Any time we have a situation with two or more players that involves known payouts or quantifiable consequences, we can use game theory to help determine the most likely outcomes. As with any concept in economics, there is the assumption of rationality. There is also an assumption of maximization. It is assumed that players within the game are rational and will strive to maximize their payoffs in the game.

This will exclude any "what if" questions that may arise. The number of players in a game can theoretically be infinite, but most games will be put into the context of two players. One of the simplest games is a sequential game involving two players. Below is a simple sequential game between two players. The numbers in the parentheses at the bottom of the tree are the payoffs at each respective point.

The game is also sequential, so Player 1 makes the first decision left or right and Player 2 makes its decision after Player 1 up or down. Backward induction, like all game theory, uses the assumptions of rationality and maximization, meaning that Player 2 will maximize his payoff in any given situation. At either information set, we have two choices, four in all. By eliminating the choices that Player 2 will not choose, we can narrow down our tree.

In this way, we will bold the lines that maximize the player's payoff at the given information set. After this reduction, Player 1 can maximize its payoffs now that Player 2's choices are made known. The result is an equilibrium found by backward induction of Player 1 choosing "right" and Player 2 choosing "up. For example, one could easily set up a game similar to the one above using companies as the players. This game could include product release scenarios.

If Company 1 wanted to release a product, what might Company 2 do in response? Will Company 2 release a similar competing product? By forecasting sales of this new product in different scenarios, we can set up a game to predict how events might unfold. Below is an example of how one might model such a game. By using simple methods of game theory, we can solve for what would be a confusing array of outcomes in a real-world situation. Using game theory as a tool for financial analysis can be very helpful in sorting out potentially messy real-world situations, from mergers to product releases.

Behavioral Economics. Automated Investing.

## Game Theory

Business Essentials. Investopedia uses cookies to provide you with a great user experience. By using Investopedia, you accept our. Your Money. Personal Finance. 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. Therefore, it is important to keep the rival guessing by mixing your moves.

Typical examples arise in sports —whether to run or to pass in a particular situation in football, or whether to hit a passing shot crosscourt 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. Although his soldiers were vastly outnumbered, this threat to fight to the death demoralized the opposition, who 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.

## What is game theory and what are some of its applications?

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 you would like them to, the outcome will be bad for everyone. Sometimes one side backs down and concedes defeat; sometimes 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. Avinash Dixit is the John J. They are coauthors of Thinking Strategically. Further Reading Introductory Ankeny, Nesmith. Poker Strategy: Winning with Game Theory. New York: Basic Books, Brandenburger, Adam, and Barry Nalebuff.

New York: Doubleday, Davis, Morton.

## Game theory | mathematics | dioluilecoopu.tk

Game Theory: A Nontechnical Introduction. Dixit, Avinash, and Barry Nalebuff. New York: W. Norton, Dixit, Avinash, and Susan Skeath. Games of Strategy.

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Luce, Duncan, and Howard Raiffa. Games and Decisions. New York: Wiley, McDonald, John.

Strategy in Poker, Business and War. Osborne, Martin. An Introduction to Game Theory. New York: Oxford University Press, Raiffa, Howard. The Art and Science of Negotiation.

Cambridge: Harvard University Press, Riker, William. The Art of Political Manipulation.