A dynamical model describes the negotiation process that led to the 2015 Paris Agreement on climate change.

This article investigates a two-timescale opinion dynamics model, named the concatenated Friedkin–Johnsen (FJ) model, which describes the evolution of the opinions of a group of agents over a sequence of discussion events. The topology of the underlying graph changes with the event, in the sense that the agents can participate or less to an event, and the agents are stubborn, with stubbornness that can vary from one event to the other. Concatenation refers to the fact that the final opinions of an event become initial conditions of the next event. We show that a concatenated FJ model can be represented as a time-varying product of stochastic transition matrices having a special form. Conditions are investigated under which a concatenated FJ model can achieve consensus in spite of the stubbornness. Four different sufficient conditions are obtained, mainly based on the special topological structure of our stochastic matrices.

Heterogeneous bounded confidence opinion dynamics with an adaptation policy of the agents' confidence thresholds is considered. The strategy implemented by each agent consists of increasing his confidence thresholds when he has no active neighbor, thus strengthening his heterophilous propensity. Moreover, his adaptation algorithm is stopped if there is a minimal number of agents within his similarity interval. The heterogeneity of the model could lead to interesting scenarios, e.g. steady-state oscillatory behaviors and practical clustering. Sufficient conditions for reaching in finite time a practical consensus are proposed. An upper bound on the maximum number of steady-state practical clusters which depends on the parameters of the confidence thresholds adaptation algorithm is obtained. The steady-state behaviors in the presence of one-sided confidence thresholds and stubbornness are discussed. Numerical simulations verify the theoretical results.

We consider complex multistage multiagent negotiation processes such as those occurring at climate conferences and ask ourselves how can an agent maximize its social power, intended as influence over the outcome of the negotiation. This question can be framed as a strategic game played over an opinion dynamics model, in which the action of an agent consists in stubbornly defending its own opinion. We show that for consensus-seeking opinion dynamics models in which the interaction weights are uniform, the optimal action obeys to an early mover advantage principle, i.e. the agents behaving stubbornly in the early phases of the negotiations achieve the highest social power. When looking at data collected from the climate change negotiations going on at the United Nations Framework Convention on Climate Change, we find evidence of the use of the early mover strategy. Furthermore, we show that the social powers computed through our model correlate very well with the perceived leadership roles assessed through independent survey data, especially when non-uniform weights incorporating economical and demographic factors are considered.