofness when the partition is the finest. For any partition, it falls between these two extremes. We establish two general properties of this new notion and apply it to the simple anonymous voting problem with two alternatives and strict preferences.
{"title":"Obvious Strategy-proofness with Respect to a Partition","authors":"R. Pablo Arribillaga, Jordi Massó, Alejandro Neme","doi":"arxiv-2409.05315","DOIUrl":"https://doi.org/arxiv-2409.05315","url":null,"abstract":"We define and study obvious strategy-proofness with respect to a partition of\u0000the set of agents. It encompasses strategy-proofness as a special case when the\u0000partition is the coarsest one and obvious strategy-proofness when the partition\u0000is the finest. For any partition, it falls between these two extremes. We\u0000establish two general properties of this new notion and apply it to the simple\u0000anonymous voting problem with two alternatives and strict preferences.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"203 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197098","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}
The volunteer's dilemma is a well-known game in game theory that models the conflict players face when deciding whether to volunteer for a collective benefit, knowing that volunteering incurs a personal cost. In this work, we introduce a quantum variant of the classical volunteer's dilemma, generalizing it by allowing players to utilize quantum strategies. Employing the Eisert-Wilkens-Lewenstein quantization framework, we analyze a multiplayer quantum volunteer's dilemma scenario with an arbitrary number of players, where the cost of volunteering is shared equally among the volunteers. We derive analytical expressions for the players' expected payoffs and demonstrate the quantum game's advantage over the classical game. In particular, we prove that the quantum volunteer's dilemma possesses symmetric Nash equilibria with larger expected payoffs compared to the unique symmetric Nash equilibrium of the classical game, wherein players use mixed strategies. Furthermore, we show that the quantum Nash equilibria we identify are Pareto optimal. Our findings reveal distinct dynamics in volunteer's dilemma scenarios when players adhere to quantum rules, underscoring a strategic advantage of decision-making in quantum settings.
{"title":"Quantum Volunteer's Dilemma","authors":"Dax Enshan Koh, Kaavya Kumar, Siong Thye Goh","doi":"arxiv-2409.05708","DOIUrl":"https://doi.org/arxiv-2409.05708","url":null,"abstract":"The volunteer's dilemma is a well-known game in game theory that models the\u0000conflict players face when deciding whether to volunteer for a collective\u0000benefit, knowing that volunteering incurs a personal cost. In this work, we\u0000introduce a quantum variant of the classical volunteer's dilemma, generalizing\u0000it by allowing players to utilize quantum strategies. Employing the\u0000Eisert-Wilkens-Lewenstein quantization framework, we analyze a multiplayer\u0000quantum volunteer's dilemma scenario with an arbitrary number of players, where\u0000the cost of volunteering is shared equally among the volunteers. We derive\u0000analytical expressions for the players' expected payoffs and demonstrate the\u0000quantum game's advantage over the classical game. In particular, we prove that\u0000the quantum volunteer's dilemma possesses symmetric Nash equilibria with larger\u0000expected payoffs compared to the unique symmetric Nash equilibrium of the\u0000classical game, wherein players use mixed strategies. Furthermore, we show that\u0000the quantum Nash equilibria we identify are Pareto optimal. Our findings reveal\u0000distinct dynamics in volunteer's dilemma scenarios when players adhere to\u0000quantum rules, underscoring a strategic advantage of decision-making in quantum\u0000settings.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197101","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}
L. Elisa Celis, Amit Kumar, Nisheeth K. Vishnoi, Andrew Xu
This paper considers the scenario in which there are multiple institutions, each with a limited capacity for candidates, and candidates, each with preferences over the institutions. A central entity evaluates the utility of each candidate to the institutions, and the goal is to select candidates for each institution in a way that maximizes utility while also considering the candidates' preferences. The paper focuses on the setting in which candidates are divided into multiple groups and the observed utilities of candidates in some groups are biased--systematically lower than their true utilities. The first result is that, in these biased settings, prior algorithms can lead to selections with sub-optimal true utility and significant discrepancies in the fraction of candidates from each group that get their preferred choices. Subsequently, an algorithm is presented along with proof that it produces selections that achieve near-optimal group fairness with respect to preferences while also nearly maximizing the true utility under distributional assumptions. Further, extensive empirical validation of these results in real-world and synthetic settings, in which the distributional assumptions may not hold, are presented.
{"title":"Centralized Selection with Preferences in the Presence of Biases","authors":"L. Elisa Celis, Amit Kumar, Nisheeth K. Vishnoi, Andrew Xu","doi":"arxiv-2409.04897","DOIUrl":"https://doi.org/arxiv-2409.04897","url":null,"abstract":"This paper considers the scenario in which there are multiple institutions,\u0000each with a limited capacity for candidates, and candidates, each with\u0000preferences over the institutions. A central entity evaluates the utility of\u0000each candidate to the institutions, and the goal is to select candidates for\u0000each institution in a way that maximizes utility while also considering the\u0000candidates' preferences. The paper focuses on the setting in which candidates\u0000are divided into multiple groups and the observed utilities of candidates in\u0000some groups are biased--systematically lower than their true utilities. The\u0000first result is that, in these biased settings, prior algorithms can lead to\u0000selections with sub-optimal true utility and significant discrepancies in the\u0000fraction of candidates from each group that get their preferred choices.\u0000Subsequently, an algorithm is presented along with proof that it produces\u0000selections that achieve near-optimal group fairness with respect to preferences\u0000while also nearly maximizing the true utility under distributional assumptions.\u0000Further, extensive empirical validation of these results in real-world and\u0000synthetic settings, in which the distributional assumptions may not hold, are\u0000presented.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142225133","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}
There has been substantial recent concern that pricing algorithms might learn to ``collude.'' Supra-competitive prices can emerge as a Nash equilibrium of repeated pricing games, in which sellers play strategies which threaten to punish their competitors who refuse to support high prices, and these strategies can be automatically learned. In fact, a standard economic intuition is that supra-competitive prices emerge from either the use of threats, or a failure of one party to optimize their payoff. Is this intuition correct? Would preventing threats in algorithmic decision-making prevent supra-competitive prices when sellers are optimizing for their own revenue? No. We show that supra-competitive prices can emerge even when both players are using algorithms which do not encode threats, and which optimize for their own revenue. We study sequential pricing games in which a first mover deploys an algorithm and then a second mover optimizes within the resulting environment. We show that if the first mover deploys any algorithm with a no-regret guarantee, and then the second mover even approximately optimizes within this now static environment, monopoly-like prices arise. The result holds for any no-regret learning algorithm deployed by the first mover and for any pricing policy of the second mover that obtains them profit at least as high as a random pricing would -- and hence the result applies even when the second mover is optimizing only within a space of non-responsive pricing distributions which are incapable of encoding threats. In fact, there exists a set of strategies, neither of which explicitly encode threats that form a Nash equilibrium of the simultaneous pricing game in algorithm space, and lead to near monopoly prices. This suggests that the definition of ``algorithmic collusion'' may need to be expanded, to include strategies without explicitly encoded threats.
{"title":"Algorithmic Collusion Without Threats","authors":"Eshwar Ram Arunachaleswaran, Natalie Collina, Sampath Kannan, Aaron Roth, Juba Ziani","doi":"arxiv-2409.03956","DOIUrl":"https://doi.org/arxiv-2409.03956","url":null,"abstract":"There has been substantial recent concern that pricing algorithms might learn\u0000to ``collude.'' Supra-competitive prices can emerge as a Nash equilibrium of\u0000repeated pricing games, in which sellers play strategies which threaten to\u0000punish their competitors who refuse to support high prices, and these\u0000strategies can be automatically learned. In fact, a standard economic intuition\u0000is that supra-competitive prices emerge from either the use of threats, or a\u0000failure of one party to optimize their payoff. Is this intuition correct? Would\u0000preventing threats in algorithmic decision-making prevent supra-competitive\u0000prices when sellers are optimizing for their own revenue? No. We show that\u0000supra-competitive prices can emerge even when both players are using algorithms\u0000which do not encode threats, and which optimize for their own revenue. We study\u0000sequential pricing games in which a first mover deploys an algorithm and then a\u0000second mover optimizes within the resulting environment. We show that if the\u0000first mover deploys any algorithm with a no-regret guarantee, and then the\u0000second mover even approximately optimizes within this now static environment,\u0000monopoly-like prices arise. The result holds for any no-regret learning\u0000algorithm deployed by the first mover and for any pricing policy of the second\u0000mover that obtains them profit at least as high as a random pricing would --\u0000and hence the result applies even when the second mover is optimizing only\u0000within a space of non-responsive pricing distributions which are incapable of\u0000encoding threats. In fact, there exists a set of strategies, neither of which\u0000explicitly encode threats that form a Nash equilibrium of the simultaneous\u0000pricing game in algorithm space, and lead to near monopoly prices. This\u0000suggests that the definition of ``algorithmic collusion'' may need to be\u0000expanded, to include strategies without explicitly encoded threats.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"129 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197104","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 equilibria of uniform price auctions where bidders have flat demands up to their respective quantity constraints. We present an iterative procedure that systematically finds a Nash equilibrium outcome under semi-complete information as well as a novel ascending auction under incomplete information that has this outcome as a dominant strategy equilibrium. Demand reduction and low price equilibrium may occur since it is sometimes advantageous for a bidder to give up some of his/her demand and get the remaining demand at a low price rather than to get his/her entire demand at a higher price.
{"title":"Uniform price auction with quantity constraints","authors":"Kiho Yoon","doi":"arxiv-2409.04047","DOIUrl":"https://doi.org/arxiv-2409.04047","url":null,"abstract":"We study the equilibria of uniform price auctions where bidders have flat\u0000demands up to their respective quantity constraints. We present an iterative\u0000procedure that systematically finds a Nash equilibrium outcome under\u0000semi-complete information as well as a novel ascending auction under incomplete\u0000information that has this outcome as a dominant strategy equilibrium. Demand\u0000reduction and low price equilibrium may occur since it is sometimes\u0000advantageous for a bidder to give up some of his/her demand and get the\u0000remaining demand at a low price rather than to get his/her entire demand at a\u0000higher price.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197102","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 principal has $m$ identical objects to allocate among a group of $n$ agents. Objects are desirable and the principal's value of assigning an object to an agent is the agent's private information. The principal can verify up to $k$ agents, where $k
{"title":"Optimal allocations with capacity constrained verification","authors":"Albin Erlanson, Andreas Kleiner","doi":"arxiv-2409.02031","DOIUrl":"https://doi.org/arxiv-2409.02031","url":null,"abstract":"A principal has $m$ identical objects to allocate among a group of $n$\u0000agents. Objects are desirable and the principal's value of assigning an object\u0000to an agent is the agent's private information. The principal can verify up to\u0000$k$ agents, where $k<m$, thereby perfectly learning the types of those\u0000verified. We find the mechanism that maximizes the principal's expected utility\u0000when no monetary transfers are available. In this mechanism, an agent receives\u0000an object if (i) his type is above a cutoff and among the $m$ highest types,\u0000(ii) his type is above some lower cutoff but among the $k$ highest types, or\u0000(iii) he receives an object in a lottery that allocates the remaining objects\u0000randomly.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142225109","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}
When comparing performance (of products, services, entities, etc.), multiple attributes are involved. This paper deals with a way of weighting these attributes when one is seeking an overall score. It presents an objective approach to generating the weights in a scoring formula which avoids personal judgement. The first step is to find the maximum possible score for each assessed entity. These upper bound scores are found using Data Envelopment Analysis. In the second step the weights in the scoring formula are found by regressing the unique DEA scores on the attribute data. Reasons for using least squares and avoiding other distance measures are given. The method is tested on data where the true scores and weights are known. The method enables the construction of an objective scoring formula which has been generated from the data arising from all assessed entities and is, in that sense, democratic.
在比较（产品、服务、实体等）性能时，会涉及多个属性。本文探讨了在寻求总体得分时如何对这些属性进行加权。它提出了一种在评分公式中生成权重的客观方法，避免了个人判断。第一步是为每个被评估实体找到可能的最高得分。这些上限分数是通过数据包络分析法找到的。第二步，通过对属性数据的独特 DEA 分数进行回归，找到评分公式中的权重。给出了使用最小二乘法而避免使用其他距离测量方法的原因。该方法在已知真实得分和权重的数据上进行了测试。该方法能够构建一个客观的评分公式，该公式由所有被评估实体的数据生成，从这个意义上说是民主的。
{"title":"Objective Weights for Scoring: The Automatic Democratic Method","authors":"Chris Tofallis","doi":"arxiv-2409.02087","DOIUrl":"https://doi.org/arxiv-2409.02087","url":null,"abstract":"When comparing performance (of products, services, entities, etc.), multiple\u0000attributes are involved. This paper deals with a way of weighting these\u0000attributes when one is seeking an overall score. It presents an objective\u0000approach to generating the weights in a scoring formula which avoids personal\u0000judgement. The first step is to find the maximum possible score for each\u0000assessed entity. These upper bound scores are found using Data Envelopment\u0000Analysis. In the second step the weights in the scoring formula are found by\u0000regressing the unique DEA scores on the attribute data. Reasons for using least\u0000squares and avoiding other distance measures are given. The method is tested on\u0000data where the true scores and weights are known. The method enables the\u0000construction of an objective scoring formula which has been generated from the\u0000data arising from all assessed entities and is, in that sense, democratic.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197109","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}
Two issues of algorithmic collusion are addressed in this paper. First, we show that in a general class of symmetric games, including Prisoner's Dilemma, Bertrand competition, and any (nonlinear) mixture of first and second price auction, only (strict) Nash Equilibrium (NE) is stochastically stable. Therefore, the tacit collusion is driven by failure to learn NE due to insufficient learning, instead of learning some strategies to sustain collusive outcomes. Second, we study how algorithms adapt to collusion in real simulations with insufficient learning. Extensive explorations in early stages and discount factors inflates the Q-value, which interrupts the sequential and alternative price undercut and leads to bilateral rebound. The process is iterated, making the price curves like Edgeworth cycles. When both exploration rate and Q-value decrease, algorithms may bilaterally rebound to relatively high common price level by coincidence, and then get stuck. Finally, we accommodate our reasoning to simulation outcomes in the literature, including optimistic initialization, market design and algorithm design.
{"title":"On Mechanism Underlying Algorithmic Collusion","authors":"Zhang Xu, Wei Zhao","doi":"arxiv-2409.01147","DOIUrl":"https://doi.org/arxiv-2409.01147","url":null,"abstract":"Two issues of algorithmic collusion are addressed in this paper. First, we\u0000show that in a general class of symmetric games, including Prisoner's Dilemma,\u0000Bertrand competition, and any (nonlinear) mixture of first and second price\u0000auction, only (strict) Nash Equilibrium (NE) is stochastically stable.\u0000Therefore, the tacit collusion is driven by failure to learn NE due to\u0000insufficient learning, instead of learning some strategies to sustain collusive\u0000outcomes. Second, we study how algorithms adapt to collusion in real\u0000simulations with insufficient learning. Extensive explorations in early stages\u0000and discount factors inflates the Q-value, which interrupts the sequential and\u0000alternative price undercut and leads to bilateral rebound. The process is\u0000iterated, making the price curves like Edgeworth cycles. When both exploration\u0000rate and Q-value decrease, algorithms may bilaterally rebound to relatively\u0000high common price level by coincidence, and then get stuck. Finally, we\u0000accommodate our reasoning to simulation outcomes in the literature, including\u0000optimistic initialization, market design and algorithm design.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"68 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197107","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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