Opinion Dynamics with Limited Information
Opinion Dynamics with Limited Information
复制标题
信息有限的舆论动态
作者：
Dimitris Fotakis;Vardis Kandiros;Vasilis Kontonis;Stratis Skoulakis
本文在Friedkin和Johsen提出的著名模型（FJ模型）的基础上研究了意见形成博弈。在当今庞大的社交网络中，假设代理人在每一轮中都会考虑所有朋友的意见来更新他们的意见是不现实的。因此，我们感兴趣的是FJ模型的简单和自然变体的收敛性质，这些变体在每一轮中使用有限的信息交换并收敛到相同的稳定点。与FJ模型一样，我们假设每个代理i在[0，1]$$ s i ∈ [ 0，1 ]中有一个内在意见$$s_i，并且在每一轮t中在[0，1]$$ x i（t）∈ [ 0，1 ]中保持一个表达意见$$x_i（t）。为了模拟有限的信息交换，我们考虑一个意见形成过程，其中每个代理i在每轮t与一个随机朋友j会面，并且只学习她当前的意见$$x_j（t）$$ x j（t）。j对i的影响量由i与j相遇的概率p_{ij} p ij反映。然后，代理i遭受的分歧成本是$$（x_i（t）- s_i）^2$$（x_i（t）- s i）2和$$（x_i（t）- x_j（t））^2$$（x i（t）- x j（t））2的凸组合。在这种情况下，一类重要的动力学是无遗憾动力学，即动力学，确保消失的遗憾对经验丰富的分歧成本的代理。我们显示了指数差距之间的收敛速度没有遗憾的动态和更一般的动态，不确保没有遗憾。我们证明了没有后悔动力学需要大约$$varOmega（1/varepsilon）$$ Ω（1 / ε）轮到FJ模型的稳定点的距离$$varepsilon $$ ε之内。另一方面，我们提供了一个意见更新规则，该规则不确保不后悔，并且在$$中收敛到$$x^*$$ x。 ilde{O}（log ^2（1/ε））$$ O ~（log 2（1 / ε））轮次。最后，在我们的FJ模型的变体中，我们证明了代理可以采用一个简单的意见更新规则，该规则确保对经验分歧成本没有遗憾，并导致意见向量收敛到FJ模型的稳定点$$x^*$$ x ^，在$$中的距离$$vareps $$ ε内。 extrm{poly}（1/vareps）$$ poly（1 / ε）rounds.考虑到我们的无悔动力学下限，这种收敛速度接近最佳可能。
We study opinion formation games based on the famous model proposed by Friedkin and Johsen (FJ model). In today’s huge social networks the assumption that in each round agents update their opinions by taking into account the opinions of all their friends is unrealistic. So, we are interested in the convergence properties of simple and natural variants of the FJ model that use limited information exchange in each round and converge to the same stable point. As in the FJ model, we assume that each agent i has an intrinsic opinion $$s_i in [0,1]$$ s i ∈ [ 0 , 1 ] and maintains an expressed opinion $$x_i(t) in [0,1]$$ x i ( t ) ∈ [ 0 , 1 ] in each round t . To model limited information exchange, we consider an opinion formation process where each agent i meets with one random friend j at each round t and learns only her current opinion $$x_j(t)$$ x j ( t ) . The amount of influence j imposes on i is reflected by the probability $$p_{ij}$$ p ij with which i meets j . Then, agent i suffers a disagreement cost that is a convex combination of $$(x_i(t) - s_i)^2$$ ( x i ( t ) - s i ) 2 and $$(x_i(t) - x_j(t))^2$$ ( x i ( t ) - x j ( t ) ) 2 . An important class of dynamics in this setting are no regret dynamics, i.e. dynamics that ensure vanishing regret against the experienced disagreement cost to the agents. We show an exponential gap between the convergence rate of no regret dynamics and of more general dynamics that do not ensure no regret. We prove that no regret dynamics require roughly $$varOmega (1/varepsilon )$$ Ω ( 1 / ε ) rounds to be within distance $$varepsilon $$ ε from the stable point of the FJ model. On the other hand, we provide an opinion update rule that does not ensure no regret and converges to $$x^*$$ x ∗ in $$ ilde{O}(log ^2(1/varepsilon ))$$ O ~ ( log 2 ( 1 / ε ) ) rounds. Finally, in our variant of the FJ model, we show that the agents can adopt a simple opinion update rule that ensures no regret to the experienced disagreement cost and results in an opinion vector that converges to the stable point $$x^*$$ x ∗ of the FJ model within distance $$varepsilon $$ ε in $$ extrm{poly}(1/varepsilon )$$ poly ( 1 / ε ) rounds. In view of our lower bound for no regret dynamics this rate of convergence is close to best possible.
影响因子：
1.1
作者：
Ferraioli, Diodato;Goldberg, Paul W.;Ventre, Carmine
通讯作者：
Ventre, Carmine