A Note on the Equivalence of Foreign Exchange Strategic Market Structures

In this paper, we compare the strategic equilibria of an international economy under two different foreign exchange market structures. One market structure consists of all possible pairwise currency markets where currencies are exchanged directly to each other (complete currency market). The other market structure consists of all pairwise markets of one major currency where all currencies are exchanged indirectly via the vehicle currency. Although such structures are equivalent in a competitive international economy, there is no proof yet that they are equivalent in strategic markets with large traders. We show that in a Shapley-Shubik market game of an international imperfectly competitive economy, the standard proof for establishing equivalence of markets structures leads to a common Nash equilibrium which is characterized by trivial trades (wash sales) in the currency markets. Thus, our result casts doubt on the equivalence of foreign exchange market sructures in imperfect competitition.