Learning by replicator and best-response: the importance of being indifferent

This paper compares two learning processes, namely those generated by replicator and best-response dynamics, from the point of view of the asymptotics of play. We base our study on the intersection of the basins of attraction of locally stable pure Nash equilibria for replicator and best-response dynamics. Local stability implies that the basin of attraction has positive measure but there are examples where the intersection of the basin of attraction for replicator and best-response dynamics is arbitrarily small. We provide conditions, involving the existence of an unstable interior Nash equilibrium, for the basins of attraction of any locally stable pure Nash equilibrium under replicator and best-response dynamics to intersect in a set of positive measure. Hence, for any choice of initial conditions in sets of positive measure, if a pure Nash equilibrium is locally stable, the outcome of learning under either procedure coincides. We provide examples illustrating the above, including some for which the basins of attraction exactly coincide for both learning dynamics. We explore the role that indifference sets play in the coincidence of the basins of attraction of the stable Nash equilibria.     

Dynamics of the UK natural gas industry: System dynamics modelling and long-term energy policy analysis

We present a dynamic model of the indigenous natural gas industry in the UK. The model has been built using a system dynamics approach. Using the model several scenarios have been analyzed. We found that management of the supply-side policy alone cannot substantially postpone the discovery, production and consumption peak. We also found that the dynamics of the main variables, namely, exploration, production and consumption, are sensitive to initial demand conditions. Postponing the onset of gas price increases can therefore be achieved more effectively through efforts to reduce demand growth. One might expect that a low taxation policy would encourage more exploration and production of gas and thereby stimulate higher consumption rates. Instead, there was no overall net effect on production and consumption in the long term. The depletion effect on cost of exploration acts as counterbalance to low taxation policy. Depletion effect causes cost and thus price to rise further which depress consumption rate. The advances in exploration and production technology can delay the peak of exploration, production and consumption. Technological improvements mean lower cost of exploration and production which pressure down the long-term pattern of price dynamics.