Game theory studies interactive decision-making, where the outcome for each participant or "player" depends on the actions of all. If you are a player in such a game, when choosing your course of action or "strategy" you must take into account the choices of others. But in thinking about their choices, you must recognise that they are thinking about yours, and in turn trying to take into account your thinking about their thinking, and so on.
For example a firm competing in a market with may be faced with a choice of charging a premium or a discount price. But the outcome of its choice depends on its competitors' pricing strategy. The competitors in turn are faced with the same choice and are also trying to guess what this firm is thinking of doing. It would seem that such thinking about thinking must be so complex and subtle that its successful practice must remain an arcane art. Indeed, some aspects such as figuring out the true motives of rivals and recognising complex patterns do often resist logical analysis. But many aspects of strategy can be studied and systematised into a science -- game theory. The term "game" stems from the formal resemblance of these interactive decision problems to parlour games such as Chess, Bridge, Poker, Monopoly, Diplomacy, or Battleship.
Applications of game theory
This science is unusual in the breadth of its potential applications. Unlike physics or chemistry, which have a clearly defined and narrow scope, the precepts of game theory are useful in a whole range of activities. For this reason game theory has been called an 'inter-discipline'.
To date, the largest single area of application has been economics; other important connections are with political science (on both the national and international levels), evolutionary biology, computer science, the foundations of mathematics, statistics, accounting, law, social psychology, and branches of philosophy such as epistemology and ethics. Situations that involve negotiation, bargaining, are particularly amenable to the tools of the theory.
Game theory got its start with the work of John von Neumann in the 1920s, which culminated in his seminal book with Oskar Morgenstern. They studied "zero-sum" games where the interests of two players were strictly opposed. John Nash treated the more general and realistic case of a mixture of common interests and rivalry and any number of players. Other theorists, most notably Reinhard Selten and John Harsanyi who shared the 1994 Nobel memorial prize with Nash, studied even more complex games with sequences of moves, and games where one player has more information than others.
The Nash Equilibrium
Here are a few examples to convey some ideas of game theory and the breadth of its scope.
The Prisoner's Dilemma
Every general reader has heard of the prisoner's dilemma. The police interrogate two suspects separately, and suggest to each that he or she should fink on the other and turn state's evidence. "If the other does not fink, then you can cut a good deal for yourself by giving evidence against the other; if the other finks and you hold out, the court will treat you especially harshly. Thus no matter what the other does, it is better for you to fink than not to fink -- finking is your uniformly best or 'dominant' strategy." This is the case whether the two are actually guilty, or innocent. Of course, when both fink, they both fare worse than they would have if both had held out; but that outcome, though jointly desirable for them, collapses in the face of their separate temptations to fink.
While the predicament of the two prisoners appears to be very dismal, a branch of game theory called 'repeated games' models ongoing relationships; the theory "predicts" phenomena such as cooperation, communication, altruism, trust, threats, punishment, revenge, rewards, secrecy, signalling, transmission of information, and so on.
Greater freedom of action seems obviously desirable. But in games of bargaining that need not be true, because freedom to act can simply become freedom to concede to the other's demands. Committing yourself to a firm final offer leaves the other party the last chance to avoid a mutually disastrous breakdown, and this can get you a better deal. But a mere verbal declaration of firmness may not be credible. Devising actions to make one's commitments credible is one of the finer arts in the realm of strategic games. Thomas Schelling a co-winner of the 2005 Nobel prize, pioneered the study of credible commitments, and other more complex "strategic moves" like threats and promises. This has found many applications in diplomacy and war, which, as military strategist Karl von Clausewitz told us long ago, are two sides of the same strategic coin.
Aligning Interests, avoiding Enrons
An application in business economics is the design of incentive schemes. Modern corporations are owned by numerous shareholders, who do not personally supervise the operations of the companies. How can they make sure that the workers and managers will make the appropriate efforts to maximise shareholder value They can hire supervisors to watch over workers, and managers to watch over supervisors. But all such monitoring is imperfect: the time on the job is easily monitored, but the quality of effort is very difficult to observe and judge. And there remains the problem of who will watch over the upper-level management. Hence the importance of compensation schemes that align the interests of the workers and managers with those of the shareholders. Game theory and information economics have given us valuable insights into these issues. Of course, we do not have perfect solutions; for example, we are just discovering how top management can manipulate and distort the performance measures to increase their own compensation while hurting shareholders and workers alike. This is a game where shareholders and the government need to find and use better counterstrategies.
Designing and participating in auctions
One of the best mechanisms to allocate resources efficiently is an auction. Auctions are used extensively to allocate resources as diverse as 3G spectrum and oil rigs. Game theory can be used to design the rules of the auction to achieve the societal goals of equity, efficiency etc., as well as the auctioneer's objective of maximising revenue. It can also be used to advise bidders on smart bidding strategies including the use of signalling to reveal and elicit information vis-a-vis competitors.
From intuition to prediction
While reading these examples, you probably thought that many of the lessons of game theory are obvious. If you have had some experience of playing similar games, you have probably intuited good strategies for them. What game theory does is to unify and systematise such intuitions. Then the general principles extend the intuitions across many related situations, and the calculation of good strategies for new games is simplified. It is no bad thing if an idea seems obvious when it is properly formulated and explained; on the contrary, a science or theory that takes simple ideas and brings out their full power and scope is all the more valuable for that.
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