ABSTRACT

Introduction Our goal in this contribution is to introduce the basic assumptions and features of our market models, and to give some early results of one of our “cyborg” experiments – that is, experiments involving human as well as robotic agents. But we will begin with a brief history of the project, written by Ralph. In 1968, after moving from the math department of Princeton University to that of the University of California at Santa Cruz, I met Dan, then a grad. student. After Dan’s PhD and some early positions, he became professor of economics at UCLA. During the 1980s I visited frequently at UCLA, and we used to meet for lunch at the faculty club. While I had no actual involvement in mathematical economics, I nevertheless kept up on the news through Dan. Then in 1985, Dan moved to UC Santa Cruz, and we continued meeting for the occasional lunch at the faculty club. Meanwhile, chaos theory was heating up as a new style of applied math, and the economics community was becoming curious. Richard Goodwin, as assistant professor at Harvard, fellow of Peterhouse College (Cambridge) and professor in Siena, had led a long-term project on non-equilibrium economics, nonlinear dynamics and so on. He became an early adopter and harbinger of chaos theory. His 1988 lectures in Siena appeared as a book in 1990, spreading his enthusiasm. All this led to my invitation to give the Jacob Marshak Lecture at UCLA in January, 1987. After my talk on “Nonlinear Systems, Complex Dynamics, and the Social Sciences” there followed a lively Q&A, during which there were several questions from an Indian gentleman revealing a deep knowledge and understanding of dynamical systems theory. At the end, I went up to him to inquire, “Who are you?” – and thus met Vela Velupillai. Shortly thereafter, I received an invitation to a Workshop on Mathematical Economics at the Certosa di Pontignano, Siena (May 1991). This was the occasion of my meeting the wonderful Richard Goodwin, having a ride in his pet car, seeing Vela again and also meeting Lionello Punzo, both former students of Goodwin. In addition, I met a group of mathematical economists reporting exciting research in bifurcations of iterated mappings of the plane, especially Laura Gardini of Urbino, with whom I did joint work in the 1990s.