Using an Annealing Mediator to Solve the Prisoners' Dilemma in the Negotiation of Complex Contracts

Research on computational models of negotiation has focused almost exclusively on defining simple contracts consisting of one or a few independent issues, implying tractable contract spaces as well as single-optima utility functions for the agents involved. Many real-world contracts, by contrast, are much more complex, consisting of multiple inter-dependent issues, resulting in intractably large contract spaces and multiple-optima utility functions. Complex contracts require negotiation algorithms substantially different than those that have been considered to date for simple contracts. Previous work by the authors has shown that endowing the negotiating agents with a time-decreasing willingness to provisionally accept inferior contracts (i.e. to ‘anneal’) results in superior final contract utilities, but creates a prisoners’ dilemma wherein agents are individually incented not to anneal. In this paper we report a solution to this problem wherein the annealing is done by a mediator, and the negotiating agents are incented to follow a truth-telling strategy that maximizes social welfare. 1 The Challenge: Negotiating Complex Contracts Work to date on computational models of negotiation has focused almost exclusively on defining contracts consisting of one or a few independent issues [1] [2]. We can frame what these techniques do as follows (see Figure 1 below). Each point on the X axis represents a candidate contract. The Y axis represents the utility of each contract to each agent. Both agents have a reservation utility value: only contracts whose utility is above that agent’s reservation value will be accepted. Since relative few issues are involved, the space of all possible contracts can be explored exhaustively, and since the issues are independent, the utility functions mapping a candidate contract to its utility for an agent are linear [3], with a single optimum in the utility function for each agent. In such a context, the reasonable strategy is for each agent to start at its own ideal contract, and concede, through iterative proposal exchange, just enough to get the other party to accept the contract. Since the utility functions are simple, it is feasible for one agent to infer enough about the opponent’s utility function through observation to make concessions likely to increase the opponent’s utility.