Inequality and Game Theory

A spirit level

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The link between income inequality and negative health and social outcomes is supported by a large and growing body of research. More economically stratified countries have higher infant mortality rates, levels of mental illness, obesity, lower levels of social mobility and trust, and numerous other worse outcomes. The evidence is reviewed in a recent book called The Spirit Level, and summarised by the authors on The Equality Trust website. A key part of their explanation of the evidence is the idea that people can behave either cooperatively or competitively towards each other, and do so in varying ratios depending on the level of inequality.

The concept of the selfish gene meaning that individuals will always behave selfishly is a fallacy that has long been debunked. Cooperation between members of a species is known as reciprocal altruism, which used to be held up as evidence for group selection: individuals doing things for the good of the species. But this model is susceptible to freeloaders, who benefit at the expense of the other group members; a model was needed that allowed for cooperation as well as punishment of selfish individuals.

In 1984, Robert Axelrod held a computer-simulated tournament to find the most successful strategy in a population of individuals who could cooperate with each other, or defect. It was based on repeated rounds of the prisoner’s dilemma, a problem from game theory. In each round, points were allocated to each player dependent on their actions (see payoff matrix). The winner was a program called Tit-for-Tat, which cooperated with its opponent on the first go, and copied its opponent’s previous move thereafter. This allowed for mutually beneficial cooperation cycles to occur, but if its opponent defected continually, Tit-for-Tat prevented exploitation by defecting too.

  Player 2
Cooperate Defect
Player 1 Cooperate Both: 3 Player 1: 0Player 2: 5
Defect Player 1: 5Player 2: 0 Both: 1

 

What the tournament showed theoretically was that reciprocal altruism evolves when it benefits individuals (any group benefit is a consequence). Being vigilant to selfish individuals is essential though, to prevent being taken advantage of. In modern societies, everyday life is full of chances to cooperate or compete with others. The ratio of cooperation to competition within a society is reflected in its emphasis on collectivism or individualism. Decisions don’t take the exact form of the prisoner’s dilemma, but it provides a useful way of thinking about behavioural differences. However, it only predicts how a given individual will behave in a given population, not how different populations will vary from each other.

So how can game theory be applied to the differences between societies identified in The Spirit Level? Trust would seem to be a critical factor in people’s choices in the prisoner’s dilemma, and trust is in shorter supply in more unequal countries. This may be a rational response to the effect inequality has on the relative payoffs of cooperation and competition. When the rungs of the social ladder are further apart, there is more to be gained or lost in competition with others. In the prisoner’s dilemma, the points can be considered to represent gains or losses to be made, relative to others, in the hierarchy of social status. Inequality increases the viability of selfishness firstly because there is more to be gained by acting selfishly when the other cooperates, and secondly there is more to be lost by cooperating when the other acts selfishly (see new payoff matrix).

  Player 2
Cooperate Defect
Player 1 Cooperate Both: 3 Player 1: -5Player 2: 10
Defect Player 1: 10Player 2: -5 Both: 1

 

The theory is testable, and predicts that people in more unequal countries are more likely to defect in the prisoner’s dilemma than people in less unequal countries. Cross-cultural studies have mostly compared individualistic and collectivist cultures, and attribute the higher level of cooperative behaviour in collectivist cultures to differing social norms. But this explanation doesn’t explain what causes the differing social norms. Differing levels of inequality could predict levels of collectivism, social norms and levels of cooperation.

The prisoner’s dilemma is just one of many games based on a trade-off between individual gain and the common good. The uplifting message from both the game theory tournament and the research behind The Spirit Level is that the two are not mutually exclusive.

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