It helps us understand what governs the balance between cooperation and competition in business, in politics, and in social settings. In the traditional version of the game, the police have arrested two suspects and are interrogating them in separate rooms. Each can either confess, thereby implicating the other, or keep silent. No matter what the other suspect does, each can improve his own position by confessing. If the other confesses, then one had better do the same to avoid the especially harsh sentence that awaits a recalcitrant holdout.
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Game Theory [An updated version of this article can be found at Game Theory in the 2nd edition. It attempts to determine mathematically and logically the actions that "players" should take to secure the best outcomes for themselves in a wide array of "games. But the games all share the common feature of interdependence.
That is, the outcome for each participant depends upon the choices strategies of all. More typical are games with the potential for either mutual gain positive sum or mutual harm negative sum , as well as some conflict. Game theory was pioneered by Princeton mathematician John von Neumann. In the early years the emphasis was on games of pure conflict zero-sum games. Other games were considered in a cooperative form.
That is, the participants were supposed to choose and implement their actions jointly. Recent research has focused on games that are neither zero-sum nor purely cooperative. In these games the players choose their actions separately, but their links to others involve elements of both competition and cooperation. Games are fundamentally different from decisions made in a neutral environment.
To illustrate the point, think of the difference between the decisions of a lumberjack and those of a general. When the lumberjack decides how to chop wood, he does not expect the wood to fight back; his environment is neutral. Like the general, a game player must recognize his interaction with other intelligent and purposive people.
His own choice must allow for both conflict and for possibilities for cooperation. The essence of a game is the interdependence of player strategies.
There are two distinct types of strategic interdependence: sequential and simultaneous. A general principle for a player in a sequential-move game is to look ahead and reason back. Each player should figure out how the other players will respond to his current move, how he will respond in turn, and so on. The player anticipates where his initial decisions will ultimately lead, and uses this information to calculate his current best choice.
In principle, any sequential game that ends after a finite sequence of moves can be "solved" completely. Simple games, such as tic-tac-toe, can be solved in this way and are therefore not challenging.
For many other games, such as chess, the calculations are too complex to perform in practice—even with computers. Therefore, the players look a few moves ahead and try to evaluate the resulting positions on the basis of experience. In contrast to the linear chain of reasoning for sequential games, a game with simultaneous moves involves a logical circle. The thinking goes: "I think that he thinks that I think His own best action is an integral part of this overall calculation.
This logical circle is squared the circular reasoning is brought to a conclusion using a concept of equilibrium developed by the Princeton mathematician John Nash. In other words, each picks his best response to what the others do. This is called a dominant strategy for that player. At other times, one player has a uniformly bad choice—a dominated strategy—in the sense that some other choice is better for him no matter what the others do.
The search for an equilibrium should begin by looking for dominant strategies and eliminating dominated ones. Some games have many such equilibria while others have none. And the dynamic process that can lead to an equilibrium is left unspecified. But in spite of these flaws, the concept has proved extremely useful in analyzing many strategic interactions. Two suspects are questioned separately, and each can confess or keep silent. If suspect A keeps silent, then suspect B can get a better deal by confessing.
If A confesses, B had better confess to avoid especially harsh treatment. The same is true for A. Therefore, in equilibrium both confess. Both would fare better if they both stayed silent. Such cooperative behavior can be achieved in repeated plays of the game because the temporary gain from cheating confession can be outweighed by the long-run loss due to the breakdown of cooperation. Strategies such as tit-for-tat are suggested in this context.
Mixing moves. In some situations of conflict, any systematic action will be discovered and exploited by the rival. Typical examples arise in sports—whether to run or to pass in a particular situation in football, or whether to hit a passing shot cross-court or down the line in tennis.
Game theory quantifies this insight and details the right proportions of such mixtures. Strategic moves. To succeed, the threats and promises must be credible. This is problematic because when the time comes, it is generally costly to carry out a threat or make good on a promise. Game theory studies several ways to enhance credibility. He purposefully eliminated retreat as an option. Although his soldiers were vastly outnumbered, this threat to fight to the death demoralized the opposition; it chose to retreat rather than fight such a determined opponent.
Polaroid Corporation used a similar strategy when it purposefully refused to diversify out of the instant photography market. It was committed to a life-or-death battle against any intruder in the market. When Kodak entered the instant photography market, Polaroid put all its resources into the fight; fourteen years later, Polaroid won a nearly billion-dollar lawsuit against Kodak and regained its monopoly market. Another way to make threats credible is to employ the adventuresome strategy of brinkmanship—deliberately creating a risk that if other players fail to act as one would like them to, the outcome will be bad for everyone.
Introduced by Thomas Schelling in The Strategy of Conflict, brinkmanship "is the tactic of deliberately letting the situation get somewhat out of hand, just because its being out of hand may be intolerable to the other party and force his accommodation. Sometimes one side backs down and concedes defeat; other times, tragedy results when they fall over the brink together.
Two players decide how to split a pie. Each wants a larger share, and both prefer to achieve agreement sooner rather than later. When the two take turns making offers, the principle of looking ahead and reasoning back determines the equilibrium shares.
Agreement is reached at once, but the cost of delay governs the shares. The player more impatient to reach agreement gets a smaller share. Concealing and revealing information. In both cases the general principle is that actions speak louder than words.
To conceal information, mix your moves. Bluffing in poker, for example, must not be systematic. For example, an extended warranty is a credible signal to the consumer that the firm believes it is producing a high-quality product.
Recent advances in game theory have succeeded in describing and prescribing appropriate strategies in several situations of conflict and cooperation. But the theory is far from complete, and in many ways the design of successful strategy remains an art. Sherred Professor of Economics at Princeton University. Further Reading Ankeny, Nesmith.
Poker Strategy: Winning with Game Theory. Brams, Steven. Game Theory and Politics. Davis, Morton. Game Theory: A Nontechnical Introduction, 2d ed. Dixit, Avinash, and Barry Nalebuff. Luce, Duncan, and Howard Raiffa. Games and Decisions. McDonald, John. Strategy in Poker, Business and War. Porter, Michael. Competitive Strategy. Raiffa, Howard. The Art and Science of Negotiation. Riker, William. The Art of Political Manipulation. Schelling, Thomas.
The Strategy of Conflict. Williams, J. The Compleat Strategyst, rev. Advanced Neumann, John von, and Oskar Morgenstern.
Theory of Games and Economic Behavior. Ordeshook, Peter. Game Theory and Political Theory. Shubik, Martin.
Thinking Strategically: The Competitive Edge in Business, Politics, and Everyday Life
Thinking Strategically: The Competitive Edge in Business, Politics, and Everyday Life