Protocols for negotiating complex contracts - Intelligent Systems, IEEE [see also IEEE Expert]

Simple and complex contracts Negotiation protocols work, in general, via the iterative exchange of proposals and counter-proposals. An agent starts with a contract that’s optimal for that agent and makes concessions, in each subsequent proposal, until either an agreement is reached or the negotiation is abandoned because the latest proposal’s utility has fallen below the agents’ reservation value—that is, the minimum level of contract utility that the agent will accept. Figure 1 shows the proposal exchange model of negotiation, applied to a simple contract. The y-axis represents a contract’s utility to each agent. Each point on the x-axis represents a possible contract, ordered in terms of its utility to agent B. Because there’s no need to negotiate over issues that both parties agree on, we consider only issues where improvement for one party represents a decrement for the other. The arrows represent how agents begin with locally optimal proposals and concede toward each other, with their subsequent proposals, as slowly as possible. We have, for presentation purposes, “flattened” the contract space onto a single dimension, but there should actually be one dimension for every issue in the contract. This approach is perfectly reasonable for simple contracts. Because issues are independent, a contract’s utility for each agent can be calculated as the weighted sum of the utility for each issue. The utility function for each agent is thus a simple one, with a single optimum and a monotonic drop-off in utility as the contract diverges from that ideal. Simple contract negotiations thus typically progress as shown in Figure 2. In this example, the contract consists of 40 binary issues. Each agent starts with a locally optimal proposed contract (at the extremes of the Pareto frontier, representing the set of optimal contracts) and is required to reduce the Hamming distance (the number of issues with different values) between the two agents’ proposals until the agents reach an agreement. With simple contracts, this results in optimal outcomes. We estimated the Pareto frontier using the standard technique of applying an annealing optimizer to differently weighted sums of the two agents’ utility functions. The proposals from each agent start at the agents’ separate ideals and then track the Pareto frontier until they meet in the middle with an optimal agreement. This happens because, with linear utility functions, an agent can easily identify the proposal that represents the minimal concession: the contract that’s minimally worse than the current one is “next” to the current one in the contract space and can be found by moving in the direction with the smallest aggregate Most real-world