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Fairness & reason in the ultimate game

Fairness & reason in the ultimate game

Derived from Nowak et al Science 289 1773-1775 (2000)

The 'ultimate game' is the substance of a thought experiment on which a wide range of negotiating theories are founded. Two agents meet without prior knowledge of each other. There is a prize - access to a water hole, use of a diamond field - which one can divide up and offer to the other. If the offer is not accepted, then neither get anything - a war breaks out, whatever meets the reader's fancy.

The rational approach is for the offer to be minimal, insofar as the receiver gets that or nothing. In fact, human players almost invariably pursue fairness, dividing the asset into even pieces. People will typically see this game as identical with the 'cake' game - where on gets to cut and the other to choose on or the other of two slices - where the observer typical choice, and also the rational choice, is to cut the cake exactly in half.

This disjunction between what rational beings ought to do and what humans actually do is of concern. There are two possible theories, both evoking empathy, but one involving information sharing and the other not. The theory that does not evoke shared information might be called 'well **** you, then'; which is to say that when the offer is too small to be attractive, and when the pique felt at denial is sufficient, then retaliation is tempting, and the proposer is denied his or her cake out of - well - spite. We have evolved to sense social needs and to avoid conflict (for what else is the emotion of embarrassment?) This insight helps us to avoid the irrational traps of rationality.

The other theory is concerned with, in effect, reputation. Indeed, it may eventually allow us to put a value on reputation (on brand, on intangibles.) In the mean time, the researchers have built a model which allows a degree of quantification to be brought to bear. A parameter sets an aspiration level, below which the "**** you" behaviour comes into play. A range of strategies (combinations of behaviours by the two players) are automated, and successful games are allowed to play themselves out in the computer, passing their 'genes' on to their progeny.

Where information on the other player is not accessible - or where there is no information about the 'going rate' - then initially mixed-strategy populations tend to collapse into one particular dominant strategy, such as fairmindedness, the "**** you" model or into one-sided subservience. Additionally, where information is shared about the partners, one set of dynamics come into play. Where information on the 'going rate' is known, then another dominate.

Where information is available, however, then more complex outcomes emerge. No one strategy dominates and the populations show 'ecologies' or societies of strategies that interact over time. For example, the costly act of rejecting a low offer establishes a reputation of one who seeks fairness, and proposers are then driven to increase their offer. This has a statistical affect on the population as a whole, and this behaviour propagates. However, there will also be defectors and free riders who feed off this tide of altruism.

In a model (and perhaps, less in reality) these results point to regularities, which emerge after 100,000 generations of simulated testing and breeding of traits. As the fraction of the population which is informed about the level of an accepted offer rises from zero to around twenty percent, the level of initial offer rises from the very small to the fair division of the spoils. In human terms, ignorant peasants get cheated by itinerant merchants, whilst urbane citizens employ market information to get a fair deal. As this equation maps fairly directly onto a range of economic parameters concerned with economic efficiency, and as the information content is specified, this seems to create the grounds for valuing both information and reputation. There are, of course, other tools (as with those employed in Bayesian risk management and option planning) which put explicit values on information. It would be interesting to see if these all gave the same answer.

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