  In repeated interactions between individuals, we do not expect that exactly
the same situation will occur from one time to another. Contrary to what is
common in models of repeated games in the literature, most real situations may
differ a lot and they are seldom completely symmetric. The purpose of this
paper is to discuss a simple model of cognitive processing in the context of a
repeated interaction with varying payoffs. The interaction between players is
modelled by a repeated game with random observable payoffs. Cooperation is not
simply associated with a certain action but needs to be understood as a
phenomenon of the behaviour in the repeated game. The players are thus faced
with a more complex situation, compared to the Prisoner's Dilemma that has been
widely used for investigating the conditions for cooperation in evolving
populations. Still, there are robust cooperating strategies that usually evolve
in a population of players. In the cooperative mode, these strategies select an
action that allows for maximizing the sum of the payoff of the two players in
each round, regardless of the own payoff. Two such players maximise the
expected total long-term payoff. If the opponent deviates from this scheme, the
strategy invokes a punishment action, which aims at lowering the opponent's
score for the rest of the (possibly infinitely) repeated game. The introduction
of mistakes to the game actually pushes evolution towards more cooperative
strategies even though the game becomes more difficult.
