Multiple Nash equilibria in tariff games

Unlike the case of competitive equilibria for which there is the index theorem, almost nothing is known about multiple equilibria in Nash games. Multiple Nash equilibria are hard to find computationally accounting for spare prior literature discussion. Existing numerical literature on tariff games either assumes uniqueness or uses restrictive functional forms that guarantees this is the case. Here, we show for pure exchange Constant Elasticity of Substitution (CES) two country models with tariffs both how the introduction of a tariff can generate multiple competitive equilibria and related examples of widely separated multiple Nash equilibria. These typically occur when substitution elasticities are low, although implied import demand elasticities can still be high if the shares of trade in consumption are small. The implication seems to be that as one moves away from the constant elasticity excess demands (offer curve) formulations used in the optimal tariff literature to explicit structural models of international trade, multiplicity of Nash equilibria may well be present.