Mumbai: The extended acrimony in Maharashtra’s political landscape may have been puzzling for most, but not for students of game theory, which analyses conflict and cooperation by rational individuals while making decisions.

After frustrating fortnight-long discussions with Shiv Sena, Bharatiya Janata Party (BJP) announced on Thursday that it was parting ways with its partner of 25 years, with just two days left to file nominations for the 15 October assembly election.

Game theorists call such negotiations non-cooperative games. In Rebel Without A Cause, a 1955 Hollywood classic starring James Dean, two characters try to settle a dispute in a game. Both will race cars to the edge of cliff and whoever jumps out first “chickens out" and admits defeat.

In the movie, Dean’s character chickens out and jumps out, while his rival has a tragic end as his car goes over the cliff. In such a game, each player tries to anticipate the rival’s move before making his own.

What played out in Maharashtra, however, is an extension of the simple two-player game with multiple moves, in what is called a sequential game. Here, each player tries to make his move after anticipating not only his immediate rival’s move, but also a parallel game played by two other players.

Seen this way, each partner in the rival alliances tries to anticipate not only its partner’s move, but also the moves in the rival camp, before making its own move. This makes it all the more harder to reach an understanding.

In a hypothetical scenario, BJP settles for fewer seats, only to see the alliance between the Congress and the Nationalist Congress Party (NCP) breaking up. It would then feel foolish to have settled, since, if it had waited a little longer, it could have also broken the alliance and contested on all seats for a possibly better outcome. As it bargains hard for more seats while awaiting a possible breakup in the rival camp, stalemate ensues.

In the second scenario, BJP walks out of the alliance, only to find that Congress and NCP have managed to stick together, and that it is left with no partner. Unlike in the first scenario where it had better prospects, in the second, its chances are diminished. Again, talks are deadlocked as BJP awaits signals from the rival camp.

All through the fortnight-long negotiations, there have been conflicting signals about the fate of the alliances. Each party selectively leaked information to the media to make its threat sound credible and force the partner to concede.

In another illustration of game theory, the US effecively used the threat of taking out missile bases in Cuba to force Russia to remove them in the 1962 Cuban missile crisis. Intransigence on both sides would have led to mutually assured destruction.

Opinion polls say the BJP-Sena coalition would have won over 200 out of 288 seats if they contested as an alliance, and if they contested separately, the BJP may emerge as the largest party, but far below the halfway mark. The BJP is expected to win 100-110 if it goes solo. Similarly, Sena may win 70-80 seats if it contests alone. So, it was in the best interest of both parties to stay together.

With the deadline to file nominations staring it in the face, the BJP finally decided to break the alliance and try its luck on its own, blaming Sena for being inflexible.

However, their prolonged reluctance to do so could be explained by Prisoner’s Dilemma in game theory, where otherwise rational individuals make irrational decisions.

The police, which has caught two criminals, do not have enough evidence to punish them for the principal offence; hence each one is separately offered the option to stay silent or betray the other to win a lesser punishment.

Under scenario one, both prisoners A and B betray each other and get two years’ imprisonment each. Under scenario two, A betrays B, while B remains silent; so A walks free while B gets three years’ imprisonment. (and vice versa). Under scenario three: both remain silent and get one year imprisonment each.

Scenario one is also known as Nash Equilibrium, named after mathematician John Nash who was awarded the Nobel Prize in 2004 for contribution to economics through the game theory.

It seems Maharashtra’s political players, in hope of scenario two playing out in their favour, were betraying their respective partners.

With inputs from Niranjan Rajadhyaksha and Pramit Bhattacharya in Mumbai and Siddharth Singh in Delhi.

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