Lately I came across the SERS theory, which claims that cooperating in a single PD game may increase the profit expectancy in the game, depending on the perceived similarity of the individual to his opponent.

According to SERS, assuming Ps is the subjective perceived similarity between players, then the expected payoff of cooperation is: R × ps + S × (1-ps) and the expected payoff of defection is: P x ps + T x (1 - ps).

This means that under some conditions, the expected payoff of cooperation is larger than the expected payoff of defection, and a rational player should prefer to cooperate and avoid defection, which is the dominant strategy in the game.

Does reducing a single PD game to a decision making process under uncertainty is valid mathematically? My feeling (and I don't have a strong mathematical background) is that it's not, and I would love to hear your insights.

Best regards


Two points. First, It's not a question of what is valid mathematically. There are different ways to model behavior, and that is not a math question. The game theory/decision theory question is an old one. Second, what the discussion glosses over is that for some values, cooperate is the best strategy for either player, so it is a non-cooperative equilibrium. And finally, mixed strategies or uncertainty about other players has a long history in game theory, so using decision making under uncertainty is certainly valid--in fact, vonNeuman and Morgenstern were among the first to justify expected utility explicitly to use in game theory.


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