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?