Prospect theory

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1. jonathanstrangeSep 2022
   Just a few non-fiction books from me this time:

   - Lewis Dartnell The Knowledge: This book made me realize the fragility of modern technology and how it is funded on chemical industry, shipping, oil, and the exploitation of natural resources.

   - Peter P. Wakker Prospect Theory: This is not an easy reading but it contains one of the few understandable and detailed explanations of rank-dependent utility theory and why early probability-weighing approaches were incorrect; a must read for anyone interested in rational decision making.

   - Vöcking, Alt, et. al Taschenbuch der Algorithmen: This marvelous Springer book unfortunately only seems to be available in German; it's not at all what the title suggests, but rather a book that brings the fun back to programming, like an 80s hobby programming book; various contributors lay out their favorite algorithms and techniques in short, easy to read chapters. It's like Christmas for programmers.

   - Rosen Handbook of Discrete and Combinatorial Mathematics (Indian Edition): believe it or not, this handbook has helped me a lot with my work in philosophy; it's also the almost ideal handbook style, extremely concise but also very understandable. Of course, I didn't "read" this book but using it for reference was definitely worth it.

   - Scott Programming Language Pragmatics: Anybody interested in creating a programming language should read this, preferably the latest edition (I don't know if it's still updated, though); I'm convinced that even though it mostly covers "generation 4" languages and earlier, if more language designers read this book, new programming languages would be better; not that anybody needs new programming languages, Common Lisp and Ada are perfectly fine.

   - Jean-Claude Ellena Atlas of Perfumed Botany: Although it sounds a bit pretentious at times like the perfume market is in general (it's 90% marketing of emotions, 10% about the scent), this is a really nice and passionate book about perfumery with beautiful illustrations, written by one of the most renowned contemporary perfumers. It's also surprisingly cheap and by MIT Press.

   - Duff / Gormly First Aid and Wilderness Medicine: This is perhaps the best first aid book out there. Of course, it doesn't replace a practical course but it's a great reference and generally good reading if you're interested in the topic.

   There was another book I read as a child in German, translated from English. It fascinated me and was the main reason why I got interested in AI and ultimately studied philosophy and linguistics. It was about the Schank/Riesbeck group or some similar symbolic AI research at the time (during the 70s or early 80s) and mentioned meetings where members of the group watched Mork from Ork and analyzed Mork's misunderstandings. If anybody has an idea which book that was, please let me know!

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2. jonathanstrangeJun 2019
   > Good. Then you know that any inference strategy that falls prey to Dutch Books is not rational. Right?

   Do you even have an idea what "rational" means? There are people who argue that having cyclic preferences is not only rational, but even sometimes the only rational representation of evaluations. I'm not one of these, but just wanted to mention that things are not as simple as you lay them out.

   If by "rational" you mean "fine for decision making", then I need to disappoint you. Dutch Books are not a working criterion for that. It is perfectly possible to make rational decisions with cyclic preferences. Your preferences need to weakly eligible and weak eligibility needs to be top-transitive (Hansson).

   Weak eligibility: There are one or more alternatives such that there is no preferred alternative to them.

   Top transitivity of weak eligibility: If a is weakly eligible and a~b, then b is also weakly eligible.

   These are conditions on preferences. You can have similar conditions on subjective plausibility, of course, once you combine preferences and subjective plausibilities.

   By the way, Expected Utility falls prey to Dutch Books. There is a money pump against every risk-averse or risk-seeking agent. Check out Wakker's book, which is much better than Jayne: Prospect Theory for risk and ambiguity. Anyway, EU is often considered rational and widely used, but according to your criterion it would be irrational. (In finance, the kind of Dutch Books are called "arbitrage" and exploited immediately, so the market prunes them away, but in other areas EU is used extensively. Are you maybe a finance guy???)

   > For reference, Jaynes Desiderata:

   Of course you can just claim "here is my list of postulates, and that's what 'rational' means", but that's not really an argument. The other theories I am talking about are also axiomatized. Take for example Fishburn's seminal work. According to your theory, Fishburn spent most of his life and efforts in decision making on irrational theories. I'm not convinced and rather be willing to talk about different kinds of rationality, if I'd be pressed to make a decision on that.

   > (1) Degrees of plausibility are represented by real numbers. (And a continuity assumption.)

   There is a vast array of literature on qualitative decision making for which this assumption does not hold. Lexicographic decision making does also not fulfill that requirement and there is a whole French-Belgium school on that, including axiomatizations and practical methods (tools like ELECTRE). For lexicographic decision making usually hyperreal numbers are used.

   Qualitative decision making comes with a host of problems and limitations due to Arrow's Theorem, but lexicographic models can be very reasonable and even required if some of the authors in the field are right about some examples of seemingly irrational preferences. In any case, just to say that these axiomatized theories are irrational because "here are my axioms" is unacceptable. I'm sure not even Jayne does that.

   As for the continuity assumption: There is a whole field of measurement theory that would tell you when you need it and when you don't need it, and I really don't see any non-measurement-theoretic way of defending such technical assumptions as rationality postulates independently. Again, just assuming these kind of things a bit too simple. After all, I can take any postulate and call it "rational", that's not a meaningful discussion of rationality, though.

   > (3b) The robot always takes into account all of the evidence it has relevant to a question. It does not arbitrarily ignore some of the information, basing its conclusions only on what remains. In other words, the robot is completely non ideological.

   This is an interesting principle, because even in probabilistic settings it completely controversial how to deal with conflicting evidence and how and when to revise beliefs in the face of evidence that directly conflicts with your existing beliefs.

   It's a very vexing and complicated problem with many different solutions. It is definitely an underdetermined problem. One of the best discussions of it has evolved from criticisms of the corresponding update rule in the Dempster-Shafer theory of evidence, so it's worth taking a look at if you're really interested in this topic. But you seem to be hell-bent on taking Jayne's book as some sort of bible, which is weird. It's not as if any of the other approaches I've mentioned in my previous post are unknown or have been proposed by outsiders - it's almost impossible to not stumble across possibility theory (Dubois & Prade) or Halpern's work if you're doing AI research, for example.

   > They're not just true, they're obvious.

   Maybe for people who do not know the literature very well, but certainly not to me. Sorry. :(

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3. zwapsDec 2017
   I use Game Theory in pretty much everything (academic) Here are some thoughts on the literature.

   There are several different strands and evolutions of Game Theory.

   1. Game Theory (non-cooperative):

   The basis was Neumann/Morgenstern Theory of Games. It has been suggested in this thread, however its focus is a bit obscure today. Still useful for repeated games, for example. Both authors are also important for Decision Theory, see below. Afterwards came Nash, defining the what the basic solution concept would be up until maybe 1990. Simple Nash equilibria are used primarily where rational agents choose in mathematically nice spaces where uncertainty is not a major factor.

   Following Nash, the Game Theory literature developed to produce equilibrium refinements. These, usually subsets of Nash equilibria, were created because Nash often predicts very little - the space of equilibria is often so large that nothing can be learned, or uncertainty requires the incorporation of different information sets of agents. The first developments came while incorporating uncertainty and multi-stage games (where people move in sequence). Harsanyi was able to show that most configurations of uncertainty situations can be represented as a Bayesian Game (the issue was the recursion of "he knows, that I know, that he knows that I know..."). The problem became, that these often produced unintuitive and large sets of equilibria. So we have refinements. Some target robustness, like Selten's Trembling Hand. Others target "natural behavior", empty threats and so on. Almost all of those refinements are a subset of a Nash concept. The development of refinements was en vogue prior to the 90's, when it stopped for reasons I will detail below. Basic Nash has survived, however, and is still the go-to tool to understand multi-agent decision problems (at least initially).

   1.a Cooperative Game Theory:

   Largely in parallel, mathematicians like Shapely and later economists like Roth also tried to think about cooperative games. Here, we don't look directly at what individual people do in isolation, but rather what groups are stable and plausible and what they can achieve. If for example a smaller group can "break" a coalition, then such a large coalition can not be considered a plausible solution. Matching theory comes from here, for example, so you will find it in most problems of assignment (say, students). Much as non-cooperative Game Theory, it is applied widely.

   2. Decision Theory:

   Decision theory developed in parallel and is a wide field. It is, however, critically important to Game Theory because it sets the stage for information, constraints and decisions that agents take. Expected utility, by Neumann and Morgenstern, was and is the basic instrument to understand how agents incorporate their knowledge. This was based on objective probabilities, so in parallel the Bayesian stream also developed. With a monumental and beautiful proof, Savage then developed Bayesian Decision Theory (based on works by de Finetti and others). This is critical to many, many fields in maths, statistics and science in general, and was then the basis for Game Theory. Aumann is associated with latter refinements of decision theory. Later on, the idea of uncertainty (Knightean uncertainy) became important. This is when you can not assign a probability to an outcome. Paradoxes by Elsberg and Allais have shown that this is actually an important decision problem in real life. Multiple approaches exist to generalize Decision Theory, such as Prospect Theory, MinMax Preferences, integration by capacities as opposed to measures. Schmeidler, Gilboa and Wakker are some names. Game Theory exists in this space as well.

   3. Evolutionary Game Theory:

   The idea came from Biology and is important because it is a way to justify Game Theoretic outcomes without even requiring purposeful action by agents. It had a huge impact on many problems, especially dynamic ones and "top down" models, but did not surplant traditional Nash in general. Some scientists believe it should. Other's think it's just one more tool. There are those who believe the whole of social sciences should be based on it... Let's say it did not achieve that yet.

   4. Economic applications:

   Economics was historically the discipline to apply Game Theory most. Initial concepts like Nash justified many early models of Markets. Earlier concepts of non-perfect competition were formalized with Game Theory. Things really started to take off when asymmetric information were introduced. Think Moral Hazard, Signaling Games, Contract Theory and so forth. What we know about economics, organizations, business, competition and many social phenomena today has largely been developed by applying Game Theory. There are too many great names to mention: Akerlof, Tirole, Spence, Hart, Homström, Myerson, Stiglitz.

   5. Mechanism Design and Auction Theory

   In the 70's and 80's, from the above applications, economists like Hurwitz, Myerson and Maskin developed mechanism design. The idea is simple and genius: If agents play games, what if we can choose the game they play? Which game do we choose without them walking away, but with us getting the desireable outcome? What is, in other words, the optimal mechanism inducing the agents to play a game? Initial examples and todays shining example of econ in action is Auction design. Which sort of auction mechanism is best to sell ads, be ebay or assign broadband licences? Mechanism design leads to very complex problems, which is why until the early 90's many simplified assumptions were used. While mechanism design has been very useful, this also lead to two developments. In econ, papers started to get more and more complex to accomodate real life issues like non-monetary transfers, dynamics, complex type sets and so forth. Computer scientists trying to implement mechanisms quickly discovered that many were simply to complex, so they started Algorithmic MD.

   6. Experimental and behavioral games:

   So earlier, I said that a whole cataloque of equilibrium refinement basically died out. Why is that? Well, with behavioral econ we were introduced to more realistic approaches to decisionmaking. Then questions arose, such as "what if I can not count on rationality of my competitor". As it turns out, this may actually break the inference of Nash equilibria pretty handily.

   At the same time, economists and psychologists put people in experiments to play games. In some situations, Nash worked well. In other situations, one could accomodate much by using more complex Decision Theory. But in many instances, people would just not play Nash. In other words, they couldn't even figure out the most basic solution concept. Indeed one can do all sorts of experiments in a Game Theory 101 class showing that people often choose much too heuristically. Equilibrium refinements make Nash more complex, it was clear they had to be abandoned. Currently, research joint in decision theory and game theory works on finding better ways to model behavior when Nash is not reached.

   Books:

   Osborne/Rubinstein has been mentioned. Contrary to what was said, this is an undergrad book and a solid intro. There are two classic works. The major one is by Tirole and Fudenberg, the other is by Myerson. The former is more standard, the latter is better. Now there is a new book by Maschler, Solan and Zamir with like 900 pages. It's really good, and I would definitly get it as a second book after an intro.

   For Mechanism Design, the best book is by Tilman Boergers. It's also free to download. Auction Theory specifically has a standard volume by Krishna. Both of those are math heavy. This is true in general, but Game Theory concepts can often be explained by intuition. For Mechanism Design, I fear that a solid math background would be required, because the space of "choosing a game" is mathematically not so nice. However solid means you should have a good grounding in analysis and optimization, perhaps dynamic systems. Basically, a math heavy undergrad education will be fine.

   hope this helps

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