Revenue Equivalence of Leveled Commitment Contracts

Tuomas Sandholm and Yunhong Zhou

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 insincerely 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 protocols lead to different decommitting thresholds and probabilities. However, this paper shows that, surprisingly, each protocol leads to the same expected social welfare when the contract price and penalties are optimized for each protocol. Our derivations allow agents to construct optimal leveled commitment contracts. We also show that such integrative bargaining does not hinder distributive bargaining: the excess can be divided arbitrarily (as long as each agent benefits), e.g. equally, without compromising optimality. Revenue equivalence ceases to hold if agents are not risk neutral. A contract optimization service is offered on the web as part of eMediator, our next generation electronic commerce server.

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