Traffic and Game Theory

Driving on a road can be thought of as a game

Saurabh Roy | October 6, 2016


#Traffic   #Game Theory  

Traffic conditions in Indian cities are among the worst in the world. I thought it was a case of a developing country – till I found that India is very peculiar in this regard. Traffic is as bad if not worse in Yangon, Lima, Kampala and Nairobi. But Delhi and Mumbai face an issue which none of these cities has, that of drivers not following lane rules. I argue that the problem we face is the case of a bad ‘Nash Equilibrium’.

Nash Equilibrium is a stable state of a system involving the interaction of different participants, in which no participant can gain by a unilateral change of strategy if the strategies of the others remain unchanged. I argue that this is essentially a failure to solve a repeated ‘Prisoner’s Dilemma’ game. Prisoner’s Dilemma, a well-known theme in maths and logic, is the difficulty of achieving the best outcome when there are obstacles to cooperation.

Driving on a road can be thought of as a game. I can choose to follow lane rules (“cooperate”) and stay behind the car in front of me, or I can choose to “not cooperate” and overtake the car, going into the wrong lane. Now, let us break this down.

Round 1: If I am driving for the first time and see that I am stuck behind a car when the opposite lane is completely empty (the usual situation during peak traffic hours), I have an incentive to “not cooperate” and switch to the opposite lane. Thus I save time and “win”.

Round 2: Other people see this and realise that it is in their interest to not follow lane rules and decide to “not cooperate”. This brings us to
a situation where everyone decides that they too should not follow lane rules and go into the wrong lane. In this scenario, the person who follows lane rules loses out and no one “cooperates”.

Now things get interesting. The way to solve a repeated prisoner’s dilemma is to repeat the action of the opposing player, that is, if he cooperates, you cooperate in the next round; and if he does not cooperate, you punish him by not cooperating in the next round. This is helpful if there is some amount of randomness in the choice that the opposing player makes and if he learns from his mistakes (or my punishment). If on the other hand, everyone is logical (as economists are wont to argue) one bad move or initial condition, and the system gets stuck in a sub-optimal equilibrium. Hence, it can be argued that the chaos that is driving in India is essentially a sub-optimal Nash equilibrium.

The solution to this problem is “altruism”, that is, you need to forgive the other player after a certain number of moves. If everyone is logical then at some point, an optimal equilibrium will be achieved. In 70 years, Indian drivers have failed to solve this basic problem hence my argument that the sub-optimal driving conditions result from either a low IQ or a lack of ‘social capital’.

Social capital is defined as “the social networks and the norms of trustworthiness and reciprocity that arise from them”. At the core of social capital is trust. Trust here means trustworthiness and not gullibility. Trust is one of the key ingredients that make a country work. How can we drive, eat or even buy and sell unless we trust other people? Trust is of course supplemented with regulation but an economy usually works better with trust than without. Trust is a solution to the prisoner’s dilemma. It is not clear how countries can build trust and social capital but what is clear is that it is one of the major determinants of development. In the 19th century, in his seminal work, “Democracy in America”, Alexis de Tocqueville observed how Americans were prone to meet and discuss all possible issues of the state and how such a high level of interaction and transparency encouraged participation from people and allowed democracy to flourish.

Social capital reduces problems of collective trust but does not solve it completely. Governments exist exactly for this reason – to solve collective action problems. Therefore, we need a strong collective effort to preserve the reputation of specific institutions. A strong regulation is a commitment that breaking certain rules will not be tolerated.

The discussion on traffic though can be rendered moot within a decade with the advent of self-driving cars and artificial intelligence-driven cars which would automatically achieve an optimal equilibrium. Therefore, it may make even more sense for the government to look into regulations for self-driving cars and mandating their use in future smart cities. The precedent for these has already been set in Helsinki, Pittsburgh and Singapore and we should not hesitate to join the ranks considering the problems we face in our best cities.

Roy is a fellow at Pahle India Foundation.

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