Games people play: A different theory

Chinmayee S

Prof. Avinash Dixit, Professor of Economics at Princeton University, John Nash’s colleague and friend, unravels the concepts of Game theory. He has taught economics courses on games of strategy, and written books on the subject for students and for the general audience.

The game theory is essentially a study of conflict - the science of "outguessing your opponent", and suggests actions based on the motives of each player. Its’ concepts have been used by leading companies. Intel has used it to boost demand for more powerful chips. ProShare, Intel's desktop videoconferencing system, is heavily subsidized to push the limits of existing microprocessors.

The most famous application of the game theory was for auctions of airwaves in various countries, such as the auction of the PCS spectrum auction held from 12 December to 26 January 2001 in the USA, which netted $16.8 billion for the State treasury.

The conventional method used government auctions, tenders or assigning licenses involved ministers and civil servants considering proposals from each company and deciding intuitively which was best. This ‘beauty contest’ approach is not always transparent, raises lesser money and often chooses the wrong companies.

How can competing businesses co-operate to achieve win-win for all players in the market?

Game theory points out the importance of repeated or ongoing interaction between businesses. If, for example, two competing stores are playing this game just once, then each has an overwhelming temptation to undercut the other. But suppose they are in this business together for the long run, and are trying to achieve a cartel that keeps prices high. If one of them undercuts the other, the gain is temporary.

When the other store finds out that the first one has cheated on their agreement, it will not trust the first any more and will retaliate by lowering its own price. This will reduce the cheater’s future profits below what they would have been if it had honored the cartel agreement. So the cheater suffers in the future in exchange for its immediate gain. If the future is sufficiently important in its calculations, it will be deterred from cheating in the first place.

In what way is John Nash’s contribution to the Game theory path-breaking?

Before Nash, the theory was more or less as developed by Von Neumann and Morgenstern. This was limited in two ways.

• Their theory of non-cooperative games (where players take their actions individually and separately) could handle only two-person zero-sum games. But most games in the real world have more than two players interacting with one another, and their interests are common in some respects and conflicting in other respects. Nash’s theory of non-cooperative games handled the fully general case of many players and arbitrary-sum games.  

Their theory of cooperative games did not yield any determinate outcome, only a range within which the outcome would be. Nash’s cooperative theory gave sharper predictions, it pinned down a particular outcome namely the Nash bargaining solution. Thus Nash’s contributions enabled users of game theory to apply it to a vastly greater set of issues and problems.  

What is the famous "Nash equilibrium"?

Nash equilibrium is the situation where these actions are mutually consistent, in the sense that each is taking the action that is best for himself given the actions of all the others. And indeed, Nash proved the existence of such an equilibrium for a very general class of games. Of course, sometimes such an equilibrium may involve the players are taking actions that are "nice", and where the outcome is "good" for them all, so it looks cooperative.

But the cooperation is the by-product of each player trying to further his own interests. This typically happens in a repeated interaction, where each player does not take the nasty or cheating action because this would reduce his own future gains.

In auctions such as the PCS spectrum auction, how did the Game theory ensure fair play?

Game theory can point the way to an "efficient" outcome, that is, one which "leaves no money on the table", bearing in mind all the limitations of information and action that pertain to any specific auction. But the division of the gains between the parties is another matter. The usual procedure is to design an auction to maximize the seller’s revenue, extracting the maximum possible amounts from the buyers. But one could take the opposite perspective and try to give away the benefits to the buyers.

Can the game theory eliminate the possibility of one of the bidders being in collusion with the auctioneer himself? ( for eg. this could be applied to the Indian scenario when government auctions and tenders.)

If the auctioneer is the seller himself, he gains nothing by colluding with one of the buyers. But typically, the auctioneer is merely the agent of the seller; in your context the seller is the government and the auctioneer is the civil servant in charge of the process. Then the government has to devise incentives to control the behavior of its agent.

The design of such incentive schemes is itself an application of game theory, and Jean-Jacques Laffont and Jean Tirole have written a wonderful book about this, "A Theory of Incentives in Procurement and Regulation," MIT Press, 1993. This should be required reading for the designers of auctions and privatization in India.

What are the areas where India needs to focus on more game theory research and analysis?

Apart from design of auctions and privatization sales, more generally, the design of incentives for public-sector workers and civil servants is a large issue that could do with better game-theoretic thinking, not only in India but also in other countries.

To some extent, political institutions and procedures could be improved, to avoid excessive influence of special interests, to reduce and overcome gridlocks in the policy-making process, and so on. The advances in game theory, including the design of the spectrum auctions, has been the work of academic researchers in the US and Europe.