arXiv - ECON - Theoretical Economics最新文献_第9页

Selection pressure/Noise driven cooperative behaviour in the thermodynamic limit of repeated games 重复博弈热力学极限中的选择压力/噪声驱动的合作行为

arXiv - ECON - Theoretical Economics Pub Date : 2024-07-22 DOI: arxiv-2407.15801

Rajdeep Tah, Colin Benjamin

{"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}

引用次数: 0

Colonel Blotto Game: An Analysis and Extension to Networks 布洛托上校游戏：对网络的分析和扩展

arXiv - ECON - Theoretical Economics Pub Date : 2024-07-21 DOI: arxiv-2407.16707

Sidarth Erat

{"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}

引用次数: 0

(Non-)Commutative Aggregation (非）交换聚合

arXiv - ECON - Theoretical Economics Pub Date : 2024-07-20 DOI: arxiv-2407.14959

Yuzhao Yang

引用次数: 0

Cohesion, Ideology, and Tolerance 凝聚力、意识形态和宽容

arXiv - ECON - Theoretical Economics Pub Date : 2024-07-19 DOI: arxiv-2407.14045

Patrick Allmis

引用次数: 0

Fair allocation of riparian water rights 河岸水权的公平分配

arXiv - ECON - Theoretical Economics Pub Date : 2024-07-19 DOI: arxiv-2407.14623

Ricardo Martinez, Juan D. Moreno-Ternero

引用次数: 0

Soviet Mathematics and Economic Theory in the Past Century: An Historical Reappraisal 上个世纪的苏联数学和经济理论：历史再评价

arXiv - ECON - Theoretical Economics Pub Date : 2024-07-19 DOI: arxiv-2407.14315

Ivan Boldyrev

引用次数: 0

Justified Fairness in House Allocation Problems: two Characterizations of Strategy-proof Mechanisms 房屋分配问题中的合理公平性：防策略机制的两个特点

arXiv - ECON - Theoretical Economics Pub Date : 2024-07-19 DOI: arxiv-2407.14101

Di Feng, Jacob Coreno

引用次数: 0

Multi-Tier Tournaments: Matching and Scoring Players 多层锦标赛：玩家匹配与计分

arXiv - ECON - Theoretical Economics Pub Date : 2024-07-18 DOI: arxiv-2407.13845

Steven J. Brams, Mehmet S. Ismail

{"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}

引用次数: 0

Continuous Social Networks 持续的社交网络

arXiv - ECON - Theoretical Economics Pub Date : 2024-07-16 DOI: arxiv-2407.11710

Julián Chitiva, Xavier Venel

引用次数: 0

Informational Size in School Choice 择校中的信息量

arXiv - ECON - Theoretical Economics Pub Date : 2024-07-15 DOI: arxiv-2407.11273

Di Feng, Yun Liu

{"title":"Informational Size in School Choice","authors":"Di Feng, Yun Liu","doi":"arxiv-2407.11273","DOIUrl":"https://doi.org/arxiv-2407.11273","url":null,"abstract":"This paper introduces a novel measurement of informational size to school\u0000choice problems, which inherits its ideas from Mount and Reiter (1974). This\u0000concept measures a matching mechanism's information size by counting the\u0000maximal relevant preference and priority rankings to secure a certain pairwise\u0000assignment of a student to a school across all possible matching problems. Our\u0000analysis uncovers two key insights. First, the three prominent strategy-proof\u0000matching mechanisms, the deferred acceptance (DA) mechanism, the top trading\u0000cycles (TTC) mechanism, and the serial dictatorship (SD) mechanism, is\u0000(strictly) less informative than the non-strategy-proof immediate acceptance\u0000(IA) mechanism. This result highlights a previously omitted advantage of IA in\u0000term of its information demand, which partially explain the its popularity in\u0000real-world matching problems especially when acquiring information is both\u0000pecuniarily and cognitively costly. Second, when the matching problem contains\u0000at least four students, the TTC demands less information compared to the DA to\u0000implement a desired allocation. The issue of comparison between TTC and DA has\u0000puzzled researchers both in theory (Gonczarowski and Thomas, 2023) and in\u0000experiment (Hakimov and Kubler, 2021). Our result responds to this issue from\u0000an informational perspective: in experiments with relatively fewer students,\u0000agents tend to prefer DA over TTC as DA requires fewer information to secure\u0000one's allocation in all problems (Guillen and Veszteg, 2021), while the\u0000opposite is true when the market size increases (Pais et al., 2011). Among\u0000others, our informational size concept offers a new perspective to understand\u0000the differences in auditability (Grigoryan and Moller, 2024), manipulation\u0000vulnerability (Pathak and Sonmez, 2013), and privacy protection (Haupt and\u0000Hitzig, 2022), among some commonly used matching mechanisms.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"90 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141718024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0