标题： 影响信念动态的二元期权市场操纵 显示英文标题

标题： Binary Option Market Manipulation by Influencing Belief Dynamics

摘要： 使用信息几何中的技术，我们构建了一个半哈密顿系统，用于模拟二元资产市场中的交易者信念，并研究信念、信息和权力的不平等或不对称对价格动态的影响。 我们表明，在没有不平等且$N$交易者完全对称的市场中，产生的动力学演化在一个由$2N + 1$维流形组成的流形上，该流形包括一个$2N-2$维中心流形、一个$2$维稳定流形和一个$1$维慢流形。 向交易者引入不对称性可能会降低中心流形的维度，我们通过参数分析证明了这一点。 使用信念模型，我们还研究了代理间通信、外生信息和不对称购买力对价格动态的影响，表明当有影响力的交易者在市场上产生过度影响时，市场泡沫可能会出现，从而影响其他交易者的信念以及价格。 当允许非正式渠道的通信时，这种影响会加剧。 还讨论了信念空间中高曲率区域的影响。 显示英文摘要

摘要： Using techniques from information geometry, we construct a semi-Hamiltonian system modelling trader beliefs in a binary asset market and study the impact of inequality or asymmetry in beliefs, information, and power on price dynamics. We show that in a market with no inequality and $N$ completely symmetric traders, the resulting dynamics evolve on a $2N + 1$ dimensional manifold consisting of a $2N-2$ dimensional centre manifold, a $2$ dimensional stable manifold and a $1$ dimensional slow manifold. Introducing asymmetry into the traders has the potential to decrease the dimension of the centre manifold, which we prove using a parameter analysis. Using the belief model, we also study the impact of inter-agent communication, exogenous information and asymmetric purchasing power on price dynamics, showing that market bubbles can emerge when powerful traders produce outsize influence in the market, thus impacting other traders' beliefs as well as the price. This process is exacerbated when back-channel communication is permitted. The impact of areas of high curvature in belief space is also discussed.