Multi-layer Cournot-congestion model

Geopolitical instability, climate change and black swan events disrupt the trade and logistics of resources around the globe. Events such as the unforeseen closure of the Suez Canal or the cessation of trade between some players due to wars or embargos are some examples of this. The problem of predicting local price change under modification of an underlying transport network unites elements of game theory, network theory and transport theory. The micro-economic Cournot oligopoly game involves modelling economic actors as rational players attempting to maximise profit. Under fixed transport conditions, analytical results can be found on the equilibria. Similarly, the transport layer can be analytically solved using techniques for selfish routing. Where trade and transport layers are linked together there is inter-layer feedback wherein players attempt to maximise their utility. We looked at the nature of the approach towards a new equilibrium under this instantaneous network change. In this respect our findings indicate that players benefit significantly from taking advantage of the non-simultaneous responses to the market rather than from moving to a new equilibrium utility. We found that when uncoupled, both the upper and lower layers have concave utility curves meaning there exist unique and stable equilibria in both cases. This leads to the multilayer model having non-unique stable equilibria for which general solutions exist.