On the steady state of continuous-time stochastic opinion dynamics with power-law confidence
This paper introduces a non-linear and continuous-time opinion dynamics model with additive noise and state-dependent interaction rates between agents. The model features interaction rates which are proportional to a negative power of the opinion distances. We establish a non-local partial different...
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| Veröffentlicht in: | Journal of applied probability 2021-09, Vol.58 (3), p.746-772 |
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| container_title | Journal of applied probability |
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| creator | Baccelli, François Vishwanath, Sriram Oh Woo, Jae |
| description | This paper introduces a non-linear and continuous-time opinion dynamics model with additive noise and state-dependent interaction rates between agents. The model features interaction rates which are proportional to a negative power of the opinion distances. We establish a non-local partial differential equation for the distribution of opinion distances and use Mellin transforms to provide an explicit formula for the stationary solution of the latter, when it exists. Our approach leads to new qualitative and quantitative results on this type of dynamics. To the best of our knowledge these Mellin transform results are the first quantitative results on the equilibria of opinion dynamics with distance-dependent interaction rates. The closed-form expressions for this class of dynamics are obtained for the two-agent case. However, the results can be used in mean-field models featuring several agents whose interaction rates depend on the empirical average of their opinions. The technique also applies to linear dynamics, namely with a constant interaction rate, on an interaction graph. |
| doi_str_mv | 10.1017/jpr.2020.113 |
| format | Article |
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The model features interaction rates which are proportional to a negative power of the opinion distances. We establish a non-local partial differential equation for the distribution of opinion distances and use Mellin transforms to provide an explicit formula for the stationary solution of the latter, when it exists. Our approach leads to new qualitative and quantitative results on this type of dynamics. To the best of our knowledge these Mellin transform results are the first quantitative results on the equilibria of opinion dynamics with distance-dependent interaction rates. The closed-form expressions for this class of dynamics are obtained for the two-agent case. However, the results can be used in mean-field models featuring several agents whose interaction rates depend on the empirical average of their opinions. 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| subjects | Computer Science Euclidean space Geometry Mathematics Mellin transforms Networking and Internet Architecture Original Article Partial differential equations Power Probability Reagents Research Papers |
| title | On the steady state of continuous-time stochastic opinion dynamics with power-law confidence |
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