I’ve wondered about, and even modeled versions of the fixed horizon IPD in the past. I concluded that so long as the finite horizon number is sufficiently large in the context of the application (100 is large for prison scenarios, tiny for other applications), a proper discounted accounting of future payoffs will restore TFT as an ESS. Axelrod used discounting schemes in various ways in his book(s).
The undiscounted case will always collapse. Recursive collapse to defect is actually rational and a good model for some situations, but you are right, in other situations it is both silly and not what people do, so it is the wrong model. If there is a finite horizon case where discounting is not appropriate, then I’d analyze it differently. To stop the recursive collapse, let the players optimize over possible symmetric reasoning futures...
I’ve wondered about, and even modeled versions of the fixed horizon IPD in the past. I concluded that so long as the finite horizon number is sufficiently large in the context of the application (100 is large for prison scenarios, tiny for other applications), a proper discounted accounting of future payoffs will restore TFT as an ESS. Axelrod used discounting schemes in various ways in his book(s).
The undiscounted case will always collapse. Recursive collapse to defect is actually rational and a good model for some situations, but you are right, in other situations it is both silly and not what people do, so it is the wrong model. If there is a finite horizon case where discounting is not appropriate, then I’d analyze it differently. To stop the recursive collapse, let the players optimize over possible symmetric reasoning futures...