Given Rice's theorem, there is no source code analysis that is guaranteed to tell you anything interesting about your opponent, unless your opponent has been written in such a way as to facilitate that analysis. This suggests two possible modifications of the competition.

Firstly, the rule could be imposed that source code is unanalysable. A competing program will not be furnished with its opponent's source, but only an opaque blob. The only operation they can perform on this blob is to supply it with another blob and see what answer it gives. Each program is given access to itself (as an opaque blob), and can contain within itself whatever other blobs it wishes to use for probing purposes. Note that if every program begins a contest by running its opponent on some example, then no-one terminates and everyone loses. Therefore a program must sometimes make a decision without having run its opponent on any examples. This looks like it severely limits the usefulness of simulating the opponent to see what it will do, perhaps to the point where it is impossible to gain anything from it, and the competition reduces to an ordinary PD tournament.

Alternatively, source code would be revealed, but in addition each program would be allowed to furnish machine-checkable proofs of assertions about itself. The machine checking would be part of the infrastructure of the competition, so competitors would be able to have complete trust in these assertions.

Or one could combine these: one receives one's opponent as an unanalysable blob together with some set of guaranteed true assertions about it, supplied by the creator of that program and verified by the competition infrastructure. The idea is that skill at analysing someone's source code is secondary to the point of the exercise.

What verifiably true assertions would it be useful for a competitor to make about itself? It would be easy to write code of which it can be proved "I always cooperate", "I always defect", "I play Tit For Tat", or any of the other ordinary PD strategies. What verifiable assertions can a program make about the sort of opponent it will cooperate or defect with? "I will cooperate with anyone who cooperates with me" would not be an admissible assertion (by Rice's theorem). Nor would "I will cooperate with anyone who verifiably asserts that they cooperate with me". But "I will cooperate with anyone who verifiably asserts that they cooperate with anyone verifiably asserting this sentence" might be, if the circularity can be handled.

ETA: But "I will cooperate with anyone who verifiably asserts that they cooperate with anyone verifiably asserting a sentence logically equivalent to this one" won't work. So there would have to be a negotiation phase before the competition in which people publish the assertions they want to make about themselves, so that people can coordinate to agree on the exact formualtion of the mutually referential sentences they want to be seen to be true of them.