← 研踪 PaperTrailarXiv:2611.17148 · v1
Learning Dynamics of the Influencer's Game in Resource Landscapes
首次提交 2026-11-13 01:33
版本更新 2026-11-13 01:33
雷达观测 2026-11-13 14:15
摘要
Across domains as varied as ecology, economics, and online platforms, individuals are incentivized to position themselves within resource-rich strategy spaces. In this work we introduce a new spatial game framework called the influencer's game. Within this new framework players' strategies are represented as positions within a trait space. Players then receive a share of a portion of a resource based on their relative influence at that resource's points traits. For the influencer's game, we show that there is a unique symmetric Nash equilibrium that exists under strict log-concavity of the influence kernel. Using the unique equilibrium we show that the stability of the system depends on the influence kernel's parameters, number of players, and the resource distribution shape. For any dimension we demonstrate a stability threshold that depends on both the scatter and curvature of the players. When this threshold is crossed, the symmetric equilibrium destabilizes and gives way to a variety of bifurcation types; including, specialist clusters, limit cycles, and sub-games that reproduce the larger game's structure. We ground these results using real-world data for resources as a demonstration of the game's application. Finally we extend the game dynamics to use multi-agent reinforcement learning and further show that the predicted bifurcation structure persists under partial observability and discretized strategy spaces. In all, the influencer's game provides a novel framework for predicting when competitive pressure drives convergence versus fragmentation with possible applications across domains.
作者备注：23 pages 6 figures
观测到的版本
相邻记录可能跳过中间版本；首次发现 v2 及以上也会标为版本更新。
v1 · 2026-11-13 01:33 · 最新观测版本
Learning Dynamics of the Influencer's Game in Resource Landscapes
Across domains as varied as ecology, economics, and online platforms, individuals are incentivized to position themselves within resource-rich strategy spaces. In this work we introduce a new spatial game framework called the influencer's game. Within this new framework players' strategies are represented as positions within a trait space. Players then receive a share of a portion of a resource based on their relative influence at that resource's points traits. For the influencer's game, we show that there is a unique symmetric Nash equilibrium that exists under strict log-concavity of the influence kernel. Using the unique equilibrium we show that the stability of the system depends on the influence kernel's parameters, number of players, and the resource distribution shape. For any dimension we demonstrate a stability threshold that depends on both the scatter and curvature of the players. When this threshold is crossed, the symmetric equilibrium destabilizes and gives way to a variety of bifurcation types; including, specialist clusters, limit cycles, and sub-games that reproduce the larger game's structure. We ground these results using real-world data for resources as a demonstration of the game's application. Finally we extend the game dynamics to use multi-agent reinforcement learning and further show that the predicted bifurcation structure persists under partial observability and discretized strategy spaces. In all, the influencer's game provides a novel framework for predicting when competitive pressure drives convergence versus fragmentation with possible applications across domains.
查看此版本解读 →查看此版本原文 ↗