Reddit reviews Evolution and the Theory of Games

Given your background, you could read Ken Binmore's Game Theory: A Very Short Introduction (2007). It's really short, but it assumes the reader is familiar with probability theory and a fair amount of mathematics. Binmore has another textbook Playing for Real (2007) which is goes much more in depth. It assumes the reader is familiar with linear algebra.

One of the central results of von Neumann and Morgenstern's Theory of Games and Economic Behavior (1928) is the minimax theorem. This was John von Neumann's favorite theorem from that book. John Nash generalized this in his PhD thesis in 1950. The minimax theorem establishes the existence of Nash equilibrium for zero-sum games with finite players and strategies. Nash's extended this and showed that any normal form game with finite players and strategies has an equilibrium. You might have seen the movie A Beautiful Mind which depicted John Nash working on this. If you are interested, you can read about Nash's proof in Luce and Raiffa's Games and Decisions: Introduction and Critical Survey (1957). The proof does assumes the reader is familiar with point set topology.

Outside of economics, game theory is also applied to evolutionary biology. One of the best books on evolutionary game theory is Martin Nowak's Evolutionary Dynamics: Exploring the Equations of Life (2006). You might also like John Maynard Smith's Evolution and the Theory of Games (1982). Maynard Smith assumes the reader is familiar with homogenous differential equations.

Hope this helps!

I'm making calculations based on your behaviour, that of an authoritarian mod who claims to be an anarchist. You don't see the inherent contradiction there? And there's no way I'm telling you what university I went to, I don't see that it's relevant. If you really want to be a detective, the author of this was one of my tutors. What university did you go to?

I recommend this if you're interested in the field. These are long books, the ideas in them are fairly easy to get across in person, but it's just not feasible in a few reddit comment boxes. If you're saying you're willing to be swayed and haven't just made up your mind, I will answer specific questions. But "Explain it" is just too broad for me, sorry.

First Idea: Language. Some-one might invent a Constructed Language or conlang, that helps thinking and communicating. Life is more complicated than language. We should reject both mistake theory and conflict theory. Politics is nasty due to linguistic poverty. Our few words muddle together different things leading to quarrels.

Examples avoiding culture war: 1)The opening paragraph here 2)the word error as used by journalists reporting on medical tests. We are really interested in positive predictive value and negative predictive value. We could work them out for ourselves if we knew the false positive rate and the false negative rate and the prevalence. Here our language is rich enough that there are words for the concepts that I claim we don't have words for. That is good, because it allows me to write down an example using words, and I can fall back on pointing out that natural language only has error. The other words and phrase belong to unnatural language :-)

Second Ideal: Quantitative Dynamic Sociology. Think about Quantitative Ecological Theory All those foxes eating hares until hares are rare and the foxes starve and die, and the hare population revives and the few remaining foxes put on weight and eventually start breeding again. Like that, but for ideas, like marriage, divorce, income tax, minimal wages,... Why do they wax and wane?

Peter Turchin is on to this and calls it Cliodynamics. Great, but I fear premature. I'm expecting a book like Evolution and the Theory of Games which gets criticized for unrealistic models. First we need some-one to come up with a compendium of toy models for Quantitative Dynamic Sociology to show what it would even look like. Then, in 2119, the great mind can revolutionize the new field with models that actually work.

Evolution and the Theory of Games