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246 Socially Intelligent AgentsA) Responsive Mechanism B) Trade−Off Mechanism C) Meta StrategyU(b(x))1.0x1.01.00101U(b)0101U(b)U(b)U(b(y))y0U(a(x))U(a)U(a(y))1.0 0U(a)1.0 0U(a)1.0Figure 30.1.Utility Dynamics of the Mechanismsilarity [14] to approximate the preference structure of the negotiation opponent.It then uses a hill-climbing technique to explore the space of possible contracttrade-offs for a contract that is most likely to be acceptable. The complexity ofthis algorithm has been shown to grow linearly with growing numbers of issues[4].The details of the algorithms can be found in [3] and [4]. The dynamics ofthe contract utility generated by each of the above mechanisms and one possiblecombination is given in figure 30.1 A, B and C respectively for the alternatingsequential protocol. The filled ovals are the utility of the offered contractsfrom agent to agent from agent ’s perspective, and the unfilled ovalsrepresent the utility of the offered contracts from agent to agent from agent ’sperspective. The patterned oval represents the joint utility of the final outcomes.The pareto-optimal line is given by the curvilinear line connecting the two pairsof payoffs ´½ ¼µ and ´¼ ½µ. Figure 30.1 A represents a possible execution tracewhere both agents generate contracts with the responsive mechanism. Eachoffer has lower utility for the agent who makes the offer, but relatively moreutility for the other. This process continues until one of the agents is satisfied(Í ´Ü Ø Ø¼µ Í´Ü µ), where is the contract offered by agent to ÜØ at time Ø. This termination criteria is referred to as the cross-over in utilities.The responsive mechanism can select different outcomes based on the rate ofconcession adopted for each issue (the angle of approach to the outcome pointin figure 30.1 A).Figure 30.1 B represents another possible utility execution trace where bothagents now generate contracts with the trade-off mechanism. Now each offerhas the same utility for the agent who makes the offer, but relatively moreutility for the other (movement towards the pareto-optimal line). The trade-offmechanism searches for outcomes that are of the same utility to the agent, butwhich may result in a higher utility for the opponent. Once again, this is asimplification for purposes of the exposition—an offer generated by agent