Millennium Post

Decoding the convoluted

Moving forward with application of Game Theory to analyse public goods dilemma

I had discussed the Prisoner's Dilemma (PD), Chicken and Assurance Games and their application to public goods dilemmas in the domestic and international arenas in these columns in December, 2019. However, the games discussed were simple one-shot games, which were good for illustration but the real world is far more complex. In the real world, there are few one-shot games, where actors have a single interaction and never meet each other again. More often than not, one encounters situations of repeated interactions when considering public policy questions, particularly those involving public goods. People interact continuously within their community or the broader social networks. Also, people's interactions with the government are not 'one-shot' affairs. We, therefore, have to look beyond one-shot Prisoners' Dilemma or Assurance Games to describe the public goods issues more accurately. In other words, we need to look at repeated games, where players have to face each other again and again and there is a possibility of conditional cooperation or punishment.

Axelrod's Evolution of Cooperation

Robert Axelrod dealt with precisely such situations in his 1984 book 'Evolution of Cooperation'. Axelrod was grappling with the problem of sub-optimal outcomes that Prisoners' Dilemma situations give rise to. He investigated conditions under which cooperation can emerge and analysed these issues using game theory. His work involved the organisation of a tournament wherein he invited game theorists to propose a strategy in a Prisoners' Dilemma (PD) situation which would be best placed for cooperation to evolve. The winner was a simple strategy which was suggested by Mathematical Psychologist Anatol Rapoport. His strategy was simple Tit for Tat (TFT). In other words, the response to 'co-operate' was 'co-operate' and to 'defect' was 'defect'. It was found that TFT strategy (being nice) was the winner because it elicited cooperation and promoted collective and mutual interest over individual interest. It appears that Axelrod had found a solution to the intractable one-shot PD Game in which Nash equilibrium was a sub-optimal outcome where both the prisoners confessed to the police and served jail time. Interestingly the TFT strategy did not require the assumption of rational behaviour or even trust at the beginning of the game. The only necessary condition for cooperation to emerge was that the players should meet again and again in the future. Axelrod called this the discount factor which indicated the probability of meeting again. It was also referred to as "shadow of the future". Axelrod later developed these ideas further in a book titled the 'Complexity of Cooperation' published in 1997, wherein, he applied iterated Prisoners' Dilemma games to a variety of public policy situations and found that TFT strategy wherein reciprocal cooperation resulted was the most robust option.

Many Game Theorists have brushed aside Axelrod's work, stating that his finding that full cooperation can result in infinitely repeated PD Games was already known to them for about 25 years. Ken Binmore has pointed out that the folk theorem of game theory proved by several authors in 1950s had demonstrated precisely this fact, viz., that all outcomes of infinitely repeated games can be sustained as equilibrium. However, Axelrod did provide an interesting and simple way to understand the outcomes of repeated Prisoners' Dilemma Games and how they can be applied in various public policy situations.

Application to Public Policy and Public Goods Dilemmas

One of the most interesting applications of Game Theory to a public policy situation was the analysis of the Cuban Missile Crisis. It may be recalled that in October 1962 when the Soviet Union sent a warship to install nuclear missiles in Cuba, the US had two strategies: A naval blockade or an airstrike. The Soviets also had two strategies viz., withdrawal of missiles or maintain the missiles. If this was a game of chicken (where both players are in a headlong collision) a nuclear war would break out. However, we all know that the Soviets withdrew after the US blockade and this led to a compromise solution. In other words, what appears at first to be a game of chicken ended up in an outcome where both sides compromised. This was obviously an indication of the long term interaction in the future that the US and Soviets had in mind.

Coming back to the public goods dilemmas discussed in earlier articles in the domestic and international arena, it is easy to see that the players are in a situation where they will be interacting repeatedly in the future. Hence, countries will continue to interact at multi-lateral forums such as WTO, UNFCC and groupings like G2O to solve intractable problems such as world trade crisis, the climate change crisis and the financial crisis. Similarly, in public goods dilemma in the domestic arena such as air pollution, water pollution and deforestation, the players (the people and the Government at all levels) are also in a situation where there will be continued interaction in the future to look for possible solutions.

Even in infinitely repeated PD games, we have to be careful as the group size increases. It is obvious that with the rise in group size, the cost of supplying public goods also rises. Also in a large group the problems of supervision and monitoring are far greater. Hence, some amount of free-riding will creep in. While some isolated instances of free-riding can be tolerated, we have to be careful that free-riding does not become too large or else a sub-optimal outcome such as the one in a one-shot PD game will result. Avoiding large scale free riding can be ensured by crafting institutions which disincentivise this. More involvement of the community as already discussed in the earlier article would also lead to the rise of social capital, lesser defection and lesser free-riding, thereby resulting in an optimal outcome.


To conclude, we have introduced real-life situations into our game theory model to continue the analysis of public goods dilemmas. As we saw above, the outcomes in repeated games are very different from one-shot games. In repeated games, actors have to meet and confront each other again and again in the future which allows individual rationality to be in greater harmony with collective rationality. Repeated games also allow institutions to develop (for example leadership) and ensure that formation of a higher level of social capital is triggered.

Dr. Krishna Gupta is the Principal Resident Commissioner, Government of West Bengal. Views expressed are strictly personal

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