This questions is on the subject of evolutionary game theory.

Imagine an infinite population of players that pair up randomly and play matches against each other. A match consists of N rounds. Each round the stage game is pictured below.

The payoff to a player for a match is the sum of their payoffs over the n rounds of that match. (dont worry aboutdiscounting)

These are our strategies:

C - play c in every round

D - play d in every round

T - play c in the first round then in all subsequent rounds play whatever partner played the round before.

1. Construct a payoff matrix for a match, this should be a 3x3 matrix
2. depending on N, can we eliminate any strictly or weakly dominated strategies?

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