Ecosystem stability and learning in linear quadratic network games

In the context of Network Games, the linear quadratic model has been extensively used to model strategic interactions between a group of individuals or organisations. In realistic scenarios, it is common to observe uncertainty on both the network structure and game properties, leading to the study of a generalized game where a player lacks informations on who he's interacting with, and the strength of his externalities. A self-confirming equilibrium can arise as the outcome of a learning process, where an agent is unaware of the identity of her neighbors, receiving only an aggregate contribution she best responds to in order to maximize her utility. The learning process may possible converge to steady states that share some features with the ones reached in the context of ecological communities through the study of the generalized Lotka-Volterra equations using a dynamical mean field method. In this work the linear quadratic model is analysed with the same approach, focusing on the role of predator-prey and mutualistic interactions, stability and connectivity of the network. Similarly to the case of ecological communities, it is shown that under some conditions on the structure of the network, the learning process can lead to inactivity traps, in which a, possibly large, fraction of the network does not contribute to the system. Non-cooperative interactions surprisingly promote stability, while also favouring an increasing fraction of surviving agents at the steady state. Connectivity plays a crucial role in the outcomes of the learning process, promoting as well the stability of the community.