Imagine a middle-aged newcomer, known to have been callow in his youth, visiting the most popular bar in town. The bar patrons are friendly but there is a Resident Sage who is rather keen on absolute control over his adoring fans. Now if the newcomer is a weakling, the Sage would like to make a scene, ridicule him, and throw him out. Always good to create an example. But if the newcomer is a tough guy, then the Sage would like to bide his time before making a decisive attack. The problem is that the Sage does not know the newcomer’s type, only the probabilities of whether he is strong or weak. And the newcomer definitely prefers the option of being allowed a foot in the door to the prospect of a scene, irrespective of whether he is weak or strong.

However, there is some hope for the Sage. The story goes that tough guys like beer while the weaklings prefer dhoklas. So perhaps the Sage’s problem can be solved if he carefully watches the choice of evening fare sampled by the newcomer. The complication arises from the fact that the weakling would prefer to drink beer rather than eat dhoklas if by doing so he can avoid a confrontation.

This scenario, the basis of the celebrated ‘beer-quiche game’ (while quiche is a delicious French pastry crust with a gooey filling, in our context, it is better to think of the interaction as a beer-dhokla game) created by In-Koo Cho and David Kreps in 1987, serves as a useful analytical tool to analyse the ascension of Rahul Gandhi to the post of president of the Indian National Congress against the backdrop of the hard-fought election in Gujarat. Gandhi is the newcomer, while the Bharatiya Janata Party (BJP) government that has ruled uninterruptedly for 22 years in Gujarat is obviously the entrenched power centre.

Gandhi, we assume, knows his true type—weak or strong—with respect to the probability of winning the election in Gujarat, but all the BJP has to go by are his actions or ‘signals’. In particular, the decision to claim the presidency of the Congress in the midst of the campaign can be seen as one kind of signal, a bold move that partly stakes his future on the election result. The choice of not doing so at an earlier stage was the alternative signal that prevailed up to this point. In response, the BJP can either subject him to scorn—if it is reasonably sure that he is weak—or treat him with the measure of respect due to a serious opponent. The only oddity in the analogy of a bar is that Gujarat is a dry state!

Can our Resident Sage make out Gandhi’s type from his actions? Was he weak when delaying his presidency and strong now? To use terminology from game theory, is there a ‘separating equilibrium’ in which ‘actions reveal the man’, or a ‘pooling equilibrium’ where the weak type would feign strength by adopting the same action as the strong type?

There are two types of equilibria of the beer-dhokla game. In case there is a high initial probability of Gandhi being weak (as was true three months ago when straw polls predicted abysmal results for the Congress and when Gandhi’s stock was running low from a string of electoral reverses starting with the 2014 general election), game theoretic analysis yields a separating equilibrium in which the BJP would be easily able to ascertain Gandhi’s true type. This is because even if a weak Gandhi pretends to be strong by adopting a bold posture, thereby attempting to generate a pooling equilibrium, given the odds that he is most likely a weak type, it would make sense for the BJP to subject him to ridicule. Thus it is futile for a weak Gandhi to send a strong signal. Similarly a strong Gandhi would not want to adopt a meek posture. In other words, the hesitation of Gandhi to step up to the Congress presidency in the early stage of his campaign could be regarded as an accurate reflection of his weakness.

But now with a much higher a priori probability that the Congress is going to put in an improved showing (as reflected in the much better poll forecasts of the last two weeks), does the ascension indicate that Gandhi is indeed strong? Will we continue to see a separating equilibrium that allows us to understand the true type of a player from his actions?

Not really, for when the initial odds are loaded in favour of a strong Gandhi, a weak Gandhi, by mimicking the actions natural to the strong type, would be able to succeed in making the BJP give him the respect of a ‘worthy opponent’. This is because even though the BJP knows that it is possible the strong signal is being sent by an entrant who is, in fact, weak, it cannot take the risk of entering into a confrontation as the a priori possibility of Gandhi being strong is too high. Thus we will see a pooling equilibrium in which both types would choose beer.

In sum, when the entrant is likely to be weak, his weakness will stand exposed. On the other hand, when the entrant is likely to be strong, his strength may be hard to demonstrate. This implies that while we could discern that Gandhi was on a weak wicket a few months ago due to his reluctance to take on the mantle of the Congress presidency, at present, regardless of his bold assumption of party leadership, we cannot be sure if he is actually strong or merely faking it.

The game theoretic analysis highlights an important truth: With less than two years to go for the general election, and a reasonable chance of an improved outcome in what should be the BJP’s most secure fortress, in a fight that pits Gandhi directly against Narendra Modi, the ascension to presidency was not a choice to be made. It was now or never.

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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