Game Theory and Economic Modelling Kreps, David M Paul E. Holden Professor of Economics, Graduate School of Business , Stanford University Contents 1. Introduction 2. The standard 3. Basic notions of non-cooperative game theory Strategic form games Extensive form games Extensive and strategic form games Dominance Nash equilibrium 4. The successes of game theory Taxonomy based on the strategic form Dynamics and extensive form games Incredible threats and incredible promises Credible threats and promises: Co-operation and reputation The importance of what players know about others Interactions among parties holding private information Concluding remarks 5. The problems of game theory The need for precise protocols Too many equilibria and no way to choose Choosing among equilibria with refinements The rules of the game 1 6. Bounded rationality and retrospection Why study Nash equilibria? The case for bounded rationality and retrospection A line of attack Historical antecedents and recent examples Objections to this general approach, with rebuttals Similarities: Or, Deduction and prospection is bounded rationality and retrospection The other problems of game theory Final words Bibliography Index 2 Acknowledgements This book provides a lengthened account of a series of lectures given at the Tel Aviv University under the aegis of the Sackler Institute for Advanced Studies and the Department of Economics in January 1990 and then at Oxford University in the Clarendon Lecture Series while I was a guest of St Catherine's College in February 1990. (Chapter 3 contains material not given in the lecture series that is useful for readers not conversant with the basic notions of non-cooperative game theory.) I am grateful to both sets of institutions for their hospitality in the event and for their financial support. I am also pleased to acknowledge the financial assistance of the John S. Guggenheim Memorial Foundation and the National Science Foundation of the United States (grant SES-8908402). I received very helpful comments and assistance from a number of colleagues both while preparing the lectures and on various drafts of this book; I am especially grateful to Anat Admati, Jeremy Bulow, Drew Fudenberg, Faruk Gul, Frank Hahn and his Quakers, Elchanan Helpman, Paul Klemperer, Marco Li Calzi, Leonardo Liederman, Gerald Meier, Margaret Meyer, Ariel Rubinstein, Tom Sargent, and Eric Van Damme. The opinions and ideas expressed here have resulted from conversations over many years with many colleagues. I cannot possibly give adequate attribution to all, but I would be terribly remiss not to cite the very important contributions of Drew Fudenberg, Faruk Gul, and Robert 3 Wilson to my thinking. (Also, I report in Chapter 6 some of the ideas developed in research I am currently conducting with Fudenberg. I will try to be careful and give appropriate acknowledgements there, but a blanket acknowledgement is called for here.) 1 Introduction Over the past decade or two, academic economics has undergone a mild revolution in methodology, viz. the language, concepts, and techniques of non-cooperative game theory have become central to the discipline. Thirty-five years ago or so, game theory seemed to hold enormous promise in economics. But that promise seemingly went unfulfilled; twenty years ago, one might perhaps have found 'game theory' in the index of textbooks in industrial organization, but the pages referenced would usually be fairly dismissive of what might be learned from game theory. And one heard nothing of the subject from macro-economists, labour economists . , the list goes on seemingly without end. Nowadays one cannot find a field of economics (or of disciplines related to economics, such as finance, accounting, marketing, political science) in which understanding the concept of a Nash equilibrium is not nearly essential to the consumption of the recent literature. I am myself something of a game theorist, and it is easy to overrate the importance of one's own subfield to the overall discipline, 4 but still I feel comfortable asserting that the basic notions of non-cooperative game theory have become a staple in the diet of students of economics. The obvious question to ask is, Why has this happened? What has game theory brought to the economists' table, that has made it such a popular tool of analysis? Nearly as obvious is, What are the deficiencies in this methodology? Methodological fads in economics are not completely unknown, and anything approaching rational expectations would lead a disinterested observer to assume that the methods of game theory have been pushed by enthusiasts (and especially those who are newly converted) into 'answering' questions that are not well addressed by this particular tool. And third, What next? Will non-cooperative game theory go the way of hula hoops, Davy Crockett coonskin caps, or — (fill in the blank with your own favourite example of a fad in economic theory), or will it remain an important tool in the economists' tool-box? Or, set in a way I think is more interesting, In what ways will this tool of analysis change and expand so that it continues to be relevant to economic questions? In this book, I will give my own answers to these questions. Along the way, I hope to provide enough information about the tools and the questions that these tools can and cannot answer so that you will be able to see what the noise has been about if you have not heretofore followed 5 this mild revolution. (If you are already conversant with the concepts of game theory, you can probably skip Chapter 3 and will probably find my pace throughout to be less than brisk.) If you are able to tolerate abstraction, you may find my manner of providing this information frustrating; I will work with examples and pictures, eschewing formal definitions throughout. If you can stand a formal treatment of the basic ideas and models, consult a proper textbook on the subject.1 Now it goes without saying that because I have been something of a protagonist in the rising popularity of game theory as a tool of economic analysis, I have a stake in its continued use by economists. I will claim that game theory's popularity reflects the sorts of things that I have worked on in the past; its weaknesses reflect the sorts of things on which I work today; and its continuing development will reflect the sorts of things on which I hope to be working in the future. Put another way, this is a highly personal statement of the successes, problems, and evolution of game theory in economics. At the same time, I belong to an intellectual tribe and most of what I will have to say reflects not brilliant personal insights but rather the collective view of that tribe, filtered through the lens of my prejudices. Had I written Chapter 6—on where the discipline is or should be heading—five years ago, I might be able to claim some powers of prescience. But my 'predictions' about the future of the subject are very 6 well informed by the current ferment and work in the subject. Any impressive insights that follow should be attributed to the tribe. And if you find yourself thinking what follows is nonsense, just put it down to my poor powers of exposition. 2 The Standard Before setting off, I want to set the standards by which game theory will be judged. For the purposes of this book, the point of game theory is to help economists understand and predict what will happen in economic contexts.1 I am willing (and able, you may conclude) to twist and turn in all manner of ways the meaning of 'to help us understand and predict'. While it is better if game-theoretic models are not refuted empirically or experimentally, I do not preclude the possibility that one can learn from an empirically falsified model things that help in achieving better understanding and predictions. But I am not interested in this book in game theory as the study per se of how ideally rational individuals would interact, if ever they existed. I also will take no notice of how game-theoretic ideas inform fields such as biology. I do not mean to preclude the possibility that economists can learn things of interest and significance to economics from applications of game theory to fields such as biology. But in my opinion we aren't there yet. And I certainly 7 recognize that studying the interactions of ideally rational individuals, if used with circumspection, can aid our understanding of the behaviour of real individuals. But studying the former should aim at understanding the latter. If the theory doesn't help understanding and predictions about real economic institutions and phenomena, then in this book it will be judged a failure. Having set out such a 'noble' standard,2 let me begin the twisting by noting how it is that understanding and predictions may be aided by the theory. (1) I take it as an axiom that improvement in understanding by itself implies improvement in predictions. This assertion is hypothetically subject to empirical falsification; ask economists to make predictions about some matter; then expose them to models that they claim improves their understanding of the situation and see if they can make more accurate predictions. But if this empirical test has been carried out, I do not know of it; and so I assume the hypothesis. (2)Game theory by itself is not meant to improve anyone's understanding of economic phenomena. Game theory (in this book) is a tool of economic analysis, and the proper test is whether economic analyses that use the concepts and language of game theory have improved our understanding. Of course, there is an identification problem here.