Game theory as a field of study gained prominence after the publication of the seminal book Theory of Games and Economic Behaviour by Von Neumann and Morgenstern in the year 1944. Afterwards, it was economists like John Nash and Shapley who provided major contributions in this field. The vast horizon of topics covered by game theory includes predicting elections and political outcomes (works of Bruce Bueno de Mesquita) and analysing love affairs (works of Peter D Sozou and Robert M Seymour).
One would expect that writers who deal with emotions and situations of conflict in their work would have dealt with similar situations as a game theorist. In game theory, the value a bargain can give the players of a game is measured as payoffs. In conflicting situations, where protagonists have different choices available to them, a writer can very well play with the intentions and implications of a choice. Similarly, a game theorist plays the game using different payoffs for different choices. His best strategy is the one which gives him the highest payoff after taking into account the strategies of other players.
In the Indian context, one story which embeds a game theoretical perspective is ‘Idgah’ by noted Hindi and Urdu writer Munshi Premchand. The story is about a boy named Hamid who joins a bunch of his friends to visit Idgah during the festival of Eid. At Idgah, they find all kinds of things to buy: toys, sweets and a ride on the merry go round. Each one of the boys has a fixed sum of money he can spend on the available commodities. They belong to a poor village and cannot afford to buy everything they like implying a budgetary constraint. Hamid has the least amount of money among all of them, just three paise.
The spending starts with the ride where Mahmood, Mohsin, Noore and Sammi, the four other boys with Hamid, spend one paise each. Hamid argues that he cannot spend one-third of his money on a ride knowing that he will have choices as they move ahead. After the rides, they come to the toys. Mahmood buys a constable, Mohsin buys a water carrier, Noore buys a lawyer and Sammi a washerwoman, spending two paise each. Hamid argues to himself about the fragility of the toys despite his childish yearnings and finally decides not to buy them making better of his rational self. His woes increase when his friends taunt him over the sweets.
Afterwards, Hamid sees an iron made tong in a shop. It strikes him that gifting it to his grandmother would help her make chapattis without getting her hands burnt and will make a useful gift. He takes into consideration the love his grandmother would shower over him after getting a tong. Under the influence of these thoughts, he bargains for the six paise tong and purchases it for three paise.
Premchand’s game theoretical skills can be seen through this. Through witty comparisons, the value of the tong and toys in the mind of children are being ascertained. The amount of satisfaction (utility) the children get from each purchase, be it toys or sweets, changes vis-a-vis the tong. Initially, the toys hold a higher value for other things as compared to the tong. But, Hamid portrays the tong as a toy by saying that it could serve as a policeman if taken on shoulders or used to play some music. He asserts the fact that the tong can survive fire, water and extreme climatic conditions, calling it his ‘Sher Bahadur’ meaning ‘the courageous lion’.
Such arguments from Hamid attract others to the tong. But they could no more afford to buy it as they have spent all their money. When they face this situation, they decide to put their efforts to show that their toy is a better bargain than Hamid’s choice by trying to downgrade the value of the tong. The payoff of buying each toy based on their qualities evolves through the arguments the little children have about their respective toys.
When the superiority of the tong has been established, Hamid has won the bargain. His payoff is the highest among the lot. Now the others who had denied him their toys earlier want to exchange it with him for a brief period. When the children return to their village, it happens as Hamid had thought. One by one the toys crack. Whereas when Hamid offers the tong to his grandmother, she showers her love on him. The tong is shown to give the highest payoff among all the other toys and hence the best strategy.