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Are there game theoretic models where one player is rational and the other is irrational (i.e., plays with behavioral limitations)?

The motivation for this question is that behavioral economics has documented how people often make choices that don't maximize expected utility, but those irrational people might be interacting with near-rational computers or organizations. I've never seen a game theory model that has both an expected utility-maximizing player and a behavioral player.

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    $\begingroup$ There is a literature on expected-profit maximizing firms dealing with behavioral consumers.Take a look at Ran Spiegler's excellent book. $\endgroup$
    – Michael Greinecker
    Nov 29, 2017 at 0:09

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Yes, a whole book has been written on Behavioral Game Theory.

More specifically, standard solution concept such as Nash equilibrium requires that players best respond to a correct belief about other players' moves. The following are examples that relax one of these cognitive restrictions:

For a complete review of models of behavioral game theory, see Chapter 13 of Dhami (2016).

For a specific example of a game with mixed players, see this paper on robust protection of fisheries. A more comprehensive treatment of mixed games is available in Rani Spiegler's Bounded Rationality and Industrial Organization per Michael Greinecker's comment on the original question.

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  • $\begingroup$ After checking out those links, I'm still a little unclear if those behavioral game frameworks allow some players to be standard rational players and other players to be behavioral players (in the same game). For instance, in the Cognitive Hierarchy Theory wiki page it sounds like all the players have finite depth reasoning, so there would be no truly rational player in that game. $\endgroup$
    – ajkeith
    Nov 29, 2017 at 0:57
  • $\begingroup$ I edited the original post to better reflect that the question is about mixing rational and irrational players $\endgroup$
    – ajkeith
    Nov 29, 2017 at 1:03
  • $\begingroup$ @ajkeith: Perhaps my answer to this question may be an example? $\endgroup$
    – Herr K.
    Nov 29, 2017 at 2:44
  • $\begingroup$ @ajkeith If everyone plays a best response, everyone is as rational as can be and can reason as deeply as possible. Everyone being rational does not imply that everyone believes everyone to be rational. $\endgroup$
    – Michael Greinecker
    Nov 29, 2017 at 8:08
  • $\begingroup$ @HerrK.: Yes, that's a great example - I was hoping for some references that are focused on those types of games with mixed players. Michael Greinecker's comment on the original question is the exact type of answer I was looking for. $\endgroup$
    – ajkeith
    Nov 29, 2017 at 14:56

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