The degree of complexity in a specific negotiation space refers to the complexity of the interaction that is supported. This will be mainly a function of the types of objects of negotiation that are supported (dimension 2) and will correspond to a certain degree of symmetry. We can, however, identify a minimal degree of complexity that must be supported in order for the system to be described as a negotiation. Three dialogue moves must at least be supported, to be realised in either or both modes (dimension 1) : OFFER (different negotiation objects proposed as candidates for mutual acceptance), ACCEPTANCE and REJECTION.
A surprisingly rich interaction can be minimally supported with even these three moves, within each of the three negotiation strategies (mutual refinement, argumentation, 'stand pat'). For example, mutual refinement can be supported by sequences of successive offers from both agents, 'punctuated' by acceptance or rejection. In this case, many indirect effects of the acts will be produced (see below) - an OFFER of "we should move ward2 from North to South" by Agent_2, that follows an OFFER of "we should move ward2" by Agent_1 communicates implicit acceptance of Agent_1's offer (since it subsumes it and elaborates on it). Similarly, the argumentation strategy can be implemented in a rudimentary way since an OFFER that follows a REJECT may be contextually interpreted as a DEFENSE of the previously rejected offer, and so on. However, a richer set of dialogue moves will be required to support more extended (and effective) negotiations, particularly those that work on the meaning of offered negotiation objects (e.g. various QUESTION forms). Finally, it should be noted that the complexity may be more or less symmetrical.
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