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I was wondering whether there is a neat overview over different interpretations of game theoretic solution concepts such as Nash equilibrium, Sequential Equilibrium and the like.

Textbooks I found incredibly lacking in this respect (they have the tough job of getting the mathematical definitions across). Often, for Nash equilibria they allude to some "consistency" or "steady state".

My question is therefore both a reference request and perhaps a call to create a nice overview over different interpretations of equilibrium concepts in game theory. If you feel this question is too broad, it may make sense to narrow it to Nash equilibria.

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    $\begingroup$ What kind of interpretations are you looking for? MWG lists five interpretations of Nash equilibrium. Osborne and Rubinstein devote pages to discuss the different ways to interpret mixed strategy Nash equilibrium. Are these not to your liking? If not, what additional content do you want to include in the "ideal" interpretation? $\endgroup$
    – Herr K.
    May 2, 2019 at 4:11
  • $\begingroup$ @HerrK. Perhaps the clearest example of a working interpretation would be a proper treatment of the MWG favored "stable social convention" interpretation. MWG themselves point to the problem of providing a formal model of the emergence of such conventions but do not resolve the problems. $\endgroup$
    – HRSE
    May 2, 2019 at 10:56
  • $\begingroup$ Young (1993) does provide such a model in his paper titled "The Evolution of Conventions". Many similar models, with varying degrees of generality, can be found in the evolutionary game theory literature. $\endgroup$
    – Herr K.
    May 2, 2019 at 22:16

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One reason why there exists no ultimate overview is that these issues are still under debate. A great entry point would be the survey "Foundations of Strategic Equilibrium" by John Hillas and Elon Kohlberg in Volume 3 of the Handbook of Game Theory with Economic Applications. A preprint version of the survey can be found here.

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