Tit-for-tat no more: new insights into the origin and evolution of cooperation

The Prisoner’s Dilemma (PD) is the paradigmatic scientific model to understand human cooperation. You would think that after several decennia of analyzing this deceivingly simple game, nothing new can be learned. Not quite. This new paper discovers a whole new class of strategies that provide a unilateral advantage to the players using them in playing the repeated version of the game. In effect, using these strategies one can force the opponent to any score one desires. The familiar tit-for-tat strategy, which so far had been assumed to be the optimal way of playing the repeated game, appears to be just the tip of an iceberg of ‘zero determinant’ strategies which ‘enforce a linear relationship between the two players’ scores’.

This is huge and people have already started to discuss the implications. But what puzzles me is the following: The search for an optimal way to play the repeated PD has been going on at least since the 1980s. The best strategies have been sought analytically, and through simulation (see Robert Axelrod’s iterated PD tournaments). And yet nobody discovered or stumbled upon ‘zero determinant’ strategies for more than 30 years of dedicated research. So can we expect a rational but not omnipotent actor to use these strategies?

I think the formal answer needs to be ‘yes’ – a rational actor plays the game in the most advantageous way for his/her interests and if zero determinant strategies provide en edge, then he/she needs to (and is expected and predicted to) play these. The alternative would be to impose some limitations to the computational capacities of rational actors, but these would always be arbitrary. Where do we draw the line? Is tit-for-tat too complicated or not? At the same time, assuming that actors can always find the optimal strategy, while consistent with the fundamental assumptions of game theory, is unsatisfying for practical reasons. If it takes a generation of social scientists 30 years to discover an optimal strategy, how is a single actor supposed to know about it and use it in real-life situations?

This new class of strategies provides undoubtedly a normatively better way to play the game, but does it have any explanatory or predictive content?

An alternative route that can lead to actors using optimal strategies that are too complicated to be analytically discovered by rational but not omnipotent beings is evolution. Actors can experiment with all kinds of strategies, some will stumble upon the optimal one, and over time natural selection will favor these lucky ones, and by implication their ‘optimal’ strategies. The problem with this reasoning is that what is ‘optimal’ for individuals playing the game is not necessarily optimal for a group of individuals all playing the ‘optimal’ strategy. And if selection acts on groups in addition to individuals these ‘optimal’ strategies might not even survive. In any case, this new paper will certainly make people reconsider not only the origins and mechanisms of cooperation, but the utility and role of game theory in social-scientific explanation as such.

Game theory and real estate negotiations

Here is a puzzle: You meet a real estate agent for a property you are interested in. The house has an asking prize and you haven’t made any offers yet. The realtor mentions casually that she has just had an offer for the house which she has rejected. Would you ask what the offer was? Would the realtor tell you? Is it a fair question to ask? (obviously, the realtor is under no obligation to reveal the truth value of the rejected offer and there is no way for me to verify the answer).

Here is a formalized description of the problem: the Seller adn the Buyer can be each of two types – High or Low.  High Buyers and Sellers prefer High Deal to No Deal no Low Deal, and Low Buyers and Sellers prefer High Deal to Low Deal to No Deal. First, the Seller announces whether she has rejected a Very low or a Moderate offer. If a Moderate offer has been (announced as) rejected, the Buyer can make either a High offer (which all Sellers accept) or No offer which ends the game. If a Very low offer has been (announced as) rejected, the Buyer can make a Low offer, No offer or a High offer (the latter two end the game). If a Low offer has been made, the Seller can either Accept or Reject it. In the case of rejection the Buyer can make a High offer or No offer – both actions end the game. Here is the game tree.

Essentially, by making an announcement that she has rejected a Moderate offer the Seller credibly commits to reject any Low offers. Importantly, Buyers suffer a cost from a rejected offer (which is realistic given the costs of the compulsory technical surveys one has to do before an offer). There is no penalty for a late deal (no time discounting). The game is of two-sided incomplete information – neither the Buyers nor the Sellers know the type of the opponent. So the questions:

1) Should you ask what the rejected offer was?
2) Should the realtor (the Seller) tell you?
3) Would the answer (announcement) of the Seller be informative?
4) Does the Seller do better under this game or a game with no signal (announcement)?
5) Does the Buyer do better under this game or a game with no signal?
6) Is this game Pareto-improving under any circumstances?

My answers are after the fold.
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