Surplus equivalence of leveled commitment contracts

In automated negotiation systems consisting of self-interested agents, contracts have traditionally been binding. Leveled commitment contracts—i.e., contracts where each party can decommit by paying a predetermined penalty—were recently shown to improve expected social welfare even if agents decommit strategically in Nash equilibrium. Such contracts differ based on whether agents have to declare their decommitting decisions sequentially or simultaneously, and whether or not agents have to pay the penalties if both decommit. For a given contract, these mechanisms lead to different decommitting thresholds, probabilities, and expected social welfare. However, this paper shows that each of these mechanisms leads to the same social welfare when the contract price and penalties are optimized for each mechanism separately. Our derivations allow agents to construct optimal leveled commitment contracts. We show that such integrative bargaining does not hinder distributive bargaining: the surplus can be divided arbitrarily (as long as each agent benefits), e.g., equally, without compromising optimality. Nonuniqueness questions are answered. We also show that surplus equivalence ceases to hold if agents are not risk neutral.