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This bibliography also contains important references on Game Theory in general. Fascination with the Prisoner's Dilemma has resulted in a study area where both mathematical and computational approaches can fruitfully interact.


Abreu, Dilip and Rubinstein, Ariel (1988) 'The Structure of Nash Equilibria in Repeated Games with Finite Automata', Econometrica, 56(6), November, pp. 1259-1281.

Adachi, N. and Matsuo, K. (1991) 'Ecological Dynamics Under Different Selection Rules in Distributed and Iterated Prisoner's Dilemma Games', Parallel Problem Solving From Nature, Lecture Notes in Computer Science Volume 496 (Berlin: Springer-Verlag), pp. 388-394.

Anderlini, Luca (1989) 'Some Notes on Church's Thesis and the Theory of Games', Theory and Decision, 29(1), pp. 19-52.

Anderlini, Luca and Sabourian, Hamid (1989) 'Computability and Infinitely Repeated Common Interest Games with No Discounting', Draft Paper, Cambridge University.

Arthur, W. Brian (1989a) 'Nash Discovering Automata for Finite Action Games', Working Paper, Santa Fe Institute, New Mexico.

+ Axelrod, Robert M. and Dion, Douglas (1988) 'The Further Evolution of Cooperation', Science, 242(4884), 9 December, pp. 1385-1390. [Analyses developments in the evolution of co-operation, investigating work varying the number of players, the range of possible choices, variations in the payoff structure, noise, the shadow of the future, population dynamics and population structure.]

Axelrod, Robert M. and Hamilton, William D. (1981) 'The Evolution of Cooperation', Science, 211(4489), pp. 1390-1396.

Aumann, Robert (1981) 'Repeated Games', in Feiwel, G. R. (ed.) Issues in Contemporary and Welfare (London: Macmillan), pp. 209-242. [First use of finite automata in game theory.]

Bacharach, Michael (1993) 'Variable Universe Games', in Binmore, K. et al. (eds.) Frontiers of Game Theory (Cambridge, MA: The M.I.T. Press).

Banerjee, Abhijit V. and Weibull, Jo:rgen W. (1993) 'Evolutionary Selection with Discriminating Players', Research Paper in Economics, University of Stockholm.

Banks, J. and Sundaram, R. (1990) 'Repeated Games, Finite Automata and Complexity', Games and Economic Behaviour, 2, pp. 97-117.

Basar, T. and Olsder, G.J. (1982) Dynamic Noncooperative Game Theory (New York, NY: Academic Press).

Ben-Porath, E. (1987) 'Repeated Games with Finite Automata', Technical Report Number 515, Institute for Mathematical Studies in the Social Sciences, Stanford University, August.

Bergin, J. and Lipman, B. (1996) 'Evolution with State-Dependent Mutations', Econometrica, 64, pp. 943-956. [The result of Kandori, Mailath and Rob turns out to depend on mutation rates that do not vary "too much", across the different states of the adaptation process. If mutation rates in different states are not taken to zero at the same rate, then by appropriate choice of rates, any desired strict equilibrium may be selected in the long run.]

Binmore, Ken (1987) 'Modeling Rational Players I', Economics and Philosophy, 3(2), pp. 179-214. [A detailed analysis of bounded rationality, with particular reference to game theory, which urges a programme of research into the thinking processes of game players to model rationality better.]

Binmore, Ken (1988) 'Modelling Rational Players II', Economics and Philosophy, 4(1), pp. 9-55. [A detailed analysis of bounded rationality, with particular reference to game theory, which urges a programme of research into the thinking processes of game players to model rationality better.]

Binmore, Ken (1994) Game Theory and the Social Contract, Volume 1: Playing Fair (Cambridge, MA: The M. I. T. Press). [Reinterprets classical social contract ideas within a game theoretic framework, building on a synthesis of the theories of John Rawls and John Harsanyi. Introduces elementary notions of game theory and implications for social contract issues. Critiques the leading arguments that have been offered in defence of the fallacy that co-operation is rational in the Prisoner's Dilemma. Provides an exposition of orthodox decision theory and presents a critique of the thick veils of ignorance proposed by Harsanyi and Rawls. In contrast, suggests a thin veil of ignorance in which persons are not called upon to forget the way society is currently organised or their empathetic preferences, which are shaped by social evolution in the medium run. The second volume of Game Theory and the Social Contract will address the problem of bargaining behind the veil of ignorance.]

+ Binmore, Ken and Samuelson, Larry (1991) 'Evolutionary Stability in Repeated Games Played By Finite Automata', Journal of Economic Theory, 57, pp. 278-305.

Binmore, Ken and Samuelson, Larry (1993) 'Muddling Through: Noisy Equilibrium Selection', Discussion Paper, University of Wisconsin.

Binmore, Ken and Samuelson, Larry (1994) 'An Economic Perspective on the Evolution of Norms', Journal of Institutional and Theoretical Economics, 150(1), pp. 45-63.

Binmore, Ken, Samuelson, Larry and Vaughan, Richard (1994) 'Musical Chairs: Modelling Noisy Evolution', Discussion Paper 94-13, Department of Economics, UCL October.

Bjo:rnerstedt, J. and Weibull, J. (1993) 'Nash Equilibrium and Evolution by Imitation', in Arrow, K. and Colombatto, E. (eds.) Rationality in Economics (New York, NY: Macmillan).

Blume, L. (1993) 'The Statistical Mechanics of Strategic Interaction', Games and Economic Behaviour, 5, pp. 387-424. [Individuals are located on a lattice and recurrently interact with their neighbours. They play stochastically perturbed myopic best responses, in the sense that the choice probability for each pure strategy is an increasing function of its current payoff. This means that more costly mistakes are assigned lower choice probabilities.]

Bolle, Friedel and Ockenfels, Peter (1990) 'Prisoner's Dilemma as a Game of Incomplete Information', Journal of Economic Psychology, 11, pp. 69-84. [*0]

+ Bonanno, Giacomo and Nehring, Klaus (1996) 'Fundamental Agreement: A New Foundation for the Harsanyi Doctrine', Working Paper Series Number 96-02, Department of Economics, University of California (Davis), February. ["There exists an important and troublesome tension within the Bayesian approach to game theory and economics. From the point of view of their decision-theoretic foundation ... probabilities are subjective, representing personal judgements on the comparative likelihood of events revealed in an agent's preferences over bets or "acts". Personal probability judgments admit two types of determinants, objective and subjective; call them "experience" and "mind-set". On the other hand, in game-theoretic and economic applications, with few exceptions, only the first type of determinant is allowed to matter. Thus, differences of beliefs are attributed entirely to differences in experience ("Harsanyi Doctrine"); correspondingly, agents are assumed to be "like minded". Following Harsanyi ... "like-mindedness" is commonly formalised by assuming agents' beliefs to be posteriors derived from a commonly known common prior."]

Bo:rgers, Tilman and Sarin, R. (1993) 'Learning Through Reinforcement and Replicator Dynamics', Technical Report, University College London.

Bo:rgers, Tilman and Sarin, R. (1996a) 'Naive Reinforcement and Replicator Dynamics', ELSE Working Paper.

Bo:rgers, Tilman and Sarin, R. (1996b) 'Learning Through Reinforcement and Replicator Dynamics', ELSE Working Paper.

Boyd, Robert and Lorberbaum, Jeffrey P. (1987) 'No Pure Strategy is Evolutionarily Stable in the Repeated Prisoner's Dilemma Game', Nature, 327, 7 May, pp. 58-59.

Boylan, Richard T. (1991) 'Laws of Large Numbers for Dynamical Systems with Randomly Matched Individuals', Journal of Economic Theory, 57, pp. 473-504. [Biologists and economists have analyzed populations where each individual interacts with randomly selected individuals. The random matching generates a very complicated stochastic system. Consequently evolutionary biologists have approximated such a system by a deterministic system. The justification of such an approximation is that the population is assumed to be very large and thus some law of large numbers must hold. In this paper we give an example for which this assumption does not hold. We then show that if we assume that the population is infinite then the stochastic and the deterministic system are the same. Finally, we show that if the process lasts finitely many periods and if the population is large enough then the deterministic model offers a good approximation of the stochastic model. In doing so we make precise what we mean by population, matching process, and evolution of the population.]

Braithwaite, R. B. (1955) The Theory of Games as a Tool for the Moral Philosopher (Cambridge: Cambridge University Press).

Brams, S. J. (1993) 'Theory of Moves', American Scientist, 81, pp. 562-570.

Brandenburger, Adam and Dekel, Eddie (1989) 'The Role of Common Knowledge Assumptions in Game Theory', in Hahn, Frank H. (ed.) The Economics of Missing Markets, Information and Games (Oxford: Clarendon Press), pp. 46-61.

* Brenner, Thomas (1998) 'Cognitive Models and Cooperation in Prisoner's Dilemma Games', Paper presented at the Workshop Agent-Based and Population-Based Modelling of Learning in Economics, Max-Planck-Institute for Research into Economic Systems, Jena, Germany, 2nd - 3rd March. [Draft: Do Not Quote Or Distribute.]

Busch, Marc L. and Reinhardt, Eric R. (1993) Nice Strategies in a World of Relative Gains: The Problem of Co-operation under Anarchy, Journal-of-Conflict-Resolution, 37(3), September, pp. 427-445. [The debate between neo-liberals and realists in the field of international relations draws heavily on the findings offered in Robert Axelrod's Evolution of Co-operation. Axelrod's well-known argument is that co-operation can emerge among egoists despite the absence of a central authority. This article assesses the robustness of Axelrod's findings in light of the realist critique that relative gains concerns make co-operation less likely than neo-liberals contend. We build on an amended prisoner's dilemma (PD) game and conduct a computer simulation tournament in which we vary (1) the payoff structure and (2) Axelrod's population of strategies. The results indicate that co-operation can emerge even under strong relative gains concerns, so long as the population of strategies is sufficiently retaliatory. On the basis of this finding, we argue that the realist critique is overstated: the introduction of greater relative gains concerns does not necessarily limit the prospects for co-operation among states.]

Cabrales, A. and Ponti, G. (1996) 'Implementation, Elimination of Weakly Dominated Strategies and Evolutionary Dynamics', ELSE Working Paper.

Canning, David (1988) 'Rationality and Game Theory When Players are Turing Machines', ST/ICERD Discussion Paper 88/183, London School of Economics, London.

Canning, David (1990c) 'Rationality, Computability and the Limits of Game Theory', Economic Theory Discussion Paper Number 152, Department of Applied Economics, University of Cambridge, July.

Canning, David (1992) 'Rationality, Computability and Nash Equilibrium', Econometrica, 60(4), July, pp. 877-888.

Cho, I.-K. and Kreps, David M. (1987) 'Signaling Games and Stable Equilibria', Quarterly Journal of Economics, 102(1), February, pp. 179-221. [*0]

Cowan, Robin A. and Miller, John H. (1990) 'Economic Life on a Lattice: Some Game Theoretic Results', Working Paper 90-010, Economics Research Program, Santa Fe Institute, New Mexico. [*0]

+ Cubitt, Robin P. and Sugden, Robert (1996) 'The Selection of Preferences Through Imitation', Draft Paper, School of Economic and Social Studies, University of East Anglia, May. [A model in which VNM utility functions are not assumed. Instead individuals play repeated games against nature in which outcomes are simply descriptions of the world. Preferences - or at least strategies - are transmitted by imitation.]

Danielson, P. (1992) Artificial Morality: Virtuous Robots for Virtual Games (xx: Routledge). [*0]

Dawes, Robyn, McTavish, Jeanne and Shaklee, Harriet (1977) 'Behaviour, Communication, and Assumptions About Other Peoples' Behavior in a Commons Dilemma Situation', Journal of Personality and Social Psychology, 31(1), xx, pp. 1-11. [*0]

Dekel, Eddie and Scotchmer, Suzanne (1992) 'On the Evolution of Optimizing Behavior', Journal of Economic Theory, 57(xx), xx, pp. 392-406. [*0]

Eaton, B. C. and Slade, M. E. (1989) 'Evolutionary Equilibrium in Market Supergames', Discussion Paper, University of British Columbia, November. [Uses GA simulations.]

Elliott, S. W. (19xx) 'Steps Towards a Psychological Calculus for Game Theory: Application of a Model of Categorisation to the Repeated Prisoners Dilemma', Doctoral Thesis.

+ Eshel, Illan, Samuelson, Larry and Shaked, Avner (1996) 'Altruists, Egoists and Hooligans in a Local Interaction Model', Draft Paper, Department of Statistics, School of Mathematical Sciences, Tel Aviv University, 14 May. [D HTML D PS]

Fader, P. S. and Hauser, J. R. (1988) 'Implicit Coalitions in a Generalised Prisoner's Dilemma', Journal of Conflict Resolution, 32(xx), xx, pp. 553-582. [*0]

+ Fogel, David B. (1993) 'Evolving Behaviours in the Iterated Prisoner's Dilemma', Evolutionary Computation, 1(1), April, pp. 77-97. [Represents agents as FSMs with varying numbers of states, evolved using evolutionary programming which has selection and mutation only. Naive cooperative agents are not evolved. Instead each population tends to develop "secret handshakes" allowing agents of a particular type to identify others of the same type. Evidence of the fact that these plays constitute arbitrary "messages" or handshakes comes when good strategies from different populations are mixed and do rather poorly, presumably because they do not "understand" each others messages.]

Forrest, Stephanie and Mayer-Kress, G. (1991) 'Genetic Algorithms, Nonlinear Dynamical Systems, and Global Stability Models', in Davis, L. (ed.) The Handbook of Genetic Algorithms (New York, NY: Van Nostrand Reinhold). [Evolutionary IPD ideas applied to international relations.]

Foster, Dean and Young, H. Peyton (1990) 'Stochastic Evolutionary Game Dynamics', Journal of Theoretical Biology, 38(xx), xx, pp. 219-232. [*0]

* Friedman, Daniel (1991) 'Evolutionary Games in Economics', Econometrica, 59(3), May, pp. 637-666. [JSTOR] [*0]

Fudenberg, Drew and Tirole, (1991) Game Theory (xx: xx). [*0]

Fudenberg, Drew and Maskin, Eric (1990) 'Evolution and Cooperation in Noisy Repeated Games', American Economic Review (Papers and Proceedings), 80(2), May, pp. 274-279. [JSTOR] [*0]

Geanakoplos, John (1990) 'Game Theory without Partitions, and Applications to Speculation and Consensus', Working Paper 90-018, Santa Fe Institute, New Mexico.

Griesinger, D. W. and Livingston, J. W. (1973) 'Towards a Model of Interpersonal Motivation in Experimental Games', Behavioral Science, 18(xx), xx, pp. 173-188. [*0]

Gu:th, Werner and Kliemt, Hartmut (1994) 'Competition or Co-operation - On the Evolutionary Economics of Trust, Exploitation and Moral Attitudes', Metroeconomica, 45(xx), xx, pp. 155-187. [*0]

Gu:th, Werner and Kliemt, Hartmut (1998) 'The Indirect Evolutionary Approach: Bridging the Gap Between Rationality and Adaptation', Rationality and Society, 10(3), xx, pp. 377 - 399. [*0]

Gu:th, Werner, Schmittberger, R. and Schwarze, B. (1982) 'An Experimental Analysis of Ultimatum Bagaining', Journal of Economic Behavior and Organization, 3, pp. 367-388. [Subjects are prepared to accept nothing instead of positive but "unfair" bargains.]

Hammerstein, P. and Selten, R. (1994) 'Game Theory and Evolutionary Biology', in Auman, R. and Hart, S. (eds.) Handbook of Game Theory with Economic Applications (Elsevier Science), volume 2, pp. 931-962.

Hansen, R. G. and Samuelson, W. F. (1988) 'Evolution in Economic Games', Journal of Economic Behavior and Organization, 10(3), October, pp. 315-338. [*0]

Hardin, Garrett (1968) 'The Tragedy of the Commons', Science, 162(3859), 13 December, pp. 1243-1248.

Hardin, Russell (1982) Collective Action (Washington, DC: Johns Hopkins University Press). [ECO HB846.8.HAR] [NUF OS] [*0]

Hechter, Michael (1988) Principles of Group Solidarity (Berkeley, CA: University of California Press). [*0]

Hechter, Michael (1992) 'The Insufficiency of Game Theory for the Solution of Real-World Collective Action Problems', Rationality and Society, 4(xx), xx, pp. 33-40. [*0]

Hines, W. G. (1987) 'Evolutionary Stable Strategies: A Review of Basic Theory', Theoretical Population Biology, 31(xx), xx, pp. 195-272. [*0]

Hirshleifer, Jack and Marti/nez-Coll, Juan Carlos (1988) 'What Strategies can Support the Evolutionary Emergence of Cooperation?', Journal of Conflict Resolution, 32(2), June, pp. 367-398. [*0]

+ Hirshleifer, Jack and Marti/nez-Coll, Juan Carlos (1992) 'Selection, Mutation and the Preservation of Diversity in Evolutionary Games (1)', Revista Espan~ola de Economia, 9(2), pp. 251-273.

Hirshleifer, Jack and Marti/nez-Coll, Juan Carlos (1992) 'Selection, Mutation and the Preservation of Diversity in Evolutionary Games', Papers on Economics and Evolution, Number 9202, edited by the European Study Group for Evolutionary Economics.

Hofbauer, J. and Sigmund, K. (1988) Evolutionary Games and Population Dynamics (Cambridge: Cambridge University Press). [The Theory of Evolution and Dynamical Systems?] [*0]

Howard, J. V. (1988) 'Cooperation in the Prisoner's Dilemma', Theory and Decision, 24(xx), xx, pp. 203-213. [*0]

+ Huberman, Bernardo A. and Glance, Natalie S. (1993) 'Evolutionary Games and Computer Simulations', Proceedings of the National Academy of Sciences of the USA, 90(16), August, pp. 7716-7718.

Ikegami, Takashi (1993) 'Ecology of Evolutionary Game Strategies', in [ECAL 93], pp. 527-536.

De Jasay (1990) Social Contract, Free Ride (Oxford: Oxford University Press). [*0]

Kandori, Michihiro, Mailath, George J. and Rob, Rafael (1993) 'Learning, Mutation, and Long Run Equilibria in Games', Econometrica, 61(1), January, pp. 29-56. [Games are played recurrently and individuals have information about the past play of the game, based on which they form beliefs about how their opponents will play and choose a best response to these beliefs. The chosen actions add to the history of play. Each player plays every other in every period. Successful strategies are adopted with higher probabilities than unsuccessful ones and there is a small probability of mistakes. The stochastic process selects the risk dominant Nash equilibrium when the mistake probability is small.] [JSTOR] [*0]

! Kelley, H. H. and Stahelski, A. J. (1970) 'Social Interaction Basis of Cooperators' and Competitors' Beliefs About Others', Journal of Personality and Social Psychology, 16(xx), xx, pp. 66-91. [*0]

Kreps, David M. (1990) Game Theory and Economic Modelling (Oxford: Clarendon Press).

Kreps, David M. and Fudenberg, Drew (1988) Learning, Experimentation, and Equilibrium in Games (Cambridge, MA: The M. I. T. Press). [*0]

Kreps, David M., Milgrom, Paul, Roberts, John, and Wilson, R. (1982) 'Rational Cooperation in the Finitely Repeated Prisoner's Dilemma', Journal of Economic Theory, 27(xx), xx, pp. 245-252. [Assume incomplete information and relax the assumption that rationality is common knowledge.] [*0]

Kuhlman, D. M. and Wimberly, D. L. (1976) 'Expectations of Choice Behaviour Held by Cooperators, Competitors, and Individualists Across Four Classes of Experimental Games', Journal of Personality and Social Psychology, 34(xx), xx, pp. 69-81. [*0]

Liebrand, Wim B. G. (1984) 'The Effect of Social Motives, Communication and Group Size on Behaviour in an N-Person Multi Stage Mixed Motive Game', European Journal of Social Psychology, 14(xx), xx, pp. 239-264. [*0]

Liebrand, Wim B. G., Messick, David M. and Wilke, H. (eds.) (1992) Social Dilemmas: Theoretical Issues and Research Findings (Oxford: Pergamon Press). [*0]

Liebrand, Wim B. G. and Messick, David M. (eds.) (1996) Frontiers in Social Dilemmas Research (Berlin: Springer-Verlag). [*0] [C]

Lindgren, Kristian and Nordahl, Mats G. (1993) 'Evolutionary Dynamics of Spatial Games', in Self Organization and Life: From Simple Rules to Global Complexity, Proceedings of the Second European Conference on Artificial Life, Brussels, Belgium 24-26 May 1993 (Cambridge, MA: MIT Press), pp. 604-616.

Lomborg, Bjo/rn (1992) 'Cooperation in the Iterated Prisoner's Dilemma', Papers on Economics and Evolution, Number 9302, edited by the European Study Group for Evolutionary Economics.

* Lomborg, Bjo/rn (1993) 'The Structure of Solutions in the Iterated Prisoner's Dilemma', Draft Paper, Institute of Political Science, University of Copenhagen, February.

Lomborg, Bjo/rn (1996) 'Nucleus and Shield: The Evolution of Social Structure in the Interated Prisoner's Dilemma', American Sociological Review, 61(2), April, pp. 278-307. [JSTOR] [BOX05] [*0]

Luce, R. D. and Raiffa, H. (1957) Games and Decisions (New York, NY: Wiley).

Mailath, George J. (1992) 'Introduction: Symposium on Evolutionary Game Theory', Journal of Economic Theory, 57(xx), xx, pp. 259-277. [*0]

+ Mailath, George J., Samuelson, Larry and Shaked, Avner (1992) 'Evolution and Endogenous Interaction', Draft Paper, Department of Economics, University of Pennsylvania, latest version 24 August 1995. [D PS] [This paper is also known as 'The Evolution of Heterogeneity', 'Evolution with Endogenous Interactions' and 'Evolution and Correlated Equilibrium'.]

Macy, Michael (1989) 'Walking Out of Social Traps: A Stochastic Learning Model for the Prisoner's Dilemma', Rationality and Society, 1(2), xx, pp. 197-219. [*0]

+ Marks, Robert E. (1989) 'Niche Strategies: The Prisoner's Dilemma Computer Tournaments Revisited', AGSM Working Paper 89-009, Australian Graduate School of Management, University of New South Wales. [Uses GA on finite automata rather than human tournaments to evolve good PD strategies, replicating Axelrod's work from 1987 but also developing it to deal with noisy PD games. A niche is defined as an unchanging environment rather than a co-evolving population of rivals. Those niches studied are C, D, TFT, Axelrod 5-rule (with and without a small chance that players will misobserve their opponents previous play) and Axelrod 8-rule.]

Marti/nez-Coll, Juan Carlos (1986) 'A Bioeconomic Model of Hobbes' State of Nature', Social Science Information, 25(2), June, pp. 493-505. [*0]

Marti/nez-Coll, Juan Carlos and Hirshleifer, Jack (1991) 'The Limits of Reciprocity: Solution Concepts and Reactive Strategies in Evolutionary Equilibrium Models', Rationality and Society, 3(1), January, pp. 35-64. [*0]

Marti/nez-Coll, Juan Carlos and Hirshleifer, Jack (1992) 'The Limits of Reciprocity Reaffirmed', Rationality and Society, 4(2), April, pp. xxx-xxx. [*0]

Matsui, Akihiko (1993) 'Evolution and Rationalizability', Working Paper: 93-19, Center for Analytic Research in Economics and the Social Sciences (CARESS), University of Pennsylvania, May. [This paper synthesises two ideas, evolution and rationalisability, in a dynamic environment. Both have drawn theorists' attentions to either justify or criticise equilibrium theory, which requires the co-ordination of beliefs and actions among players. A drawback of rationalisability is its poor predictive power while that of evolution is lack of rationality in the decision making process. We show that the integration of these two ideas will be free of their respective drawbacks. We attempt to do this in a dynamic environment in which players are anonymous. A player's payoff depends only on his choice of action and the distribution of strategies in a society. A rationalisable foresight path is a path along which each player makes a rationalisable decision. We define social stability by making use of rationalisable foresight paths. A state is socially stable under rationalisable foresight if there exists no rationalizable foresight path that escapes from that state. We also define socially stable states under perfect foresight as the states from which no perfect foresight paths escape and show that social stability under rationalisable foresight sometimes makes sharper prediction than that under perfect foresight. Application to location theory is provided to show the usefulness of the stability captured by the concept of rationalizable foresight.]

May, R. M., Bohoeffer, S. and Nowak, Martin A. (1995) 'Spatial Games and the Evolution of Cooperation', in Mora/n, F., Moreno, A., Morelo, J. J. and Chaco/n, P. (eds.) Advances in Artificial Life: Proceedings of the Third European Conference on Artificial Life (ECAL95) (Berlin: Sprnger-Verlag), pp. 749-759.

Maynard-Smith, John (1976) 'Evolution and the Theory of Games', American Scientist, 64(1), January, pp. 41-45. [*0]

Maynard-Smith, John (1982) Evolution and the Theory of Games (Cambridge: Cambridge University Press).

Miller, John H. (1988) 'The Evolution of Automata in the Repeated Prisoner's Dilemma', in Two Essays on the Economics of Imperfect Information, Doctoral Dissertation, Department of Economics, University of Michigan (Ann Arbor).

Miller, John H. (1989) 'The Coevolution of Automata in the Repeated Prisoner's Dilemma', Working Paper 89-003, Santa Fe Institute, New Mexico.

Miller, John H. (1996) 'The Coevolution of Automata in the Repeated Prisoner's Dilemma', Journal of Economic Behavior and Organization, 29(1), January, pp. 87-112. [D]

Miller, John H. and Shubik, Martin (1992) 'Some Dynamics of a Strategic Market Game with a Large Number of Agents', Working Paper 92-11-057, Santa Fe Institute, New Mexico.

Miller, John H. and Shubik, Martin (1994) 'Some Dynamics of a Strategic Market Game', Journal of Economics, 60(xx), xx, pp. xxx-xxx. [*0]

Nachbar, John H. (1990) '"Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties', International Journal of Game Theory, 19(xx), xx, pp. 59-89. [*0]

Nachbar, John H. (1992) 'Evolution in the Finitely Repeated Prisoner's Dilemma: A Methodological Comment and Some Simulations', Journal of Economic Behaviour and Organization, 19(3), December, pp. 307-326. [*0]

Neyman, A. (1985) 'Bounded Complexity Justifies Cooperation in the Finitely Repeated Prisoner's Dilemma', Economics Letters, 19, pp. 227-229. [Replaces fully rational players with automata in a finitely repeated PD and shows that when players are restricted to finite automata, no matter gow much larger these machines are than the number of repetitions, there exist equilibria with payoffs that are on average close to the cooperative payoff.]

Nowak, Martin A. (1993) 'Evolutionary And Spatial Dynamics Of The Prisoner's Dilemma', in [ECAL 93].

Nowak, Martin A. and May, Robert M. (1992) 'Evolutionary Games and Spatial Chaos', Nature, 359(6398), 29 October, pp. 826-829.

Nowak, Martin A. and May, Robert M. (1993) 'The Spatial Dilemmas of Evolution', International Journal of Bifurcation and Chaos, 3(xx), xx, pp. 35-78. [*0]

Nowak, Martin A. and Sigmund, K. (1992) 'Tit For Tat in Heterogenous Populations', Nature, 359, pp. 250-253. [*0]

Ockenfels, Peter (1993) 'Cooperation in Prisoner's Dilemma - An Evolutionary Approach', European Journal of Political Economy, 9(xx), xx, pp. 567-579. [*0]

Olson, Mancur (1965) The Logic of Collective Action: Public Goods and the Theory of Groups (Cambridge, MA: Harvard University Press). [PIRS HB846.8.OLS (short loan)] [*0]

Ostrom, Elinor (1995) Governing the Commons (Cambridge: Cambridge University Press). [*0]

Radner, Roy (1986) 'Can Bounded Rationality Resove the Prisoner's Dilemma?', in Hildenbrand, W. and Mas-Collell, A. (eds.) Contributions to Mathematical Economics in Honor of Ge/rard Debreu (Amsterdam: North-Holland), pp. 387-399. [Uses finite automata.]

Rapoport, A. and Chammah, A. M. (1965) Prisoner's Dilemma (Ann Arbor, MI: University of Michigan Press). [*0]

Rasmussen, E. (1989) Games and Information: An Introduction to Game Theory (Oxford: Basil Blackwell). [*0]

Reijnders, L. (1978) 'On the Applicability of Game Theory to Evolution', Journal of Theoretical Biology, 75(1), xx, pp. 245-247. [*0]

Robles, J. (1998) 'Evolution with Changing Mutation Rates', Journal of Economic Theory, 79, pp. 207-223. [Extends the result of Kandori, Mailath and by letting mutation rates decline to zero over time. They also study state dependent mutation rates.]

Robson, Arthur J. (1990) 'Efficiency in Evolutionary Games: Darwin, Nash and the Secret Handshake', Journal of Theoretical Biology, 144, pp. 379-396. [Non utilitarian populations are susceptible to invasion by mutants who use a 'secret handshake' to indicate their type. They co-operate amongst themselves but treat the outsiders as the outsiders treat each other. The higher payoff resulting means that they dominate and only utilitarian machines are immune to this invasion.]

Roth, A. (1992) 'Game Theory as Part of Empirical Economics', in Hey, John D. (ed.) The Future of Economics (Cambridge: Blackwell).

Rubinstein, Ariel (1986) 'Finite Automata Play the Repeated Prisoner's Dilemma', Journal of Economic Theory, 39(1), June, pp. 83-96. [Players choose Moore machines rather than strategies.] [*0]

Sandholm, T. and Crites, R. (1996) 'Multiagent Reinforcement Learning in the Iterated Prisoner's Dilemma', Biosystems, 37(xx), xx, pp. 147-166. [*0]

* Schlag, Karl H. (1998) 'Why Imitate, And If So, How? A Boundedly Rational Approach to Multi-Armed Bandits', Journal of Economic Theory, 78(1), January, pp. 130-156. [Individuals in a finite population repeatedly choose among actions yielding uncertain payoffs. Between choices, each individual observes the action and realised outcome of one other individual. We restrict our search to learning rules with limited memory that increase expected payoffs regardless of the distribution underlying their realisations. It is shown that the rule that outperforms all others is that which imitates the action of an observed individual (whose realised outcome is better than self) with a probability proportional to the difference in these realisations. When each individual uses this best rule the aggregate population behaviour is approximated by the replicator dynamic.] [schlag_96.pdf] [*0]

Scodel, A. and Sayer, M. J. (1960) 'The Behavior of Prisoners in a "Prisoner's Dilemma" Game', Journal of Psychology, 50(xx), xx, pp. 133-158. [*0]

Schulz, U., Albers, W. and Mueller, U. (eds.) (1994) Social Dilemmas and Cooperation (Berlin: Springer-Verlag). [*0]

Schuster, P. and Sigmund, K. (1983) 'Replicator Dynamics', Journal of Theoretical Biology, xx(xx), xx, pp. 533-538. [*0]

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+ Sinclair, P. J. N. (1990) 'The Economics of Imitation', Scottish Journal of Political Economy, 37(2), May, pp. 113-144.

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+ Van Damme, E. and Weibull, J.W. (1998) 'Evolution with Mutations Driven by Control Costs', Draft Paper, Center for Economic Research Tilburg University, 29th September. [Bergin and Lipman (1996) show that the refinement effect from the random mutations in the adaptive dynamics in Kandori, Mailath and Rob (1993) and Young (1993) is due to restrictions on how these mutation rates vary across population states. We here model these mutation rates as endogenously determined mistake probabilities, by assuming that players at some cost or disutility can control their mistake probability: the probability of implementing another pure strategy than intended. This is shown to corroborate the result in Kandori-Mailath-Rob and Young that the risk-dominant equilibrium is selected in 2 x 2-coordination games.] [D POSTSCRIPT] [D PDF]

* Vega-Redondo, Fernando (1996) Evolution, Games, and Economic Behaviour (Oxford: Oxford University Press). [*0]

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+ Witt, Ulrich (1989a) 'The Evolution of Economic Institutions as a Propagation Process', Public Choice, 62(2), August, pp. 155-172. [An evolutionary game theoretic analysis of the spread of institutions as a diffusion process distinguishing between cases of spontaneous emergence and cases in which collective action is necessary to introduce the institution. Collective action is represented as organisation by 'change agents' who build a coalition taking the society above some threshold needed for spontaneous propagation.]

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+ Young, H. Peyton (1991) 'The Evolution of Conventions', Working Paper 91-10-043, Economics Research Program, Santa Fe Institute, New Mexico, fourth draft, June.

+ Young, H. Peyton (1992) 'An Evolutionary Model of Bargaining', Working Paper 92-02-009, Economics Research Program, Santa Fe Institute, New Mexico, November 1989 revised September 1991.

* Young, H. Peyton (1993) 'The Evolution of Conventions', Econometrica, 61(1), January, pp. 57-84. [Games are played recurrently and individuals have information about the past play of the game, based on which they form beliefs about how their opponents will play and choose a best response to these beliefs. The chosen actions add to the history of play.] [JSTOR] [young_91.pdf] [*0]

Young, H. Peyton and Foster, Dean (1991) 'Cooperation in the Short and in the Long Run', Games and Economic Behavior, 3(xx), xx, pp. 145-156. [

* Young, H. Peyton (2001) Individual Strategy and Social Strategy: An Evolutionary Theory of Institutions (Princeton, NJ: Princeton University Press). [@0.00] [*0]

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