Program equilibrium

In a computerized setting, players’ strategies can be implemented by computer programs, to be executed on a shared computational devise. This situation becomes typical to new Internet economies, where agent technologies play a major role. This allows the definition of a program equilibrium. Following the fundamental ideas introduced by von Neumann in the 40s (in parallel to his seminal contribution to game theory), a computer program can be used both as a set of instructions, as well as a file that can be read and compared with other files. We show that this idea implies that in a program equilibrium of the one-shot prisoners dilemma mutual cooperation is obtained. More generally, we show that the set of program equilibrium payoffs of a game coincides with the set of feasible and individually rational payoffs of it. Journal of Economic Literature Numbers: C72 C70 C60 1 The basic setting and idea The Internet creates a new economy, where existing theories and techniques are challenged. Many of the new theories have to do with extensions of existing theories due to possibilities emerging in the Internet. Examples include work on issues such as selfish routing [11] or incorporating distributed systems features into game-theoretic models [7]. In such contexts, when considering e.g. Internet auctions, the extended theories have to deal with issues such as the structure of the communication network and its effects. However, the fact we talk about computer programs rather than people plays a somewhat lesser role; the new medium suggests new problems, but the fact protocols are to run by computer programs do not play a significant role. Nevertheless, the Internet also allows sophisticated use of computer programs that should be studied very carefully. In particular, the new medium allows the use of software agents, programs (also called proxies) that are designed to behave on behalf of a user. Perhaps the most famous, although rather simple, use of such agent is in e-bay auctions (www.ebay.com), where agents are simple proxies that can be instructed how to bid on behalf of users. Such simple ideas may have huge ramifications. When several programs (agents [9], proxies [1]) are to run on a computer in service of different users, basic issues in the foundations of computer science should be taken into account as part of the economic theory.1 One of them, exposed in this paper, is a program’s (agent’s) ability to refer to computations done in parallel by other programs. As it turns out, this leads to surprising phenomena, based on the very basic principles of computing introduced by Von Neumann. This paper exposes these phenomena and how they effect basic game-theoretic reasoning. In [14], von Neumann introduced one of the most important concepts in computer science. In his work, termed “the first draft”, von Neumann explains the dual role of computer programs: 1. A computer program can serve as a set of instructions. 1Indeed, the above references refer already to non-trivial basic economic activities, such as selling, buying, and auctioning.