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Saturday, 24 August 2013

94. The Ultimatum Game and the Economics of Fair Play



The real-life experience with the Traveller's Dilemma (TD) game I discussed in Part 93 results in two conclusions:

1. The most ‘efficient’ game for the two players to play, that would give the maximum total payoff, is that each chooses 100, giving a payoff (100, 100); i.e. 200. This goes against the grain of classical economics, which was based on the ‘libertarian presumption’ that if individuals are left to their own selfish devices, the economy would run efficiently.

2. People do not always tend to play the Nash-equilibrium strategy, which in the TD game will give a payoff (2, 2). This violates the assumption of classical economy that people take rational decisions.

Thus people do not always make selfish rational choices. The ultimatum game (UG) illustrates this point further.


Imagine Mr. A and Mr. B, not known to each other, and in separate rooms, unable to communicate with each other. Somebody plays the ultimatum game with them: He offers $100, which must be shared between them according to certain strict rules. The rules are known to both Mr. A and Mr. B. One of them, chosen at random, has to decide how the money is to be divided and makes this offer to the other person. If the other person accepts the offer, the deal is closed. If he rejects the offer, none of them gets anything. What amount will be offered by the person who has been chosen at random to make the offer?

Our first response may be: 50%. But is this what really happens in practice? Suppose Mr. A has been chosen to make the offer to Mr. B. He may very well think that even if he offers 40%, Mr. B is going to accept it, because $40 is much better than getting nothing at all. But then why not offer just $30? How about $20, 10, … , or even $1? Will Mr. B accept $1 dollar, which is, after all, better than getting nothing at all, even though Mr. A walks away with $99?


Experimentally, it is found that two-thirds of the offers are between 40 and 50% (Sigmund, Fehr and Nowak 2002). Only 4% people offer less than 20% money; offering such a small share is considered risky because the offer may get rejected.  More than 50% of all responders reject offers that are less than 20%. But the question is: Why should anyone reject an offer as ‘too small’? Obviously, factors such as sense of fair play and/or sense of outrage are at play.

The economics of fair play


Analyses based on Darwinian evolution demonstrate that fairness evolves if the proposer has some information about what deals the responder has accepted in the past (Nowak, Page and Sigmund 2000). Thus, evolution of a sense of fair play, like the evolution of cooperation (Maynard Smith and Price 1973), is linked to reputation. The opposite is also true. If an individual has the reputation of being content with low offers, he is more likely to be offered small shares. [Reminds me of something I learnt early in life: Often you have to train the people around you about how they should behave with you.]

Theoretical classical economics modelled a human being as Homo economicus: a rational and purely selfish individual. Studies on the UG and its variants reveal, however, that humans actually are a cross between H. economicus and H. emoticus. Emotions like generosity, revengefulness, altruism can override purely logical and selfish pursuits sometimes. How did this trait evolve in the Darwinian sense? There must have been some evolutionary advantage in this for such genes to survive and propagate.


Yes indeed. Unfair play arouses acts of moral indignation and revenge, which can be costly to the social group or the species. Fair play and altruism may not appear to be of immediate benefit to the individual, but can have long-term benefits to the group or the species. Over several generations, those genotypes can evolve for which the phenotype is such that, in pairwise encounters, a purely self-centred strategy is not adopted; instead, due account is taken of the other player’s conduct. A player is not interested only in his own payoff, but compares it with that of the other player, and demands fair play.

Such departures from the classical game-theoretic predictions of the UG have been rationalized in various ways. The chief among them is the premise that the strict rules prescribed by the UG are far too removed from what actually happens when real people deal with one another. For example, haggling is not permitted in the UG, whereas it must have been a common theme in the social life of our ancestors. Therefore, real players are likely to forget or ignore that the UG is a one-off game (the deal is either on or off), with no bargains or second chances.

Another factor to consider is the existence of rather strongly knit groups within a species. Such groups provide a sense of belonging, as also the assurance of protection against enemies or rival groups. Naturally, it makes sense not to outcompete or injure other members of one's own group to such an extent that successful contests with other groups are jeopardized. But while this line of reasoning does explain why proposers offer large sums, it cannot explain why low offers are rejected by responders.

Another approach softens the strict condition of the UG that there is complete secrecy, and that a contestant has no access to information about the other contestant (cf. Sigmund, Fehr and Nowak 2002). The fact is that our social evolution has been such that we expect that others will notice our actions and decisions. For example, suppose a player is known to become angry and reject a low offer, others are likely to make him high offers. Therefore, emotional responses to low offers must have been favoured by evolution. In due course, self-esteem entered the picture, making it necessary for a player to reject a low offer ‘as a matter of principle,’ making it a matter of dignity.

Other factors which influence the outcome of the UG, and of some of the ‘Public Goods’ games which include a punishment rule, are emotions like a sense of revenge, and satisfaction of punishing selfish action (Sigmund, Fehr and Nowak 2002). Such responses have evolutionary underpinnings which ensure fitness advantage for the social group. In times of war, pestilence, or famine, an above-average proportion of punishers helps the group to survive as a whole. Moral guidelines are an offshoot of such tendencies, and they apply to the economic affairs of the community as well.