{"title":"具有异质代理的(n,k)博弈","authors":"Hsin-Lun Li","doi":"arxiv-2409.09364","DOIUrl":null,"url":null,"abstract":"The \\((n,k)\\) game models a group of \\(n\\) individuals with binary opinions,\nsay 1 and 0, where a decision is made if at least \\(k\\) individuals hold\nopinion 1. This paper explores the dynamics of the game with heterogeneous\nagents under both synchronous and asynchronous settings. We consider various\nagent types, including consentors, who always hold opinion 1, rejectors, who\nconsistently hold opinion 0, random followers, who imitate one of their social\nneighbors at random, and majority followers, who adopt the majority opinion\namong their social neighbors. We investigate the likelihood of a decision being\nmade in finite time. In circumstances where a decision cannot almost surely be\nmade in finite time, we derive a nontrivial bound to offer insight into the\nprobability of a decision being made in finite time.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"19 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The (n,k) game with heterogeneous agents\",\"authors\":\"Hsin-Lun Li\",\"doi\":\"arxiv-2409.09364\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The \\\\((n,k)\\\\) game models a group of \\\\(n\\\\) individuals with binary opinions,\\nsay 1 and 0, where a decision is made if at least \\\\(k\\\\) individuals hold\\nopinion 1. This paper explores the dynamics of the game with heterogeneous\\nagents under both synchronous and asynchronous settings. We consider various\\nagent types, including consentors, who always hold opinion 1, rejectors, who\\nconsistently hold opinion 0, random followers, who imitate one of their social\\nneighbors at random, and majority followers, who adopt the majority opinion\\namong their social neighbors. We investigate the likelihood of a decision being\\nmade in finite time. In circumstances where a decision cannot almost surely be\\nmade in finite time, we derive a nontrivial bound to offer insight into the\\nprobability of a decision being made in finite time.\",\"PeriodicalId\":501245,\"journal\":{\"name\":\"arXiv - MATH - Probability\",\"volume\":\"19 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Probability\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.09364\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09364","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The \((n,k)\) game models a group of \(n\) individuals with binary opinions,
say 1 and 0, where a decision is made if at least \(k\) individuals hold
opinion 1. This paper explores the dynamics of the game with heterogeneous
agents under both synchronous and asynchronous settings. We consider various
agent types, including consentors, who always hold opinion 1, rejectors, who
consistently hold opinion 0, random followers, who imitate one of their social
neighbors at random, and majority followers, who adopt the majority opinion
among their social neighbors. We investigate the likelihood of a decision being
made in finite time. In circumstances where a decision cannot almost surely be
made in finite time, we derive a nontrivial bound to offer insight into the
probability of a decision being made in finite time.