Network Effects in Performative Prediction Games

This paper studies the multi-agent performative prediction (Multi-PP) games over multiplex networks. We consider a distributed learning setting where agents partially cooperate on an agent network, while during learning, the data samples drawn depend on the prediction models of the agent itself and neighboring agents on a population network. The dynamics of Multi-PP games is hence affected by the interplay between both networks. This paper concentrates on this Multi-PP game with the following contributions. Firstly, we analyze sufficient conditions for the existence of the performative stable equilibrium (PSE) and Nash equilibrium (NE) of the Multi-PP games. Secondly, we analyze the changes to the equilibrium induced by perturbed data distributions, and derive the closed-form solutions where the network topologies are explicit. Our results connect the existence of PSE/NE with strengths of agents' cooperation, and the changes of equilibrium solutions across agents with their node centrality, etc. Lastly, we show that a stochastic gradient descent (SGD) based distributed learning procedure finds the PSE under the said sufficient condition. Numerical illustrations on the network effects in Multi-PP games corroborate our findings.