Interesting article, actually. I think game theory has the potential to be a powerful tool for any cypherpunk to have in his or her mental arsenal, (so to speak.) For those of you who haven't been introduced to game theory, how it works, and what it's used for, here's a modified excerpt from an essay outlining the basics... Game theory can be described as the study of interactive decision making. Although game theory is relevant to parlor games such as poker or bridge, most research in game theory focuses on how groups of people interact. There are two main branches of game theory: cooperative and noncooperative game theory. Noncooperative game theory deals largely with how intelligent individuals interact with one another in an effort to achieve their own goals. Decision theory can be viewed as a theory of one person games, or a game of a single player against nature. The focus is on preferences and the formation of beliefs. The most widely used form of decision theory argues that preferences among risky alternatives can be described by the maximization the expected value of a numerical utility function, where utility may depend on a number of things, but in situations of interest to economists often depends on money income. Probability theory is heavily used in order to represent the uncertainty of outcomes, and Bayes Law is frequently used to model the way in which new information is used to revise beliefs. Decision theory is often used in the form of decision analysis, which shows how best to acquire information before making a decision. General equilibrium theory can be viewed as a specialized branch of game theory that deals with trade and production, and typically with a relatively large number of individual consumers and producers. It is widely used in the macroeconomic analysis of broad based economic policies such as monetary or tax policy, in finance to analyze stock markets, to study interest and exchange rates and other prices. In recent years, political economy has emerged as a combination of general equilibrium theory and game theory in which the private sector of the economy is modeled by general equilibrium theory, while voting behavior and the incentive of governments is analyzed using game theory. Issues studied include tax policy, trade policy, and the role of international trade agreements such as the European Union. Mechanism design theory differs from game theory in that game theory takes the rules of the game as given, while mechanism design theory asks about the consequences of different types of rules. Naturally this relies heavily on game theory. Questions addressed by mechanism design theory include the design of compensation and wage agreements that effectively spread risk while maintaining incentives, and the design of auctions to maximize revenue, or achieve other goals. An Instructive Example One way to describe a game is by listing the players (or individuals) participating in the game, and for each player, listing the alternative choices (called actions or strategies) available to that player. In the case of a two-player game, the actions of the first player form the rows, and the actions of the second player the columns, of a matrix. The entries in the matrix are two numbers representing the utility or payoff to the first and second player respectively. A very famous game is the Prisoner's Dilemma game. In this game the two players are partners in a crime who have been captured by the police. Each suspect is placed in a separate cell, and offered the opportunity to confess to the crime. The game can be represented by the following matrix of payoffs: not confess confess not confess 5,5 0,10 confess 10,0 1,1 Note that higher numbers are better (more utility). If neither suspect confesses, they go free, and split the proceeds of their crime which we represent by 5 units of utility for each suspect. However, if one prisoner confesses and the other does not, the prisoner who confesses testifies against the other in exchange for going free and gets the entire 10 units of utility, while the prisoner who did not confess goes to prison and gets nothing. If both prisoners confess, then both are given a reduced term, but both are convicted, which we represent by giving each 1 unit of utility: better than having the other prisoner confess, but not so good as going free. This game has fascinated game theorists for a variety of reasons. First, it is a simple representation of a variety of important situations. For example, instead of confess/not confess we could label the strategies "contribute to the common good" or "behave selfishly." This captures a variety of situations economists describe as public goods problems. An example is the construction of a bridge. It is best for everyone if the bridge is built, but best for each individual if someone else builds the bridge. This is sometimes refered to in economics as an externality. Similarly this game could describe the alternative of two firms competing in the same market, and instead of confess/not confess we could label the strategies "set a high price" and "set a low price." Naturally is is best for both firms if they both set high prices, but best for each individual firm to set a low price while the opposition sets a high price. A second feature of this game, is that it is self-evident how an intelligent individual should behave. No matter what a suspect believes his partner is going to do, is is always best to confess. If the partner in the other cell is not confessing, it is possible to get 10 instead of 5. If the partner in the other cell is confessing, it is possible to get 1 instead of 0. Yet the pursuit of individually sensible behavior results in each player getting only 1 unit of utility, much less than the 5 units each that they would get if neither confessed. This conflict between the pursuit of individual goals and the common good is at the heart of many game theoretic problems. A third feature of this game is that it changes in a very significant way if the game is repeated, or if the players will interact with each other again in the future. Suppose for example that after this game is over, and the suspects either are freed or are released from jail they will commit another crime and the game will be played again. In this case in the first period the suspects may reason that they should not confess because if they do not their partner will not confess in the second game. Strictly speaking, this conclusion is not valid, since in the second game both suspects will confess no matter what happened in the first game. However, repetition opens up the possibility of being rewarded or punished in the future for current behavior, and game theorists have provided a number of theories to explain the obvious intuition that if the game is repeated often enough, the suspects ought to cooperate. One of the most entertaining intro books is "The Compleat Strategist: Being a Primer on the Theory of Games of Strategy", (J.D. Williams, McGraw-Hill, New York 1966.) David Levine recommends "Thinking Strategically" by A. Dixit and B. Nalebuff (Norton, 1991) as good general reading. If you're interested in getting deeper into the subject you should try Game Theory with Economic Applications by H. Bierman and L. Fernandez (Addison-Wesley, 1993). The next step up is the graduate level text Game Theory by D. Fudenberg and J. Tirole from MIT Press. There are also two other advanced textbooks worth taking a look at: "Fun and Games: A Text on Game Theory by K. Binmore" (D.C. Heath, 1992), a very focused and mathematical treatment... --------------------- "Golden Age" History --------------------- 1944 "Theory of Games and Economic Behavior" by John von Neumann and Oskar Morgenstern is published. As well as expounding two-person zero sum theory this book is the seminal work in areas of game theory such as the notion of a cooperative game, with transferable utility (TU), its coalitional form and its von Neumann-Morgenstern stable sets. It was also the account of axiomatic utility theory given here that led to its wide spread adoption within economics. 1945 Herbert Simon writes the first review of von Neumann-Morgenstern. 1946 The first entirely algebraic proof of the minimax theorem is due to L. H. Loomis's,On a Theorem of von Neumann, paper. 1950 Contributions to the Theory of Games I, H. W. Kuhn and A. W. Tucker eds., published. 1950 In January 1950 Melvin Dresher and Merrill Flood carry out, at the Rand Corporation, the experiment which introduced the game now known as the Prisoner's Dilemma. The famous story associated with this game is due to A. W. Tucker, A Two-Person Dilemma, (memo, Stanford University). Howard Raiffa independently conducted, unpublished, experiments with the Prisoner's Dilemma. 1950-53 In four papers between 1950 and 1953 John Nash made seminal contributions to both non-cooperative game theory and to bargaining theory. In two papers, "Equilibrium Points in N- Person Games" (1950) and "Non-cooperative Games" (1951), Nash proved the existence of a strategic equilibrium for non- cooperative games - the Nash equilibrium - and proposed the"Nash program", in which he suggested approaching the study of cooperative games via their reduction to non-cooperative form. In his two papers on bargaining theory, The Bargaining Problem (1950) and Two-Person Cooperative Games (1953), he founded axiomatic bargaining theory, proved the existence of the Nash bargaining solution and provided the first execution of the Nash program. 1951 George W. Brown described and discussed a simple iterative method for approximating solutions of discrete zero-sum games in his paper Iterative Solutions of Games by Fictitious Play. 1952 The first textbook on game theory: John Charles C. McKinsey, "Introduction to the Theory of Games". 1952 Merrill Flood's report, (Rand Corporation research memorandum, Some Experimental Games, RM-789, June), on the 1950 Dresher/Flood experiments appears. 1952 The Ford Foundation and the University of Michigan sponsor a seminar on the"Design of Experiments in Decision Processes" in Santa Monica.This was the first experimental economics/ experimental game theory conference. 1952-53 The notion of the Core as a general solution concept was developed by L. S. Shapley (Rand Corporation research memorandum, Notes on the N-Person Game III: Some Variants of the von-Neumann-Morgenstern Definition of Solution, RM- 817, 1952) and D.B. Gillies (Some Theorems on N-Person Games, Ph.D. thesis, Department of Mathematics, Princeton University, 1953). The core is the set of allocations that cannot be improved upon by any coalition. 1953 Lloyd Shapley in his paper A" Value for N-Person Games" characterised, by a set of axioms, a solution concept that associates with each coalitional game,v, a unique out- come, v. This solution in now known as the Shapley Value. 1953 Lloyd Shapley's paper "Stochastic Games" showed that for the strictly competitive case, with future payoff discounted at a fixed rate, such games are determined and that they have optimal strategies that depend only on the game being played, not on the history or even on the date, i.e.: the strategies are stationary. 1953 Extensive form games allow the modeller to specify the exact order in which players have to make their decisions and to formulate the assumptions about the information possessed by the players in all stages of the game. H. W. Kuhn's paper, "Extensive Games and the Problem of Information" includes the formulation of extensive form games which is currently used, and also some basic theorems pertaining to this class of games. 1953 "Contributions to the Theory of Games II," H. W. Kuhn and A. W. Tucker eds., published. 1954 One of the earliest applications of game theory to political science is L. S. Shapley and M. Shubik with their paper "A Method for Evaluating the Distribution of Power in a Committee System." They use the Shapley value to determine the power of the members of the UN Security Council. 1954-55 Differential Games were developed by Rufus Isaacs in the early 1950s. They grew out of the problem of forming and solving military pursuit games. The first publications in the area were Rand Corporation research memoranda, by Isaacs, RM-1391 (30 November 1954), RM-1399 (30 November 1954), RM-1411 (21 December 1954) and RM-1486 (25 March 1955) all entitled, in part, Differential Games. 1955 One of the first applications of game theory to philosophy is R. B. Braithwaite's "Theory of Games as a Tool for the Moral Philosopher." 1957 "Games and Decisions: Introduction and Critical Survey" by Robert Duncan Luce and Howard Raiffa published. 1957 Contributions to the Theory of Games III, M. A.Dresher, A. W. Tucker and P. Wolfe eds., published. 1959 The notion of a Strong Equilibrium was introduced by R. J. Aumann in the paper Acceptable Points in General Cooperative N-Person Games. 1959 The relationship between Edgeworth's idea of the contract curve and the core was pointed out by Martin Shubik in his paper Edgeworth Market Games. One limitation with this paper is that Shubik worked within the confines of TU games whereas Edgeworth's idea is more appropriately modelled as an NTU game. 1959 Contributions to the Theory of Games IV, A. W.Tucker and R. D. Luce eds., published. 1959 Publication of Martin Shubik's "Strategy and Market Structure: Competition, Oligopoly, and the Theory of Games". This was one of the first books to take an explicitly non-cooperative game theoretic approach to modelling oligopoly. It also contains an early statement of the Folk Theorem. Late 50's Near the end of this decade came the first studies of repeated games. The main result to appear at this time was the Folk Theorem. This states that the equilibrium outcomes in an infinitely repeated game coincide with the feasible and strongly individually rational outcomes of the one-shot game on which it is based. Authorship of the theorem is obscure.