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I recently had to take a course on economic game theory. In general I don't understand how the definition of a rational agent is used.I can give an example of a proof that I don't understand.

In a finitely repeated game, of prisoners dilemma the conclusion is that both players always will betray each other. This result is derived from looking at the last time, where one of the payers cooperates. Then the strategy where both players always will betray each other from this point on is an improvement for both. So the strategies chosen before couldn't be optimal. Hence both players always betray each other.

I do not see how this proof gives any useful information. Yes player A can improve his strategy given the strategy of player B if he cooperates. Player A does not know the strategy of player B, so he can't use this information.

Mutual knowledge of each others strategies is assumed, and finding a Nash equilibrium is the same as ruling out every case where mutual knowledge leads to a contradiction. The strategies that are left are called strategies that a rational agent would choose,instead of strategies that you end up with after this procedure.

I also tried to find some critique that sheds light on this issue or resolves it, but all I could find was babbling on how we can not assume that every person is rational, not that the definition of a rational agent is wrong. Am I beeing crazy? Is this a basic issue, everyone is aware of?

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Nash equilibrium is just one solution concept and there are others if you don't like that (minimax, maximin, $\epsilon$-equilibriu, sub-game-perfect equilibrium, trembling hand equilibrium, and so on and so on) depending on the settings.

The assumption that you know the strategy of the other helps achieve basic features of the equilibrium:

Stability - if everyone plays the equilibrium strategy, nobody deviates.

Regret minimization - in retrospect, after learning the strategy of the others, I couldn't have done anything better.

It fits many real-life scenarios. For example, I know that everyone is driving on the right side of the road, so I'll do it too, although in principle if tomorrow all the people decide to drive on the other side, everything will still be OK.

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  • $\begingroup$ Thanks for the answer. The info I got out of my lectures was:"Every rational person would act in this way. Since people in real life are not rational they do not act in this way...".This makes much more sense. So my takeaway is, if the mutual knowledge condition is satisfied Nashequilibria are reasonable. $\endgroup$
    – Dude1662
    May 5, 2021 at 17:09
  • $\begingroup$ I just dont get why regret minimization is important in the case of finitely repeated games. A justifcation for that may be, that after a certain amount of repetition of this finitely repeated game players would always improve on their strategy, until they inevitebaly play the Nash-Equilibrium at the end. However when players know of this finite repetition, they would play different strategies and not increase their value iteratively. $\endgroup$
    – Dude1662
    May 7, 2021 at 20:15

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