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this is a better (written by Myerson, a Nobel laureate), more precise, still fruitfully intuitive picture of Nash equilibrium putting in perspective of economic

• linhchi 11y ago
  I post here my 2 cent summary about game theory, if someone needs reference, i can post later: In noncooperative game theory, a player is supposed to be rational and intelligent. Being rational at least means that player doesn't use a dominated strategy (like in one-shot PD, cooperation is dominated by defection). Being intelligent means that player can bet in the rationality of opponents (which means one knows that the other will not play a dominated strategy ~ cooperation). -> Just these two conditions can solve the Prisoner's Dilemma. However, in other games, after iterating away all the dominated strategies, player needs a stronger notion of rationality: player maximizes expected utility given accurate prediction about opponent's strategy. As before, with the intelligent assumption standing, both players' keen consistency in their action will lead to Nash equilibrium (NE). NE is a broad and fundamental concept. It's broad because it bases only on belief, not necessarily on what's real. Given the convergence of action and belief in equilibrium, what wasn't justified before will become justified. However, too broad is also its inherent issue because game theory loses its predictive power in many games by dictating too many possible Nash equilibria. Speaking of that, this concept is still so fundamental that it becomes the unit test for any kind of stricter equilibrium concept that one would like to build. -> Many giants have tried to make major refinements built on top of NE. But along this literature, the further they go, the heavier the burden of rationality assumptions on modelling decision makers becomes. Player has to bear an exhaustive rationality in analysing the game in all the nodes that may never happen, or in face of background noise, or in thinking from future back to present.. Even making mistake needs to be justified. That requires ability to do complex optimization and infinite recursive thinking of common knowledge. So they say, what is the point of a theory starting with assumptions about players that are not even close to the statistically real truth? And if the collective reality doesn't matter, what matters? -> Until now the narrative has substantially shifted from these ideal players to less demanding subjects. Just as applied economics of behavioral, experimental, neuro-economics trying to figure out a reasonable approach to modelling decision makers by adding cognitive and psychological knowledge, theorists bring evolution into game theory. Starting from an amusing observation that nature doesn't assume any rationality of its creatures but its solution many times becomes our definition of perfect, evolutionary game theory (EGT) offers a less pervasive way of thinking into games by replacing strict assumptions by adaptive learning and letting the itera- tive selection process do its job. Surprisingly, sometimes it gives us the perfect equilibrium just like in the classical regime.