Housefull Economics

The Game Theory of Retribution

Our weekly explainer on economics using lessons from popular culture. In Installment 12, Ram Gopal Varma explains why some regimes are more violent than others.

Director Ram Gopal Varma released his movie Company in 2002. The second part of his gangster trilogy, it explored the innards of the Mumbai underworld. It chronicled the story of an ambitious and shrewd criminal usurping a criminal empire and moulding it in the shape of a commercial enterprise (hence the name). The movie begins with the story of a certain Aslam Bhai (Madan Joshi). Once upon a time a ferocious Don, Aslam Bhai is old, infirm and ailing. His two henchmen, Saeed (Rajendra Sethi) and Malik (Ajay Devgan), are jostling for power as his grip loosens. Faced with their rift, he tries to broker a peace between them and ostensibly manages to convince both to stay united. The truce is short-lived, however.

As Saeed, along with his brother, walks out of the meeting, settling himself in the front seat of his car, he plots his future strategy. His brother asks, “Now what?” He replies, “What else. Either Malik (will survive), or we will.” Almost immediately, there is a relaxed voice from the rear seat: Maine bhi yehi socha hai. Phark sirf itna hai ki tumse pehle socha. (“I also had the same thought. The difference is, I had it before you.“) Unknown to them, Malik had sneaked in the rear seat and ambushed them. A couple of minutes later, both Saeed and his brother were shot dead. A night of long knives follows. By a deft combination of carrots and sticks, Saeed’s associates are either made to switch their loyalty or neutralized. By the next morning, Malik has consolidated his power.

I was reminded of this movie sequence while reading a brilliant paper by the game theorists Georgy Egorov and Konstantin Sonin: “The killing game: A theory of non-democratic succession”. Their paper studies the emergence of retributive norms in non-democratic regimes, particularly during succession battles. In non-democratic regimes, succession is rarely peaceful. Quite often, it is a brutal saga of imprisonment, torture and murder.

Egorov and Sonin document a partial list of countries that have witnessed at least two killings of the fallen leaders during the last 50 years. These include Afghanistan (Mohammad Daoud, Mohammad Taraki, Hafizullah Amino), Bangladesh (Mujibur Rahman, Khalid Musharaf, Ziaur Rahman), Iraq (Faisal II, Nuri as-Said, Abdul Karim Kassem), Nigeria (Abubakar Tafwa Balewa, Johnson Aguiyi-Ironsi, Murtala Ramat Muhammad), Comoros (Ali Soilih, Ahmed Abdallah Abderemane), and Liberia (William Tolbert, Samuel Doe). Other rulers killed during this period include Melchior Ndadaye in Burundi, Carlos Castillo Armas in Guatemala, Thomas Sankara in Burkina Faso, Long Boreth in Cambodia, Sylvanus Olimpio in Togo, Fran�ois Tombalbaye in Chad, and Nicolae Ceausescu in Romania. This list is obviously truncated as in many cases political murders remain a mystery and investigations remain incomplete for obvious reasons.

Even so, not all non-democratic countries develop these norms; some countries do develop strong norms against political vendetta. In such countries, losing politicians not only survive but even manage to stage comebacks and resurrect their political careers, quite repeatedly. Mexican General de Santa Anna is one such example. He lost power at least five times, and managed successful comebacks each time.

What explains these differences? Why do some countries establish a ‘spare-your-opponent’ norm and others ‘kill-your-opponent’ norm? Is it possible for a country to change those norms? Are democracies fundamentally different from non-democracies in this respect? Specifically, is it possible for a democracy to lapse into a more violent equilibrium?

The paper answers some of these questions directly and gives a framework for thinking about others. Unsurprisingly, answers depend on the cost and benefit of respective choices. Imagine a dictator mulling over the decision to execute his opponent. There are two types of costs and benefits involved: immediate and reputational. Immediate benefit and cost include the prospect of enjoying power for a single period and the moral cost of assassinating an opponent. Besides these immediate benefits and costs, he should also factor in reputational benefit and cost of carrying out the execution.

When a winning politician decides to execute his opponent, he establishes a reputation for ruthlessness. The benefit of a ‘tough-guy’ image is that it deters other competitors. However, what goes around comes around. Rulers know that their rule is not eternal, and someday they may be vanquished by challengers. And then reputation for ruthlessness becomes an albatross. Once a dictator is generally perceived as ‘tough’, chances are high that he won’t be spared in the scenario when he ends up losing his throne. The decision to execute thus depends on trading off these costs and benefits.

The interesting thing about Egorov’s paper is that reputational costs and benefits are not merely assumed but explained. They depend on a number of ‘deep determinants’ which include frequency of rebellion, incumbency advantage, harshness of punishment and degree of impatience. Together with the immediate benefit and cost of executing opponent, these four factors determine what kind of norm emerges. The main insights of their paper are as follows:

The ‘Spare-your-opponent’ norm is both valuable and fragile

Killing your enemy is like riding a tiger. In the long run, it makes both the winner and loser worse off. In the terminology of economics, more benign norms pareto-dominate stronger ones. Unfortunately, benign norms are also the most fragile ones; they can easily be destroyed.

Think of a criminal who has committed ten murders. Since ten murders are enough to send him to gallows anyway, the additional cost of an eleventh murder is essentially zero. Similar reasoning applies here. As dictators execute more opponents, the cost of additional execution keeps falling. This peculiar dynamics implies that countries have a sort of slippery slope. Unless contained by other factors, they have an inherent tendency to gravitate towards violent polity.

Founders tend to have huge influence on norm-selection

Much of the contrasting political dynamics in India and Pakistan is explained by the difference in founding fathers. This insight is vindicated by the paper. Erogov and Sorin’s model has a strong Founder Effect. Essentially, the strategy adopted by the first player gets replicated indefinitely. Of course, the real world is more complex than that. Even Pakistan seems to have made a transition to a ‘spare-and-exile-your-opponent’ norm in recent years. But the huge impact of founders is undeniable, and comes out quite naturally.

The bigger the prize, the more vicious the competition

The size of the pie matters a lot. The bigger is the prize associated with winning the lottery, the more people would be willing to pay for it. Most violent equilibria often have a ‘winner-takes-all’ character. In such competitions there are no silver medals; you either win all the power or resources, or get killed with your friends and family. These games have a natural first-mover advantage. The person who thinks first, leaps for the gun and fires the first bullet often emerges as the winner. (Remember what Malik said: tumse pehle socha).

Vibrant opposition reduces the likelihood of ‘kill-your-opponent’ norm

The frequency with which a politician meets his challenger determines his ruthlessness. If, due to custom and indoctrination, the frequency of rebellion has been reduced, then the optimal strategy is to treat sporadic insurrection as ruthlessly as possible. By contrast, where the regime expects frequent challengers, then the most profitable strategy is to adopt a moderate stance.

Insecure regimes are more vindictive

Incumbents are said to have an advantage if they’re able to defeat challengers with high probability. The insecurity of a regime is captured by the absence of the incumbency advantage. As and when this advantage gets eroded, the tolerance threshold of dictators goes down. It explains why dictatorial regimes adopt cruel tactics when they have imperfect control over the levers of power, or when they are dealing with multiple challenges simultaneously.

Retributive norms in a democratic polity

Egorov and Sonin do not consider democratic regimes in their paper explicitly. They just assume that democratic regimes are able to manage orderly and peaceful succession. But their framework allows us to ask what features of a democracy make it amenable to peaceful transition of power.

A democratic setup is not a ‘winner-takes-all’ contest in the following sense. Power is decentralized and distributed. There are checks and balances. The rule of law prevails, making victimization of opposition tough if not impossible. The tenure of the government is limited; they have to seek reelection. Furthermore, the federal system means that the opposition is ruling in some province, and thus is the part of ruling elite. Everyone gets a second and third chance. Finally, there is spirit of political equality, which make challenges more frequent and forces the ruler to adopt a more reconciliatory attitude.

All of these features make the ‘prize’ of winning smaller, and soften the competition, relatively speaking. Rather than mutual hostility between opposing leaders, one may even see mutual admiration. Historian Ramchandra Guha has documented a poignant speech made in parliament by Atal Bihari Vajpayee after the death of Jawaharlal Nehru:

The leader has gone, but the followers remain. The sun has set, yet by the shadow of stars we must find our way. These are testing times, but we must dedicate ourselves to his great aim, so that India can become strong, capable and prosperous.

This is an extraordinary tribute. But more than to a person, it is a tribute to the constitutional democracy. In a democratic set up, rather than purges and assassinations, transitions become a moment to ‘answer old questions anew.’

Sometimes the best way of understanding the importance of something is to imagine a counterfactual. What kind of political contest would prevail if the norms of political immunity and civility ever break down?

General Gelu Voican Voiculescu, who presided over the execution of the Romanian dictator Nicolae Ceauşescus and his wife, gave an answer: “The decision to try the couple was dictated by desire to survive – either them, or us.” Far from the genial rivalry of a parliamentary democracy, it does look like the dark and grim battle for survival that Ram Gopal Varma depicted in his movie.

About the author

Avinash M Tripathi

Avinash M. Tripathi is an Associate Research Fellow (Economics) at the Takshashila Institution. His research interests include competition policy and financial risk management. He prefers a profound answer to a silly question rather than the other way around.