Jean-Louis Rullière

Are game theoretic concepts suitable negotiation support tools? From Nash equilibrium refinements toward a cognitive concept of rationality

If game theory is to be used as a negotiation support tool, it should be able to provide unambiguous recommendations for a target to aim at and for actions to reach this target. This need cannot be satisfied with the Nash equilibrium concept, based on the standard instrumental concept of rationality. These equilibria, as is well known, are generally multiple in a game. The concept of substantive or instrumental rationality has proved to be so pregnant, however, that researchers, instead of re-evaluating its use in game theory, have simply tried to design concepts related to the Nash equilibrium, but with the property of being unique in a game — i.e., they have devised ways ofselecting among Nash equilibria. These concepts have been labeledrefined Nash equilibria.The purpose of this paper is to show the following.(a)The different types of refined Nash equilibria, based on the principle of backward induction, can lead to severe contradictions within the framework itself. This makes these concepts utterly unsatisfactory and calls for a new appraisal of the reasoning process of the players.(b)The degree of confidence in the principle of backward induction depends upon the evaluation of potential deviations with respect to the extended Nash equilibrium concept used and upon the possible interpretations of such deviations by the different players. Our goal is to show that the nature of these possible interpretations reinforces the argument that a serious conceptual reappraisal is necessary.(c)Some form of forward induction should then become the real yardstick of rationality, extending Simonianprocedural rationality towards the concept ofcognitive rationality. This could open the way to a renewed game theoretic approach to negotiation support systems. Such a research program, which would be a revision of the basic game theoretic concepts, is dealt with in the end of the paper.