Speculative and hedging interaction model in oil and U.S. dollar markets: Nash equilibria for one or more banks

We determine the (refined) Nash equilibria for a bounded rational Carfi'-Musolino speculative and hedging model. This model shows two types of operators: a real economic subject (Air) and one or more investment banks (Bank). We consider the bank agents' behavior to equilibrate much more quickly than that of Air, as they react to the move of Air. In this sense, Air is an acting external agent, whereas the action of the banks is `annealed' - i.e., equilibrates before Air makes its next transaction. When Air makes no purchases of oil futures as a hedge, two Nash equilibria exist for the bank agents. However, a unique Nash equilibrium exists for the bank agents when Air makes a purchase. This is a result of Air's purchase breaking a symmetry of the potential. The existence of multiple equilibriums in this two-market model is in the spirit of the Sonnenschein-Mantel-Debreu theorem, and is associated with phase transitions in statistical mechanics.