1 Collective Dynamics of Faustian Agents ULRICH KRAUSE University of Bremen Department of Mathematics, Bibliothekstr. MZH, 28334 Bremen, Germany krause@math.uni-bremen.de http://www.informatik.uni-bremen.de/~krause/ Paper dedicated to Ian Steedman on the occasion of his retirement 1 Introduction In the meantime things have changed a lot – the rational agent, representative or not, is no longer the main character on stage. Other characters came into play like bounded rational agents, heterogeneous agents, reciprocators, imitators, .... A recent survey on heterogeneous agent models in economics and finance starts with the following statement [7] “Economics and finance are witnessing an important paradigm shift, from a representative, rational agent approach towards a behavioral, agent-based approach in which markets are populated with boundedly rational, heterogeneous agents using rule of thumb strategies.” This was very different when Ian Steedman and I published about twenty years ago an article on multi-faceted individuals or Faustian decision-takers. (See [19]). Opening up the black box of the rational decision-taker in that article, we found a huge variety of diverse characters, ranging from a Pareto-type over hierarchical-types to the harmonic-type, of which the rational character is a special case. This paper discussed also the question of the identity of a person in spite of this variety. Interestingly, this became recently an issue in economics (see [2], [9], [16]). The present paper starts with the concept of a Faustian agent, and analyzes the dynamics of many interacting agents of this kind. Though the social and economic life is full of interactions among different kinds of people, the dynamics of interaction has been widely neglected in economic theory. The concept of a representative agent, for example, wipes out any interaction. One may think also of the difficulties in general equilibrium theory to prove stability for equilibria (see the critical assessments in [1], [8]). The dynamics of interaction, as modelled in the present paper, originates from the field of opinion dynamics (see for this [5], [6], [12]). One of the main issues in this field is whether the agents will reach a consensus. Thus, in this paper conditions will be examined under which heterogeneous agents approach a joint action by using thumb rules of compromising. In Section 2 the concept of a Faustian agent and of an agent's character will be outlined following [19]. In Section 3 we concentrate on a particular kind of character which seeks for a compromise by taking a mean of values. Since there are many kinds of means, there are many possible compromising characters. In Section 4 the interaction among compromising