We generalize the DeGroot model for opinion dynamics to better capture realistic social scenarios. We introduce a model where each agent has their own individual cognitive biases. Society is represented as a directed graph whose edges indicate how much agents influence one another. Biases are represented as the functions in the square region $[-1,1]^2$ and categorized into four sub-regions based on the potential reactions they may elicit in an agent during instances of opinion disagreement. Under the assumption that each bias of every agent is a continuous function within the region of receptive but resistant reactions ($\mathbf{R}$), we show that the society converges to a consensus if the graph is strongly connected. Under the same assumption, we also establish that the entire society converges to a unanimous opinion if and only if the source components of the graph-namely, strongly connected components with no external influence-converge to that opinion. We illustrate that convergence is not guaranteed for strongly connected graphs when biases are either discontinuous functions in $\mathbf{R}$ or not included in $\mathbf{R}$. We showcase our model through a series of examples and simulations, offering insights into how opinions form in social networks under cognitive biases.

翻译：我们推广了用于观点动力学的DeGroot模型，以更好地捕捉真实社会场景。我们引入了一个每个智能体都具有各自认知偏差的模型。社会被表示为一个有向图，其边指示智能体之间相互影响的程度。偏差被表示为方形区域$[-1,1]^2$中的函数，并根据它们在观点分歧情境下可能引发的智能体潜在反应划分为四个子区域。假设每个智能体的每个偏差都是接受但抗拒反应区域（$\mathbf{R}$）内的连续函数，我们证明若图是强连通的，则社会将收敛至共识。在相同假设下，我们进一步证明整个社会收敛至一致意见当且仅当图的源组件（即无外部影响的强连通分量）收敛至该意见。我们通过实例和仿真展示了模型，揭示了认知偏差下社会网络中观点的形成机制。