International commodity markets have most commonly been analysed with the use of perfectly competitive models, ignoring the effects of government intervention combined with market power. Such models are unable to account for retaliation and other strategic effects that have recently been observed in wheat and other agricultural markets. In this thesis, a framework is developed for analysing strategic interactions in agricultural trade. Policymakers set domestic prices to optimise weighted welfare functions, where the weights reflect the relative influence of consumers, producers and taxpayers. These weights are estimated from observed domestic prices in each region. Non-cooperative, game-theoretic equilibria are utilised to determine the outcome of trade wars under various scenarios. Cournot-Nash, Stackelberg and conjectural variations solutions are obtained in a static framework. The analysis is then extended to include lags in production and decision making, and the strategic and dynamic elements of the policymaker's problem are examined in a dynamic difference game. Prices are set in each region to optimise a quadratic objective function, subject to linear intertemporal constraints. A dynamic programming approach, using Riccati equations, is developed to solve for the single controller problem. An iterative procedure is then applied to take account of the interdependence of all countries' policies. To incorporate storage in the deterministic model, multi-period quadratic programming is used to find the optimum tariffs and stock levels simultaneously. This approach allows the restriction that stocks must be non-negative. The analysis is applied to a model of the international wheat market. The results indicate that strategic behaviour can significantly influence optimal trade policy, and hence prices, trade flows and the distribution of welfare.