game theory?

Question

what is game theory? how is it used?

Answer 1

Missed from the earlier answers is why we call it "game" theory. It is called game theory because, while it deals in probability, as both answerers correctly indicate, it deals with two or more decision makers using those probabilities to come up with competing strategies. That is, game theory is about how one competitor would play a game to win against the other competitor...whatever that game might be.

A classic example of game theory is shown in the textbooks as a 3X3 matrix, or some small size. Each of the three rows represents an actiion Competitor A can take and each of the three columns represents an action Competitor B can take. The nine elements represent nine possible outcomes of Competitor A choosing one action out of the three rows and Competitor B choosing one among the three columns.

The object of the game is to win. Both A and B want to do that; so they each choose an action that they think will give them the winning advantage. It can be shown that, if each competitor had perfect information about the probabilities associated with each of the nine possible outcomes, the two strategists would finally settle on just one of the nine elements (one row and column intersection)...that would be the strategy that maximized the win and minimized the loss for both competitors.

Unless there have been breakthroughs since I took gaming theory (back when the abacus was the computer), gaming theory has found very little application. That's because it requires "perfect" information to settle on that one best element formed by the two strategies of the competitors. Without perfect information, which means to know all the probabilities and expected outcomes, the one best answer is unattainable for the most part.

Answer 2

Game theory is useful for predicting possible outcomes. Everyone is free to make choices, however, the choices can be assigned probabilities. For example people could be given a choice between cleaning horse manure from a barn or driving to the state capital to pick up $1,000,000 in lottery winnings. The probability in this case is more than 99% would go for the money and if I were modeling it, I would put it at 100%.

Unfortunately, most choices in game theory are not that easily predicted. Usually there are more than 2 choices and usually the choices are much closer or less distinguishable. For example a person could walk to the store , drive to the store or ride their bike to the store. If gas were $7 per gallon I'm not sure anybody could say with certainty the odds of each choice being implemented for any population. Hence, you could make some assumptions and implement game theory to study the possiblities. This is done through mathmatical modeling or computer simulation. You can build as many scenarios as you have time or resources to accommodate. With various scenarios you could decide if you wanted to build a grocery store closer to the residents, or open a bicycle shop to sell more bicycles, or a shoe store as more walking shoes will be required. Furthermore, you could implement game theory to predict when gasoline might reach $7 per gallon.

This is a simplified example of how an entrepeneur might see a grwoing population and rising gas prices and use game theory to decide on a profitable venture. Game theory is used in the business world.

Answer 3

Actually this question belongs in mathematics category or economics...

It mainly deals with modeling of game space where equations representing strategy based on probabilities of potential decisions (moves) can be solved leading to the 'best' solution.

Please see references provided.