Consider the scenario where an infinite number of players (i.e., the textit{thermodynamic} limit) find themselves in a Prisoner's dilemma type situation, in a textit{repeated} setting. Is it reasonable to anticipate that, in these circumstances, cooperation will emerge? This paper addresses this question by examining the emergence of cooperative behaviour, in the presence of textit{noise} (or, under textit{selection pressure}), in repeated Prisoner's Dilemma games, involving strategies such as textit{Tit-for-Tat}, textit{Always Defect}, textit{GRIM}, textit{Win-Stay, Lose-Shift}, and others. To analyze these games, we employ a numerical Agent-Based Model (ABM) and compare it with the analytical Nash Equilibrium Mapping (NEM) technique, both based on the textit{1D}-Ising chain. We use textit{game magnetization} as an indicator of cooperative behaviour. A significant finding is that for some repeated games, a discontinuity in the game magnetization indicates a textit{first}-order textit{selection pressure/noise}-driven phase transition. The phase transition is particular to strategies where players do not severely punish a single defection. We also observe that in these particular cases, the phase transition critically depends on the number of textit{rounds} the game is played in the thermodynamic limit. For all five games, we find that both ABM and NEM, in conjunction with game magnetization, provide crucial inputs on how cooperative behaviour can emerge in an infinite-player repeated Prisoner's dilemma game.
{"title":"Selection pressure/Noise driven cooperative behaviour in the thermodynamic limit of repeated games","authors":"Rajdeep Tah, Colin Benjamin","doi":"arxiv-2407.15801","DOIUrl":"https://doi.org/arxiv-2407.15801","url":null,"abstract":"Consider the scenario where an infinite number of players (i.e., the\u0000textit{thermodynamic} limit) find themselves in a Prisoner's dilemma type\u0000situation, in a textit{repeated} setting. Is it reasonable to anticipate that,\u0000in these circumstances, cooperation will emerge? This paper addresses this\u0000question by examining the emergence of cooperative behaviour, in the presence\u0000of textit{noise} (or, under textit{selection pressure}), in repeated\u0000Prisoner's Dilemma games, involving strategies such as textit{Tit-for-Tat},\u0000textit{Always Defect}, textit{GRIM}, textit{Win-Stay, Lose-Shift}, and\u0000others. To analyze these games, we employ a numerical Agent-Based Model (ABM)\u0000and compare it with the analytical Nash Equilibrium Mapping (NEM) technique,\u0000both based on the textit{1D}-Ising chain. We use textit{game magnetization}\u0000as an indicator of cooperative behaviour. A significant finding is that for\u0000some repeated games, a discontinuity in the game magnetization indicates a\u0000textit{first}-order textit{selection pressure/noise}-driven phase transition.\u0000The phase transition is particular to strategies where players do not severely\u0000punish a single defection. We also observe that in these particular cases, the\u0000phase transition critically depends on the number of textit{rounds} the game\u0000is played in the thermodynamic limit. For all five games, we find that both ABM\u0000and NEM, in conjunction with game magnetization, provide crucial inputs on how\u0000cooperative behaviour can emerge in an infinite-player repeated Prisoner's\u0000dilemma game.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782331","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 Colonel Blotto game, introduced by Borel in the 1920s, is often used for modeling various real-life settings, such as elections, lobbying, etc. The game is based on the allocation of limited resources by players to a set of fields. Each field is ``won'' and a corresponding field-specific value is obtained by the player who sends the most resources. In this paper, we formulate a discrete Blotto game played on a general textit{accessibility network} (i.e., the bipartite graph made of players and the fields they can allocate resources to). The primary goal is to find how the topology of the accessibility network controls the existence and uniqueness of equilibrium allocations, and how it affects the fraction of fields that are entered and the average payoff of players at equilibrium. We establish that, in a 2-regular topology, when the values of fields are close enough and the number of players is not a multiple of 4, then there is a unique equilbrium. We also prove that players are better off and fields are more likely to be entered in a regular topology than a random topology. We find numerically that dispersion of field weights negatively affects average player payoff. The main contribution is a framework for analyzing contests where players are permitted access to some (but not necessarily all) venues of competition.
{"title":"Colonel Blotto Game: An Analysis and Extension to Networks","authors":"Sidarth Erat","doi":"arxiv-2407.16707","DOIUrl":"https://doi.org/arxiv-2407.16707","url":null,"abstract":"The Colonel Blotto game, introduced by Borel in the 1920s, is often used for\u0000modeling various real-life settings, such as elections, lobbying, etc. The game\u0000is based on the allocation of limited resources by players to a set of fields.\u0000Each field is ``won'' and a corresponding field-specific value is obtained by\u0000the player who sends the most resources. In this paper, we formulate a discrete\u0000Blotto game played on a general textit{accessibility network} (i.e., the\u0000bipartite graph made of players and the fields they can allocate resources to).\u0000The primary goal is to find how the topology of the accessibility network\u0000controls the existence and uniqueness of equilibrium allocations, and how it\u0000affects the fraction of fields that are entered and the average payoff of\u0000players at equilibrium. We establish that, in a 2-regular topology, when the\u0000values of fields are close enough and the number of players is not a multiple\u0000of 4, then there is a unique equilbrium. We also prove that players are better\u0000off and fields are more likely to be entered in a regular topology than a\u0000random topology. We find numerically that dispersion of field weights\u0000negatively affects average player payoff. The main contribution is a framework\u0000for analyzing contests where players are permitted access to some (but not\u0000necessarily all) venues of competition.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782326","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}
Commutativity is a normative criterion of aggregation and updating stating that the aggregation of expert posteriors should be identical to the update of the aggregated priors. I propose a thought experiment that raises questions about the normative appeal of Commutativity. I propose a weakened version of Commutativity and show how that assumption plays central roles in the characterization of linear belief aggregation, multiple-weight aggregation, and an aggregation rule which can be viewed as the outcome of a game played by "dual-selves," Pessimism and Optimism. Under suitable conditions, I establish equivalences between various relaxations of Commutativity and classic axioms for decision-making under uncertainty, including Independence, C-Independence, and Ambiguity Aversion.
{"title":"(Non-)Commutative Aggregation","authors":"Yuzhao Yang","doi":"arxiv-2407.14959","DOIUrl":"https://doi.org/arxiv-2407.14959","url":null,"abstract":"Commutativity is a normative criterion of aggregation and updating stating\u0000that the aggregation of expert posteriors should be identical to the update of\u0000the aggregated priors. I propose a thought experiment that raises questions\u0000about the normative appeal of Commutativity. I propose a weakened version of\u0000Commutativity and show how that assumption plays central roles in the\u0000characterization of linear belief aggregation, multiple-weight aggregation, and\u0000an aggregation rule which can be viewed as the outcome of a game played by\u0000\"dual-selves,\" Pessimism and Optimism. Under suitable conditions, I establish\u0000equivalences between various relaxations of Commutativity and classic axioms\u0000for decision-making under uncertainty, including Independence, C-Independence,\u0000and Ambiguity Aversion.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"100 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782328","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}
Agents with different ideologies often form alliances to achieve their goals. Paradoxically, ideologically similar agents are often opponents. In this paper, ideologically heterogeneous agents choose the ideological composition of their neighborhood, their tolerance, and invest into connections. The resulting weighted network describes allies, opponents, and strengths. Disputes with opponents determine benefits, which increase in an agent's strength and cohesion. Cohesive agents have fewer mutual allies with opponents. In equilibrium, the network is segregated when cohesion is effective enough and some agents tolerate ideologically distant types to oppose closer ones. Subsidizing connections dampens polarization in societies on the verge of segregation.
{"title":"Cohesion, Ideology, and Tolerance","authors":"Patrick Allmis","doi":"arxiv-2407.14045","DOIUrl":"https://doi.org/arxiv-2407.14045","url":null,"abstract":"Agents with different ideologies often form alliances to achieve their goals.\u0000Paradoxically, ideologically similar agents are often opponents. In this paper,\u0000ideologically heterogeneous agents choose the ideological composition of their\u0000neighborhood, their tolerance, and invest into connections. The resulting\u0000weighted network describes allies, opponents, and strengths. Disputes with\u0000opponents determine benefits, which increase in an agent's strength and\u0000cohesion. Cohesive agents have fewer mutual allies with opponents. In\u0000equilibrium, the network is segregated when cohesion is effective enough and\u0000some agents tolerate ideologically distant types to oppose closer ones.\u0000Subsidizing connections dampens polarization in societies on the verge of\u0000segregation.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743956","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 take an axiomatic approach to the allocation of riparian water rights. We formalize ethical or structural properties as axioms of allocation rules. We show that several combinations of these axioms characterize focal rules implementing the principle of Territorial Integration of all Basin States in various forms. One of them connects to the Shapley value, the long-standing centerpiece of cooperative game theory. The others offer natural compromises between the polar principles of Absolute Territorial Sovereignty and Unlimited Territorial Integrity. We complete our study with an empirical application to the allocation of riparian water rights in the Nile River.
{"title":"Fair allocation of riparian water rights","authors":"Ricardo Martinez, Juan D. Moreno-Ternero","doi":"arxiv-2407.14623","DOIUrl":"https://doi.org/arxiv-2407.14623","url":null,"abstract":"We take an axiomatic approach to the allocation of riparian water rights. We\u0000formalize ethical or structural properties as axioms of allocation rules. We\u0000show that several combinations of these axioms characterize focal rules\u0000implementing the principle of Territorial Integration of all Basin States in\u0000various forms. One of them connects to the Shapley value, the long-standing\u0000centerpiece of cooperative game theory. The others offer natural compromises\u0000between the polar principles of Absolute Territorial Sovereignty and Unlimited\u0000Territorial Integrity. We complete our study with an empirical application to\u0000the allocation of riparian water rights in the Nile River.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782329","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}
What are the effects of authoritarian regimes on scholarly research in economics? And how might economic theory survive ideological pressures? The article addresses these questions by focusing on the mathematization of economics over the past century and drawing on the history of Soviet science. Mathematics in the USSR remained internationally competitive and generated many ideas that were taken up and played important roles in economic theory. These same ideas, however, were disregarded or adopted only in piecemeal fashion by Soviet economists, despite the efforts of influential scholars to change the economic research agenda. The article draws this contrast into sharper focus by exploring the work of Soviet mathematicians in optimization, game theory, and probability theory that was used in Western economics. While the intellectual exchange across the Iron Curtain did help advance the formal modeling apparatus, economics could only thrive in an intellectually open environment absent under the Soviet rule.
{"title":"Soviet Mathematics and Economic Theory in the Past Century: An Historical Reappraisal","authors":"Ivan Boldyrev","doi":"arxiv-2407.14315","DOIUrl":"https://doi.org/arxiv-2407.14315","url":null,"abstract":"What are the effects of authoritarian regimes on scholarly research in\u0000economics? And how might economic theory survive ideological pressures? The\u0000article addresses these questions by focusing on the mathematization of\u0000economics over the past century and drawing on the history of Soviet science.\u0000Mathematics in the USSR remained internationally competitive and generated many\u0000ideas that were taken up and played important roles in economic theory. These\u0000same ideas, however, were disregarded or adopted only in piecemeal fashion by\u0000Soviet economists, despite the efforts of influential scholars to change the\u0000economic research agenda. The article draws this contrast into sharper focus by\u0000exploring the work of Soviet mathematicians in optimization, game theory, and\u0000probability theory that was used in Western economics. While the intellectual\u0000exchange across the Iron Curtain did help advance the formal modeling\u0000apparatus, economics could only thrive in an intellectually open environment\u0000absent under the Soviet rule.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743949","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 the house allocation problems with strict preferences, where monetary transfers are not allowed. We propose two properties in the spirit of justified fairness. Interestingly, together with other well-studied properties (strategy-proofness and non-bossiness), our two new properties identify serial dictatorships and sequential dictatorships, respectively.
{"title":"Justified Fairness in House Allocation Problems: two Characterizations of Strategy-proof Mechanisms","authors":"Di Feng, Jacob Coreno","doi":"arxiv-2407.14101","DOIUrl":"https://doi.org/arxiv-2407.14101","url":null,"abstract":"We consider the house allocation problems with strict preferences, where\u0000monetary transfers are not allowed. We propose two properties in the spirit of\u0000justified fairness. Interestingly, together with other well-studied properties\u0000(strategy-proofness and non-bossiness), our two new properties identify serial\u0000dictatorships and sequential dictatorships, respectively.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743945","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 introduce a novel system of matching and scoring players in tournaments, called Multi-Tier Tournaments, illustrated by chess and based on the following rules: 1. Players are divided into skill-based tiers, based on their Elo ratings. 2. Starting with one or more mini-tournaments of the least skilled players (Tier 1), the winner or winners -- after playing multiple opponents -- move to the next-higher tier. 3. The winners progress to a final tier of the best-performing players from lower tiers as well as players with the highest Elo ratings. 4. Performance in each tier is given by a player's Tournament Score (TS), which depends on his/her wins, losses, and draws (not on his/her Elo rating). Whereas a player's Elo rating determines in which mini-tournament he/she starts play, TS and its associated tie-breaking rules determine whether a player moves up to higher tiers and, in the final mini-tournament, wins the tournament. This combination of players' past Elo ratings and current TS's provides a fair and accurate measure of a player's standing among the players in the tournament. We apply a variation of Multi-Tier Tournaments to the top 20 active chess players in the world (as of February 2024). Using a dataset of 1209 head-to-head games, we illustrate the viability of giving lower-rated players the opportunity to progress and challenge higher-rated players. We also briefly discuss the application of Multi-Tier Tournaments to baseball, soccer, and other sports that emphasize physical rather than mental skills.
我们以国际象棋为例，基于以下规则，介绍了一种在锦标赛中匹配棋手并为其计分的新系统，称为多层锦标赛（Multi-Tier Tournaments）：1.1. 根据棋手的 Elo 等级，将棋手划分为不同的技术等级。2.2. 从技术最差的棋手（第 1 层）的一场或多场小型比赛开始，获胜者在与多个对手交手后，进入下一个更高的层级。3.3. 获胜者进入由较低级别中表现最好的选手以及 Elo 等级最高的选手组成的最后级别。4.4. 每个级别的成绩由选手的锦标赛得分（TS）决定，锦标赛得分取决于选手的胜负和平局（而非 Elo 等级）。棋手的 Elo 等级决定了他/她在哪个迷你锦标赛中开始比赛，而 TS 及其相关的决胜规则则决定了棋手是否晋级到更高的级别，以及在最后的迷你锦标赛中是否获胜。球员过去的 Elo 等级和当前的 TS 等级相结合，可以公平、准确地衡量球员在锦标赛中的地位。我们对世界排名前 20 的活跃棋手（截至 2024 年 2 月）采用了多层锦标赛的变体。通过 1209 盘正面对决的数据集，我们说明了给予低等级棋手进步和挑战高等级棋手的机会的可行性。我们还简要讨论了多层锦标赛在棒球、足球和其他强调体能而非心智技能的运动中的应用。
{"title":"Multi-Tier Tournaments: Matching and Scoring Players","authors":"Steven J. Brams, Mehmet S. Ismail","doi":"arxiv-2407.13845","DOIUrl":"https://doi.org/arxiv-2407.13845","url":null,"abstract":"We introduce a novel system of matching and scoring players in tournaments,\u0000called Multi-Tier Tournaments, illustrated by chess and based on the following\u0000rules: 1. Players are divided into skill-based tiers, based on their Elo ratings. 2. Starting with one or more mini-tournaments of the least skilled players\u0000(Tier 1), the winner or winners -- after playing multiple opponents -- move to\u0000the next-higher tier. 3. The winners progress to a final tier of the best-performing players from\u0000lower tiers as well as players with the highest Elo ratings. 4. Performance in each tier is given by a player's Tournament Score (TS),\u0000which depends on his/her wins, losses, and draws (not on his/her Elo rating). Whereas a player's Elo rating determines in which mini-tournament he/she\u0000starts play, TS and its associated tie-breaking rules determine whether a\u0000player moves up to higher tiers and, in the final mini-tournament, wins the\u0000tournament. This combination of players' past Elo ratings and current TS's\u0000provides a fair and accurate measure of a player's standing among the players\u0000in the tournament. We apply a variation of Multi-Tier Tournaments to the top 20\u0000active chess players in the world (as of February 2024). Using a dataset of\u00001209 head-to-head games, we illustrate the viability of giving lower-rated\u0000players the opportunity to progress and challenge higher-rated players. We also\u0000briefly discuss the application of Multi-Tier Tournaments to baseball, soccer,\u0000and other sports that emphasize physical rather than mental skills.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"89 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743948","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 develop an extension of the classical model of DeGroot (1974) to a continuum of agents when they interact among them according to a DiKernel $W$. We show that, under some regularity assumptions, the continuous model is the limit case of the discrete one. We provide some applications of this result. First, we establish a canonical way to reduce the dimensionality of matrices by comparing matrices of different dimensions in the space of DiKernels. Then, we develop a model of Lobby Competition where two lobbies compete to bias the opinion of a continuum of agents. We give sufficient conditions for the existence of a Nash Equilibrium. Furthermore, we establish the conditions under which a Nash Equilibrium of the game induce an $varepsilon$-Nash Equilibrium of the discretization of the game. Finally, we put forward some elements for the characterization of equilibrium strategies.
{"title":"Continuous Social Networks","authors":"Julián Chitiva, Xavier Venel","doi":"arxiv-2407.11710","DOIUrl":"https://doi.org/arxiv-2407.11710","url":null,"abstract":"We develop an extension of the classical model of DeGroot (1974) to a\u0000continuum of agents when they interact among them according to a DiKernel $W$.\u0000We show that, under some regularity assumptions, the continuous model is the\u0000limit case of the discrete one. We provide some applications of this result.\u0000First, we establish a canonical way to reduce the dimensionality of matrices by\u0000comparing matrices of different dimensions in the space of DiKernels. Then, we\u0000develop a model of Lobby Competition where two lobbies compete to bias the\u0000opinion of a continuum of agents. We give sufficient conditions for the\u0000existence of a Nash Equilibrium. Furthermore, we establish the conditions under\u0000which a Nash Equilibrium of the game induce an $varepsilon$-Nash Equilibrium\u0000of the discretization of the game. Finally, we put forward some elements for\u0000the characterization of equilibrium strategies.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141718023","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}
This paper introduces a novel measurement of informational size to school choice problems, which inherits its ideas from Mount and Reiter (1974). This concept measures a matching mechanism's information size by counting the maximal relevant preference and priority rankings to secure a certain pairwise assignment of a student to a school across all possible matching problems. Our analysis uncovers two key insights. First, the three prominent strategy-proof matching mechanisms, the deferred acceptance (DA) mechanism, the top trading cycles (TTC) mechanism, and the serial dictatorship (SD) mechanism, is (strictly) less informative than the non-strategy-proof immediate acceptance (IA) mechanism. This result highlights a previously omitted advantage of IA in term of its information demand, which partially explain the its popularity in real-world matching problems especially when acquiring information is both pecuniarily and cognitively costly. Second, when the matching problem contains at least four students, the TTC demands less information compared to the DA to implement a desired allocation. The issue of comparison between TTC and DA has puzzled researchers both in theory (Gonczarowski and Thomas, 2023) and in experiment (Hakimov and Kubler, 2021). Our result responds to this issue from an informational perspective: in experiments with relatively fewer students, agents tend to prefer DA over TTC as DA requires fewer information to secure one's allocation in all problems (Guillen and Veszteg, 2021), while the opposite is true when the market size increases (Pais et al., 2011). Among others, our informational size concept offers a new perspective to understand the differences in auditability (Grigoryan and Moller, 2024), manipulation vulnerability (Pathak and Sonmez, 2013), and privacy protection (Haupt and Hitzig, 2022), among some commonly used matching mechanisms.
本文继承了 Mount 和 Reiter（1974）的观点，为择校问题引入了一种新的信息量测量方法。这一概念通过计算在所有可能的择校问题中，为确保将某个学生配对分配到某所学校而进行的最大相关偏好和优先排序，来测量匹配机制的信息量。我们的分析揭示了两个关键问题。首先，三种著名的防策略匹配机制--延迟接受（DA）机制、最高交易循环（TTC）机制和序列独裁（SD）机制--的信息量（严格来说）都小于非防策略的立即接受（IA）机制。这一结果凸显了 IA 机制之前被忽略的优势，即它对信息的需求，这也部分解释了它在现实匹配问题中受欢迎的原因，尤其是当获取信息既需要高昂的金钱成本又需要高昂的认知成本时。其次，当匹配问题至少包含四个学生时，TTC 与 DA 相比对信息的需求更少，更容易实现理想的分配。TTC 和 DA 之间的比较问题在理论上（Gonczarowski 和 Thomas，2023 年）和实验中（Hakimov 和 Kubler，2021 年）都令研究人员感到困惑。我们的结果从信息角度回应了这一问题：在学生人数相对较少的实验中，代理人倾向于选择 DA 而不是 TTC，因为 DA 在所有问题中都需要较少的信息来确保分配（Guillen 和 Veszteg，2021 年），而当市场规模扩大时，情况则恰恰相反（Pais 等人，2011 年）。此外，我们的信息规模概念为理解一些常用匹配机制在可审计性（Grigoryan 和 Moller，2024 年）、易操纵性（Pathak 和 Sonmez，2013 年）和隐私保护（Haupt 和 Hitzig，2022 年）方面的差异提供了一个新视角。
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