Is it possible to collude in a perfect information game?

Question

Is it possible to collude in a perfect information game?

Exercise 10-7 from book "Algorithms And Networking For Computer Games" - Jouni Smed, Harri Hakonen, p 225

Answer 1

Yes, consider the following situation: Suppose we have two companies $A$ and $B$ that produce oranges. Company $A$ chooses some amount $q_A$ of oranges to produce. Given this information, company $B$ chooses $q_B$ of oranges to produce. The goal of both companies is to maximize their profits. We know that the total quantity is $Q = q_A+ q_B$ and the demand is $f(Q)$. So it is possible for both companies to jointly maximize their profits.

Answer 2

An extensive form is a complete desription of the strategic environment faces. So players have exactly the options available that the game tree presents. In some cases, one might think about some background story in which one can interpret some moves as "colluding", but such an interpretation lies outside game theory.

Edit: It seems the book considers "colluding" as players in a computer game cheating by not following the explicit rules. In a perfect information game, players cannot cheat by exchanging information. In a generic finite game of perfec information, super-rational players can't collude by the usual backward-induction logic. In infite games, they might be able to coordinate by pre-play communication.