The exit of the Telugu Desam Party (TDP) from the National Democratic Alliance (NDA) has placed the spotlight on the inner dynamics of the NDA. The hard choices before each ally of the NDA can be modelled by the game of “chicken".

Think of the much reprised “chickie run" from the Hollywood classic Rebel Without A Cause. Jim (memorably played by James Dean) and Buzz are two leaders of high school gangs who dare each other to drive a car full tilt toward a cliff. The person who stops or exits the car first is chicken, and loses. If neither stops, both experience a terrible car crash. If both swerve, there is a status quo.

The game of chicken is a collective action problem where the total surplus of a collective is maximized when a few members—the “chickens"—yield, while others remain unbending, and win. The winners enjoy the benefits generated by the chickens without incurring the costs. If all members play tough, then a very unpleasant outcome for everyone results— all members end up falling over the cliff.

In the story of the chickie run, the aggressive player wins. But there is another version of the chicken story, referred to as “snowdrift", where the player that is able to remain passive for the longest amount of time emerges victorious. In this story, a car gets stuck in a snowdrift. The driver and the fellow passenger both want the snowdrift to be removed. But each wants the other to do the work while they themselves remain in the comfort of the car. If both shovel, each will survive but both will have put in unnecessary labour. If neither shovels, both will freeze to death.

The game between the constituents of the United Progressive Alliance (UPA), including the Congress, exhibits the features of a chickie run while that between the members of the NDA, excluding the Bharatiya Janata Party (BJP), is like snowdrift.

In the UPA, several constituents, both current and potential, are claiming their right to lead the coalition. The Trinamool Congress has trotted out a set of eligibility criteria for the leader of the opposition which sounds suspiciously like Mamata Banerjee’s resume. The Congress has declared it is the only party which can bring together the different groups within the country in amicable fashion. Thus, all contenders are going toe to toe, hoping the other will back down. In the absence of an agreement, each party runs the risk of total irrelevance.

In the NDA, on the other hand, it is clear that the continued power of the BJP will rapidly erode the power of its allies. In fact, the BJP has been accused of actively triggering such possibilities by playing one regional party against another. Hence, the cumulative welfare of the allies of the BJP will be maximized if a few allies leave, while the others stay on in a weakened NDA, which still has a decent shot at coming to power in 2019.

Who will leave and risk being left out in the cold, and who will stay to taste the sweet fruits of power?

Both the chickie run and the snowdrift are identical from a mathematical point of view. But, practically speaking, they require different behaviours from the players. A player who is able to exhibit increasingly audacious activity, like Mamata Banerjee, is likely to triumph in the chickie run, while the player capable of remaining stubbornly inert, while continually issuing statements that provoke others to leave, like Shiv Sena chief Uddhav Thakeray, will win in snowdrift. Both capabilities are unlikely to be found in the same player.

In the chickie run of the UPA, there are as many equilibria in pure strategies as the number of claimants to the crown. In each equilibrium, one of the claimants stays adamant while others back down. In the snowdrift game of the NDA, there are hundreds of equilibria. In each equilibrium, a certain set of the allies who constitute the coalition leaves, weakening the overall structure enough for the remaining allies to be secure, but without jeopardizing the chances of the coalition as a whole. For example, the Rashtriya Lok Samta Party in Bihar, and the Kerala Congress (Nationalist) could leave, while the others stay on with a chastened BJP.

The problem of indeterminacy due to multiple equilibria in the games of chicken and snowdrift is often resolved through a process of brinkmanship, wherein each entity refuses to back down, increasing the risk of mutual disaster with every passing moment, till finally, someone is forced to buckle.

In such situations, game theory also advocates the use of a probabilistic strategy, i.e. tossing a coin or spinning a roulette wheel to decide one’s course of action. The higher the number of claimants in the UPA game, the lower the probability with which one should aim to remain adamant. On the other hand, the higher the number of combinations whose exit could suffice to weaken the NDA sufficiently, the higher the optimal probability of choosing to stay for each BJP ally. Of course, some allies like the Janata Dal (United) have no freedom of action due to their past choices. Irrespective of whether the NDA wins or loses, their future is likely to be bleak.

In the chickie run of the movie, Jim exits his car at the last minute and loses, but by now it is too late and Buzz, the winner, fails to stop his car from going over the cliff. As the endgame of the 2019 election approaches, the constituents of the UPA as well as the allies of the BJP would do well to remember the sad end of Buzz. There is no time to lose.

Rohit Prasad is a professor at MDI, Gurgaon, and author of Blood Red River. Game Sutra is a fortnightly column based on game theory.

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