A fascinating piece on chess computers versus people by Gary Kasparov in The  New York Review of Books.  With the defeat of humans by compiuters – Kasparov claims that these days Grand Masters would be challenged by many $50 programs – chess is now a new game. Broader issues of strategy matter [...]]]>

A fascinating piece on chess computers versus people by Gary Kasparov in The  New York Review of Books.  With the defeat of humans by compiuters – Kasparov claims that these days Grand Masters would be challenged by many $50 programs – chess is now a new game. Broader issues of strategy matter more than tactics and there is the possibility of tandem people+machine competiting among themselves.  Chess as a game of full information is under attack from games with randomness where bluffing and psychology play a role – the current poker boom is an instance – but even here computers are making inroads.  Kasparov is a thoughtful, unaffected guy and positions himself well – as the first of the Grand Masters to lose to a computer – to understand the broader implications of this development.

So if A offers B [...]]]> The ultimatum game takes the following form: There is an opportunity for Mr A to share some money, say $100, with Mr B but there is a requirement that B accept the offer that only A can make regarding the division of the $100 – otherwise neither player gets anything.

So if A offers B $20 and B accepts then B gets $20 and A gets $80. If B rejects A’s offer then neither party gets anything. The game problem is to work out what A should offer B.
Reasoning backwards A should only offer B a small reward (say $1) and B should accept. Otherwise B gets nothing and is worse off. The paradox is that in experimental situations A generally offers B much more than a minimal amount and, if they don’t, B often rejects the offer even though they are then made worse-off.

This rejection by B seems inconsistent with optimising behaviour.

This game has important implications for situations where a deal is being done and where one party can make an ultimatum to another. So suppose I want to sell my bomb car to you for at least $5000 and I know that you will pay up to $6000 we should be able to do a deal and share $1000 worth of gains-from-trade. If I could put myself in a position where I could credibly make you a take-it-or-leave-it offer then optimising economic theory suggests I should demand $5999 for my car leaving you with gains of $1 and me with gains of $999. Moreover you should accept.

The ultimatum game paradox is that you might well reject this offer, even though it costs you $1, on the ‘fairness’ grounds that I am getting too big a share of the gains. The idea is that you might not be concerned with your payoff alone but with your payoff relative to mine. In short that you are concerned with your relative status after the exchange.

The Economist this week looks at the effects of a male’s testosterone endowment – a proxy for concern with his status and his aggression – on playing this game. The full article by Terence Burnham is here. The game is played experimentally with males and their propensity to make and accept low offers is related to a measure of their testosterone levels.

It turns out that high testosterone levels are associated with Mr B rejecting low offers although, even though there is a positive relationship, there are no statistically significant effect of testosterone on Mr A’s offer size.

Since testosterone modulates behaviour across many species, and in settings that may be construed to be similar to the ultimatum game, it allows an interesting test of this explanation. If ultimatum game rejections result from the inappropriate activation of reputation-management machinery, then a body of research suggests that rejections will be more probable among high-testosterone men.

High-testosterone animals are more likely to respond aggressively to a challenge, and low offers may be viewed as challenges. Across multiple species, including humans, high testosterone levels are correlated with dominance-seeking behaviour and dominants are less likely to back down from challenges.

The more aggressive one is the less likely you are to take being slighted in a game where some degree of reciprocal altruism might be involved. In settings where people might interact repeatedly punishment may enhance the reputation of the punisher B and alter the behaviour of the punished A. Both routes may produce benefits to the punisher that exceed the cost of punishment. It is likely too that high testosterone would have relatively stronger emotional responses to low offers.

Ultimatum game rejections have become important because mainstream economic theory fails to predict them. This failure has played a role in the rise of behavioural economics. Economics might be improved by an understanding of hormones as well as neurological activity.