Proof. See Appendix
4.3 Strategic Ignorance in Argumentation-based Negotiation
4.3.1 Motivation
To date, argument-based negotiation (ABN) among artificial agents has of necessity been less complicated than among humans, because humans have the creativity to use arguments which are beyond/broader than the context of the negotiated issues, and to seek/request the exact meaning of their opponent’s argument when it is ambiguous;
none of which can be done by artificial agents due to limitations in their ontology, knowledge and reasoning.
When the negotiated issues or protocol are complicated such as in an ABN, the cost incurred from the negotiation process, in terms of time and computational complexity, cannot be ignored. Intuitively, this cost increases with an increasing number of possible arguments in the ABN. And it will also increase if agents do not trust each other, because it will take some time to assess the validity of each argument, as described
in generating/interpreting an argument, then those agents may need more time to respond and/or understand the meaning of their opponent’s argument. Excessive costs occurring from these factors may diminish the agent’s gains from using an ABN, thus discouraging the agent from using argumentation, especially when there are alternative solutions such as negotiating with other sellers/buyers who will not use argumentation [Karunatillake and Jennings, 2005].
In this section, we assume that the context of the negotiation is the same, i.e. the purchasing of a product or service with its price as the primary issue, but based on ABN protocol. Our focus here is on an ABN between a buyer and a seller agent who do not necessarily trust each other, and both agents may have different ontologies, knowledge and/or reasoning engines. Note that these cannot be completely different, because for the negotiation to work properly there needs to be at least some common ground such as the description of the service/item and the unit price. Here, argumentation could be used either to persuade an opponent to accept an offer or to change its stance (e.g. trust) toward the proponent, as shown in Figure 4-3.
Realizing that an agent’s argument may not be understood by its opponent, agents should agree at least to inform their opponent that they do not understand the argument being received or they are unable to reply to the argument. This is important because misunderstanding or ignorance may cause an indeterminate process/stall in the negotiation. However, allowing agents to do so means allowing them to ignore their opponent’s arguments when they do not want to respond to them. Thus, a rational agent may use ignorance as a strategy to avoid a dialog which may lead it into a weaker position (e.g. lower expected payoff) during the negotiation. In addition, an agent may
also deliberately choose not to use specific arguments during negotiation. For example, if a property agent (seller) knows that a buyer drives a car, then persuading the buyer by argument “this apartment is less than a minute walking distance from the bus station” will be useless or even cause a negative impact because the buyer may not like a crowded area. We call this agent’s strategy of avoiding argumentation, either by pretending that it cannot understand the argument or avoiding the use of specific arguments, as strategic ignorance.
Figure 4-3 An illustrative example of ABN in natural and agent language
To the best of our knowledge, this strategy has not been broadly explored in the automated negotiation literature, especially in the context of ABN. Perhaps the work that comes closest to exploring strategic ignorance is by Karunatillake and Jennings [2005]
who have shown the benefit of avoiding argumentation (evading conflict) when the ABN Negotiation over a used car in natural language
Buyer: How much does it cost?
Seller: $5000, plus a new tire and a stereo.
Buyer: How about $4000?
Seller: $5000 is very cheap. It only has 120,000 Km. It’s rarely been used.
Buyer: Yeah… But it’s manual. I can have an automatic one for $5000.
Seller: Believe me, you can’t find a better one for this price.
..…
Negotiation in agent language Buyer: ask( price )
Seller: offer( price(this, 5000) ∧ add(tire, 1) ∧ add(stereo, 1) ) Buyer: offer( price(this, 4000) )
Seller: inform( quality(kms(this, 120000) ∧ usage(this, rare)) → offer_price(5000, cheap) ) Buyer: inform( quality(transmission(this, manual)) → ¬ offer_price(5000, cheap) )
Seller: inform( ¬∃ X (price(X, 5000) ∧ better_quality(X, this)) ) ..…
other sellers (or what they called ‘resources’ in their paper). Using empirical simulation, they found that when the availability of ‘resources’ are high, then arguing is less favorable, because the cost from arguing may be higher than the cost of seeking other
‘resources’. Our work is similar to theirs in that argumentation may incur some costs, but different in the sense that we do not assume the existence of any other non-arguing
‘resources’. So, our agent can avoid argumentation by sending a statement “refusal to argue” for specific issues, such as “I do not understand your argument” or “No comments” without breaking the negotiation. For this supposition to work, we assume that all agents have universal understanding toward this statement and will avoid reiterating similar argumentation upon receiving it.
Finally, it is worth mentioning that ignorance in argumentation is not the same as argument from ignorance (argumentum ad ignorantiam) [Walton, 1995]. The latter concept is used to describe arguments without solid knowledge/evidence that are subject to rebuttal, an issue commonly studied in the area of non-monotonic logic and reasoning.
4.3.2 Basic Model
Suppose that a buyer B wants to buy an item from a seller S, where other buyers/sellers may be available but each negotiation session is exclusively between a buyer and a seller only (concurrent bilateral negotiation in Assumption 4-4). In our ABN protocol, either party opens the negotiation by sending a message (an offer and/or an argument) to the other party, who is obliged to reply by offer and/or counter-argument. As usual, our approach here presumes an uncertain environment, in which deliberation and meta-reasoning is needed by the agent in maximizing their expected
utility. Moreover, arguments are used by both parties to persuade their opponent to accept their offer or to justify their refusal of their opponent’s proposal (Assumption 4-5).
Since both parties represent different owners, they may have different (or identical) ontologies, knowledge, and reasoning engines for generating and understanding the arguments. Both parties know that their opponent may not necessarily understand all their arguments, and they can inform them if any argument is not understood. Suppose also that the buyer does not necessarily know the real value of the negotiated item (this assumption is slightly different from Assumption 4-6).
Assumption 4-7. (Uncertain valuation) The buyer’s estimated valuation Bt is not