Contracting Strategy Based on Markov Process Modeling

One of the fundamental activities in multiagent systems is the exchange of tasks among agents (Davis & Smith 1983). In particular, we are interested in contracts among selfinterested agents (Sandholm & Lesser 1995), where a contractor desires to find a contractee that will perform the task for the lowest payment, and a contractee wants to perform tasks that maximize its profit (payment received less the cost of doing the task). Multiple, concurrent contracts take place such that a contract may be retracted because of other contracts. In our work, we are asking the question: What payment should a contractor offer to maximize its expected utility? If the contractor knows the costs of the agents and knows that the agent(s) with the minimum cost are available, then it can offer to pay some small amount above that cost. But the contractor usually will face uncertainty: it might have only probabilistic information about the costs of other agents for a task, and also about their current and future availability. A risk-averse contractor therefore needs to offer a payment that is not only likely to be acceptable to some contractee, but which also is sufficiently high that the contractee will be unlikely to retract on the deal as other tasks are announced by other contractors. A risk-taking contractor, on the other hand, may want to pay a little less and risk non-acceptance or eventual retraction. This abstract defines the contractor’s decision problem, and presents a contracting strategy by which the contractor can determine an optimal payment to offer. The contractor’s decision problem in the contracting process is to find a payment that maximizes its expected utility. The contractor’s utility for the payment, p, is defined as Ps x U(Payofss(p)) + PF x U(PayofliAp)), where UC.) is the utility function, Ps/F denote the probability of success (S) and failure (F) of accomplishing a contract, and Payofw are the payoff of S and F, respectively, given p. We have developed a four-step contracting strategy for the contractor to compute Psn; and Payo& and thus to find the best payment to offer. First, the contractor models the future contracting process stochastically as a Markov Process (MP). An example MP model is shown in Figure l-(a). StateZ is the initial state, and state A is the announced state. State C is the contracted state, where the contractor has awarded the task to one of those who accepted its offer. State Sand F are success and failure states, respectively. From A, the