Bounded Rational Speculative and Hedging Interaction Model in Oil and U.S. Dollar Markets

A ‘bounded rational’ overlay is constructed for a model of an interaction between two players who speculate on oil and the U.S. dollar, subject to financial transaction taxes. This model also has two types of operators: a real economic subject (Air) and an investment bank (Bank). Many investment operators (banks) are also considered. Their behavior equilibrates much more quickly, as they react to the move of Air. In this sense, Air is an acting external agent (such as with an external magnetic field in a magnetic system), whereas the random component of the bounded rational behavior of banks is ‘annealed’ (i.e., averaged out before Air makes its next transaction). Under certain conditions for the model, the equilibrium measure for the bank agents, after Air has played its strategy, is a Gibbs measure from statistical mechanics, as the interactions between operators are that for a Potential game.