意见动态的微分对策模型：一致与不一致作为纳什均衡
A Differential Game Model of Opinion Dynamics: Accord and Discord as Nash Equilibria
摘要：
提出了一个意见动态的非合作微分（动态）对策模型。在这个博弈中，代理人的动机取决于他们对他人意见的性质的期望，以及他们受他人影响的敏感程度，他们有多固执，以及他们愿意在规定的时间间隔内改变他们对一系列问题的看法。这些动机是由所有行为者独立形成的。网络中纳什均衡的存在意味着一种集体行为是在局部互动规则和这些个体动机的基础上产生的。我们证明了一个唯一的纳什均衡可能存在于完全不同的情况下的游戏。它不仅可能存在于网络中的代理人之间的感知和谐，而且也可能存在于代理人对问题之间的相关性有不同看法的情况下。第一种导致网络中的一致，通常表现为部分共识，第二种导致意见不一致，表现为摇摆不定。在达成一致的情况下，网络中的和谐可能表现为对问题的成对概念的相似性，但也可能是对网络中“领导者”地位的一致意见。只有当网络处于不协调状态时，纳什均衡才可能不存在。
英文摘要：
A noncooperative differential (dynamic) game model of opinion dynamics is proposed. In this game, the agents' motives are shaped by their expectations of the nature of others' opinions as well as how susceptible they are to get influenced by others, how stubborn they are, and how quick they are willing to change their opinions on a set of issues in a prescribed time interval. These motives are independently formed by all agents. The existence of a Nash equilibrium in the network means that a collective behavior emerges out of local interaction rules and these individual motives. We prove that a unique Nash equilibrium may exist in the game under quite different circumstances. It may exist not only if there is a harmony of perceptions among the agents of the network, but also when agents have different views about the correlation among issues. The first leads to an accord in the network usually expressed as a partial consensus, and the second to a discord in the form of oscillating opinions. In case of an accord, the harmony in the network may be in the form of similarity in pairwise conceptions about the issues but may also be an agreement on the status of a "leader" in the network. A Nash equilibrium may fail to exist only when the network is in a state of discord.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
