Defeat Among Negotiation Arguments Ronald P. Loui, 1 Fernando Tohmé, 2 Guillermo Simari 3 Abstract. Recent work by Parsons-Sierra-Jennings and Kraus-Sycara-Evenchik, and others, has put formal representations of argument together with negotiation dialogues. Unfortunately, the analysis has not been as penetrating as perhaps it could be. This is because the authors have been (i) attempting to formalize negotiation speech acts too broadly while (ii) including explicit argument moves in the dialogue which (iii) refer to domain features. Here, we aim to simplify the issues. First, we restrict the ontology to abstract properties of the game. The same basic CBR ideas are rendered using a simple representation of prior negotiations. The advantage is that defeat among arguments referring to precedent settlements can be seen clearly. This gives way to a more complicated Simari-Loui style of argument as we consider the meta- strategies for how much each party would like to base negotiation on argumentation. 1 ARGUMENT AND NEGOTIATION The idea that negotiation dialogues contain argumentation subdialogues is prevalent in AI. Sycara and Carberry (with Chu-Carroll and Lambert) are early notable authors on the subject. Recently, Parsons (with Noriega, Sierra, Jennings, Wooldridge, McBurney, and others) and Kraus (with Sycara and Evenchik) have produced papers that have had many followers (e.g., Qiu-Tambe, Rueda-García-Simari, Rahwan-Sonenberg, Koit-Õim, Torroni, Brito-Novais- Neves) . Work by Ferguson (with Allen) represents a bridge between the two, where planning dialogues are “mixed-initiative” and contain explicit arguments. The advent of formal methods for representing arguments makes clear the possibility of formalizing the argument subdialogues within a formal model of negotiation. Much work on argument theorizes about the argument-moves and speech acts appropriate to the dialectical process (e.g., Gordon, Leenes-Lodder-Hage, Verheij). 1 Washington University in St. Louis, USA, loui@cs.wustl.edu. 2,3 Universidad Nacional del Sur, Bahía Blanca, ARGENTINA. Loui suggested that the same could be done for argument in negotiation dialogues in two earlier. Our problem is that the scope of the resulting work has been broad and the ideas diffuse. This is not altogether a bad thing, as the formalization of argument and negotiation may mean many things to many people. However, we believe the picture can be greatly simplified. There can be is such a thing as too much good notation. Instead of trying to define numerous formal protocols that seek to capture the wide variety of speech acts related to persuasion and negotiation, we ask two simple questions: I. What is the minimal economic model upon which meaningful negotiation arguments can be constructed, and what is the dynamics of this small model? and II. What is the cost to the negotiator who declines to accept rational argumentation; that is, what game contains the argument-in-negotiation game as a sub- game? The answer to the first is not surprising, and it is proposed as a “blocks-world” simplification of what has become a complicated area. The AI ideas deserve to be exported to the related social science fields in a clear form, and our simplest economic ontology aims to be a candidate for such export. The answer to the second is a bit surprising, as it contemplates a meta-game with payoffs attached to both the degree to which and the manner in which a negotiator is reasonable. 2 ABSTRACT ECONOMIC ONTOLOGY Sycara’s PERSUADER, in the case-based tradition, did not fix the ontology upon which disputes would be judged similar. In a Labor-Management dispute, it would be fair to consider past wage settlements, even past settlements of competitors’ disputes, adjusted by such things as the financial situation of the firm, the productivity of the