Negotiations between the EU and the UK have reached deadlock, with the positions of the UK (no backstop, no single market, no customs union, no dependence on the ECJ), Ireland (backstop, no hard border) and the EU (backstop, indivisibility of the four freedoms, no cherry-picking) all being mutually exclusive. In the current stage of negotiations (or lack of, as the EU insists there will be no re-opening of talks) a hard Brexit is the only possible equilibrium. From a game theoretical perspective, the backstop is inacceptable for any British government as it permanently manifests only one sub-game perfect equilibrium, which is the backstop itself. Conversely, a time limitation on the backstop is unacceptable for the EU, as it risks manifesting another sub-game perfect equilibrium, which is hard Brexit. There­fore, neither renegotiation of the backstop nor elections or the extension of the withdrawal period of Article 50 TFEU can break the deadlock. A first-best solution, which from a trade perspective would be the continuation of UK membership in a reformed EU, is beyond the scope of this analysis. We instead take Brexit as given and discuss terms that limit its political and economic damage. We focus on the contentious issues only; we do not elaborate on the provisions of the Withdrawal Agreement itself, for which a settlement has been reached that appears to be satisfactory for both sides. Because the core debate revolves around the backstop and the issue of a possible border between the Northern Ireland and the Republic of Ireland, we mostly deal with trade policy arrangements.