Tα Παι δí α Παíζε ι The Interaction Between Algorithms and Game Theory

Abstract

The theories of algorithms and games were arguably born within a year of each other, in the wake of two quite distinct breakthroughs by John von Neumann, in the former case to investigate the great opportunities – as well as the ever mysterious obstacles – in attacking problems by computers, in the latter to model and study rational selfish behavior in the context of interaction, competition and cooperation. For more than half a century the two fields advanced as gloriously as they did separately. There was, of course, a tradition of computational considerations in equilibria initiated by Scarf [13], work on computing Nash and other equilibria [6,7], and reciprocal isolated works by algorithms researchers [8], as well as two important points of contact between the two fields à propos the issues of repeated games and bounded rationality [15] and learning in games [2]. But the current intensive interaction and cross-fertilization between the two disciplines, and the creation of a solid and growing body of work at their interface, must be seen as a direct consequence of the Internet.

Research supported by NSF ITR grant CCR-0121555 and by a grant from Microsoft Research. The title phrase, a Greek version of “games children play”, is a common classroom example of a syntactic peculiarity (singular verb form with neutral plural subject)in the Attic dialect of ancient Greek.