Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction (Second Edition),   ISBN:9780691140506

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The book explicates with several examples the part related to "evolution" of the game theory. This aspect is very important for the application to the biology, not only to the economy. The examples are several and they are showed in a simple way. It's important the equilibrium of the Nash bargaining and the connections with the chaos theory.

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The problem with this book,as with practically all game theory approaches,is that it is based on the subjective,Bayesian approach to probability ,which asserts that the coherent (rational) decision maker's probability assessments will always be consistent with the purely mathematical laws of the probability calculus(the addition and multiplication rules used in all tree diagrams and decision trees).This requires that all probabilities are unique,additive,precise,determinate,exact,sharp point estimates.All probability distributions are unique.Only one distribution will be applied by the decision maker, who knows what this specific distribution is for certain.Invariably,this turns out to be the normal probability distribution.The decision maker will engage in Bayesian updating(this should not be confused with Keynesian revision ,which allows the decision maker to change to a different probability distribution entirely when new evidence is obtained if the new evidence shows that the previously assumed distribution was erroneous),which means that the new evidence allows him to update the estimates of the probability parameters specified by the unique probability distribution.However,the probability distribution itself NEVER changes-only the estimates of the parameter values change.Gintis constantly makes reference to the subjective,Bayesian approach ,on about 150 of the pages in his book,as being the foundation for the rational actor model that underlies game theory applications.

The second problem is that the outcomes( Morgenstern-von Neumann utilities) are assumed to be point estimates ; they are just as exact and precise as the probabilities were assumed to be.A decision is reached by simply adding up the expected utilities obtained when the point probabilities are multiplied by the point utilities and summed.This is no different than the original claims made by Jeremy Bentham in 1787.Only the mathematical apparatus has changed.

J M Keynes completely demolished this fictitious view of decision making in 1921 when he published his A Treatise on Probability(TP).Keynes proved that the general case ,for both probabilities and outcomes,was that both probabilities and outcomes are only representable by intervals.Only in very special cases,usually occurring in the physical and life sciences(physics,biology,chemistry,engineering)can a decision maker reliably estimate sharp point probabilities and outcomes.Keynes established his conclusions in chapters 15,17,20,22,26,and 29 of the TP.Keynes also put forth a systematic analysis of decision weights that could be sub and super additive(proportional)or convex -concave.Unfortunately,Frank Plumpton Ramsey decided that he could review Keynes's book based only on a preliminary reading of chapters 3 and 4,with 7-10 other pages apparently chosen at random from the rest of the book.Ramsey made the silly and stupid claim that Keynes's system of probability was based on non numerical(non comparative) probabilities and non numerical(non comparative) degrees of belief.Of course,Keynes defined his nonnumerical probabilities to be intervals representable by inequality constraints and upper-lower bounds(least upper bound-greatest lower bound).Point estimates are special cases where the upper and lower bounds are equal.Keynes had told the reader of chapter 3 TWICE (1921;p. 37,p.38) that the reader should wait until Part II of the TP was reached before drawing any conclusions from chapter 3 about the measurement of probabilities.Ramsey ignored these warnings and based his queer reviews on 2 out of the 33 chapters of the TP.Gintis's entire framework and edifice essentially rests on a foundational approach to probability based on Ramsey's error filled reviews that all probabilities and outcomes can be represented by a single number.


There are severe problems with the logical foundations of subjective probability.Recently,Kadane,Schervish,and Siedenfeld,in their " Rethinking the Foundations of Statistics "(Cambridge University Press,1999), have completely thrown in the towel and admitted implicitly that Keynes was right and Ramsey,De Finetti,and Savage were incorrect.The book is composed of 16 essays,all of which have been previously published in academic journals and/or other books.Throughout the book,the authors concede that there are many holes and deficiencies in the logical foundations of the subjectivist approach.The biggest hole is vastly understated by KSS: " In fact,it seems reasonable to deny that there are consequences in practical decisions.Thus,our position is that,lacking consequences,expected utility theory must treat probability distributions as extraneous(italicized)..."(KSS,1999,p.195).Of course,"...lacking consequences...", means that the outcomes are state independent.On pp.157-160,KSS had already demonstrated the near impossibility in the real world of being able to specify outcomes that would make their utilities state independent.Given that the subjective probabilities are completely extraneous,there is no longer any way in which the a priori beliefs of a decision maker can be represented by a unique probability distribution on purely decision theoretic grounds alone.This means that unique,definite,precise,numerical ,single number estimates of subjective probabilities do not exist.This result goes to the heart of the entire edifice erected by Ramsey,De Finetti,and Savage,in particular.Savage argued that,based on a careful elicitation of subjective preferences based on betting quotients,a unique probability measure(distribution)can be defined to represent the agent's preference relation.Nowhere is it stated by KSS that this position( of Savage) goes to the heart of the dispute between Keynes and Ramsey about the inherent indeterminateness of many probability estimates.The comparative -interval estimate-approach to estimating probabilities,presented by Keynes for the first time in the A Treatise on Probability(TP;1921,pp.160-163,pp.186-194),is fully operational since all of the problems that used the difficult Boolean approach used by Keynes can instead use the substantially easier integer-mixed integer linear programming approach of Theodore Hailperin in order to obtain solutions.It appears that Ramsey's approach is a very special case of Keynes's approach that is applicable only when a single,unique probability distribution can be specified a priori. KSS's technical result,first presented in 1990 in the Journal of the American Statistical Association(JASA), completely undermines the logical ,decision theoretic foundations of the subjectivist approach to estimating probabilities.
Gintis has overlooked the numerous logical deficiencies in the current Bayesian approach.Keynes has been right all along.Gintis's book needs to be completely rewritten since it is primarily based on bizarre assessments and assertions made by Ramsey about Keynes's approach in two very,very poor book reviews in 1922 and 1926. Otherwise,all of the results of the many problems covered by Gintis can only hold under the very special assumptions made by subjectivist Bayesians about all probabilities and outcomes being point estimates.The reader should also note that the work of Gilboa and Schmeidler done between 1987-2007 on convex -concave capacities and case based decision making is really a rediscovery of the work of Keynes,although,since they have not read the TP,they,like Gintis ,are ignorant of what it was that Keynes did in 1921(Keynes's 1907 and 1908 Fellowship theses also contain his interval estimate approach to probability based on the application of Boole's system of algebra to probability ).

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I am using this book for independent study of Game Theory.

The pros. The problems in the book are excellent. They range from easy to fairly difficult, and manage to cover most nooks and crannies needed for a thorough introduction to contemporary game theory, with some evolutionary and economics background for good measure. For professors, I think this is a good book to use to prepare a class. It has the examples one needs to set up a "zone of proximal development", meaning, an exposition in which one leads the students bit by bit toward better mastery of the ideas. In fact, the choice of problems, the flow from one vignette to another, and the interweaving of problems with important theoretical concepts and expositions leave the impression that the book is closely based on Prof. Gintis's lecture notes.

The cons. The blessing is also the curse: the book reads like a chalkboard with commentary rather than like a textbook. If you are expecting the familiar cadence of background - theory - examples - problems, you will not find it here. This can be refreshing, but takes getting used to. A more serious drawback is that solutions at the end of the book are very sketchy, so beginners will find it difficult to connect all the dots without outside help. Students expecting a more thorough style are likely to find the book infuriating.

In brief, the quality of material is high, but the treatment could have used a once- or a twice-over. Solid reference, very good for preparing a class, but if you are using it for home study, have someone to call on when you get stuck on a problem. Also, if you are a mathematically competent social scientist, I would recommend another book in parallel, such as Hargreaves-Heap & Varoufakis "Game Theory - A Critical Text". While Gintis is very hands-on, Hargreaves-Heap and Varoufakis spend much more time on warranted and unwarranted assumptions game theory makes about human psychology, as well as epistemological concerns - details needed to understand how the theory fits within social sciences. These two books complement each other quite well.

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I recently purchased this book through Amazon.com. The book is excellent. The treatment of the topic is in depth and the examples are very profound. The exercises also are very though provoking and it is a great book for anyone who wants to learn more about Game Theory.

The service by amazon was also outstanding. I obtained the book on the promised date. All queries regarding the order were answered promptly and professionally.

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I bought the 2000 edition of this book, which has so many errors that it's unreadable, and some of the problems are unsolvable because of the errors. I found enough errors in the second chapter alone to make me give up on it. The author has a link to a file of errata on his web page, but the link was dead. I contacted the author to ask for the errata, and he told me to buy the 2002 edition. I insisted, and he e-mailed me the file. I didn't find either of two major errors that I had noticed in the errata. The book has very few examples, so it took me a long time to realize that my trouble with the problems as presented was because of errors with the problems, not because the problems were particularly hard. Don't buy this book, period.