The paper proposes a theory for two-player dynamic deterministic games where the players cannot make formal and unconditionally binding contracts, but can cooperate by the way of reaching informal agreements whose violation at any stage of the game is prevented by the threat of retaliations at subsequent stages. The theory is based on the introduction of equilibrium memory strategies with the embodied retaliation mechanism, and on the extension of the classical bargaining theory to the case where the set of acceptable outcomes of the game is a nonconvex and possibly disconnected subset of the set of all achievable pay-offs. The proposed approach permits the definition of a bargaining solution over which neither player will be tempted to cheat, and which is selected according to a set of rules that seem reasonable, even though they are to some extent arbitrary.