A beautiful strategy: John Nash's 'game theory' explained

  • Gaurav Choudhury, Hindustan Times
  • Updated: May 25, 2015 19:40 IST

John Nash, 86, the brilliant mathematician who won the Nobel in economics and whose life inspired a book and Oscar-winning flick `A Beautiful Mind’, died in a car crash on Saturday night. Nash’s contribution helped `Game Theory’ gain popularity, leading to its widespread use by firms as mainstream corporate strategy.

What is game theory?

Game theory is a branch of mathematical economics first theorised by Jon Von Neumann in the 1930s. It involves the principles of probability in a multi-player world where each player (agent, firm etc) attaches a certain probability to the other players’ behaviour to an action he himself undertakes.

Which are the areas of application of game theory?

Game theory is applied in several areas of current research including space sciences, engineering, stock markets, auctions, multi-firm bids in corporate mergers and acquisitions, and even in geo-political diplomatic strategies of war and peace.

How does it work?

Game theory has several branches: Cooperative Games, Non-Cooperative Games, Strategic Games etc. Its work can be best explained in the context of auctions.

An auction is a non-cooperative game involving several players. Each player assumes that the other players would react in a certain way for every action of his.

A game of chess explains this more clearly. A chess player bases his moves assuming that his opponent would respond in a particular way and vice-versa. The strategies and tactics are based on these assumptions. In mathematics, these are called as “mixed probabilities” where the assumptions are based on incomplete information on opponents.

Are there any specific examples that can be cited that has used game theoretic tools as mainstream corporate strategy?

Yes, there are. The acquisition of a European steel maker by an Indian company (Tata Steel) in 2007 reflects the principles of a non-cooperative game theoretic strategy. After the bids were submitted, both the Indian company and its rival, a South American firm, were asked to participate in an auction to win the rights of ownership of the target company. As the auction began and reached the ninth round, the Indian company announced the tactic saying that it would bid five pence more than whatever the South American rival bids.

The strategy was based on the probability that South American company would not bid beyond the certain point as the Indian company’s bid would anyway be higher by five pence than its rival’s. This move was based on the assumption that the probability of the rival continuing to bid beyond a certain level would be negligible. It turned out as planned. The probabilities were based on the financial muscle and other issues of the rival company, which the Indian firm had factored into the auction process.

What does Facebook’s acquisition of WhatsApp last year mean for the buyer in a game theoretic approach?

Facebook’s decision to buy WhatsApp for such a high price was probably based on its plans to penetrate the mobile internet arena, which is billed as the next big thing in the realm of social networking. WhatsApp, and some of its peers such as Viber, WeChat and Hike, could eventually bring the curtains down on SMS, the short messaging service.

For Facebook it was critical to embrace the emerging group messaging culture that is fast changing the grammar of social media communication. The deal brings on WhatsApp’s then 450 million subscribers, of which 10% were then in India, to its fold, enabling its immediate expansion as an on-the-move network from mostly desktops and smart-phones. Facebook can use its mobile ad technology in a combo offer where it can aggregate for advertisers audiences based on both social networking and messaging.

How can Facebook’s agreement to pay such a heavy price for this purchase be explained through game theory?

Facebook’s strategy was simple: price out the rivals from the market. There were reports that internet giant Google was also in active discussions to buy out WhatsApp. Initial reports had claimed that Google had bid $10 billion for the company, just about half of the amount Facebook offered. Later reports suggest that Google upped its offer for WhatsApp after it learned how much Facebook would eventually pay the messaging service. It is an example of a game theoretic exercise, where firms try to out-think each other in a competitive market.

What is Nash Equilibrium?

Nash equilibrium is the solution to a `game’ where each player thinks about his best strategy irrespective of what others would be doing. John Nash used a situation called the “Prisoners Dilemma” to explain Game theory to students of psychology. The concept is that; in a closed cell, a prisoner would rather seek to maximise his gains than to “cooperate”.

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