Next Frontier in Agent-Based Complex Automated Negotiation by Katsuhide Fujita Takayuki Ito Minjie Zhang & Valentin Robu

Author:Katsuhide Fujita, Takayuki Ito, Minjie Zhang & Valentin Robu
Language: eng
Format: epub
Publisher: Springer Japan, Tokyo

2 Negotiation with Nonlinear Utilities

We begin with the situation where agents want to reach an agreement. There are issues, , to be negotiated. The number of dimensions of the utility space is the number of issues . For example, if there are two issues, the utility space has three dimensions. An issue has a value drawn from the domain of integers , i.e., . A contract is represented by a vector of issue values .

An agents utility function is described in terms of constraints. There are constraints, . Each constraint represents a region with one or more dimensions and has an associated utility value. A constraint has value if and only if it is satisfied by contract .

Figure 1 shows a model of a utility space with interdependent issues. A node indicates an issue and an edge indicates a constraint. This model can represent unary constraints, binomial constraints, and ternary constraints. In this example, this constraint has a value of 100 and holds if the value for issue 1 is in the range of [4, 8] and the value for issue 2 is in the range of [3, 7]. Similarly, the constraint has a value of 100 and holds if the value for issue 1 is in the range of [1, 3], the value for issue 2 is in the range of [2, 7], and the value for issue 3 is in the range of [4, 5].

An agent’s utility for a contract is defined as , where is a set of possible contracts (solutions) of . Every agent that participates in the negotiations has its own, typically unique, set of constraints.

In this paper, we assume the fundamental form of a decision-making problem, such as that of designing a car. As a specific example, we can cite the problem of deciding the hall style for an academic meeting or conference. In this example, there are specific issues, such as cost and capacity, with options of 500–700 thousand yen or 700–900 thousand yen, and 50–100 people or 100–150 people. We set the evaluation value considering the relationship of each issue and another issue against each choice (for example, we can spend more if we can reserve the larger hall) and decide the answer for each issue. Now, the preference information that the agent should have is the combination between the alternative solution for each issue and that for another issue and the evaluation value. The constraint representation in this paper is sufficient to express this information and can accommodate the assumptive problem.

The object function for our protocol can be described as:

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