Game Theory is a way of analyzing successful outcomes based on the potential conflicts or coordination between two or more parties. Game Theory tries to predict both optimum outcomes and strategic choices for parties in various complex situations. It will often use matrices – imagine a collection of boxes – to clarify many choices. The games are problems or relationships between parties to examine the choices. The most basic type of game is a zero sum game.

A zero sum game is a straightforward situation where there is one winner and loser. Whether it is two people or two companies there is no reason for anything but direct competition. Imagine two businesses competing for a $3,000 contract to put a new roof on John’s house. If company A gets the contract, then company B receives nothing, and vice versa. It is a zero sum because there was only $3,000 and if one gains then the other loses. Game Theory moves beyond simple zero sum games to find the best benefit in situations that are more complex.

The Prisoner’s Dilemma is one of the most famous Game Theory games. Two criminals, Bonnie and Clyde, are picked up after breaking into a store. They are in separate rooms and do not know what the other is doing. Bonnie’s lawyer tells her he has arranged the following deal: confess and turn state’s evidence and she will get one year while Clyde receives ten years.He also mentions that Clyde is receiving the same offer, and if they both confess they will both receive 3 years. However, if neither confesses then there isn’t enough evidence to convict and they will both be set free.

Game theory examines situations like the Prisoner’s Dilemma and recognizes that the best possible outcome would be for them to collaborate. If neither Bonnie nor Clyde confesses then both will be set free. However, this is the most risky situation as well. The safest option would be for Bonnie to confess because the worst that can happen is a 3-year sentence, while the worst that could happen if she doesn’t confess is ten years.

There are very few examples of Game Theory prior to the twentieth century. The first example appeared in a letter written in 1713, and James Madison actually composed what is now considered a Game Theory analysis in 1787 when he was writing about the impact of different forms of taxation between states. John Von Neumann is the father of modern Game Theory. He wrote his first paper on the topic in 1928, then wrote the “Theory of Games and Economic Behavior” with Oskar Morgenstern in 1944. At the time most of the focus was on cooperative game problems.

While most of the coordination Game Theory involves complex equations to examine the creation of coalitions between parties, there are simple examples of coordination problems. One of the most obvious is deciding which side of the road to drive on. If two drivers meet when driving down the middle of a narrow road, the drivers will be safest if they both agree to drive on their right side or on their left side. The difficulty is if they oppose each other. This can be demonstrated with a two box by two-box matrix, labeling the boxes for the choices – left or right – that driver A or driver B can make. For example the top left box would be left for A and left for B (good result), the top right would be left for driver A and right for driver B (bad result). The bottom left box would be right for A and left for B (bad result) and bottom right box would be right for driver A and right for B (good result).

In the 1950’s and 1960’s there was a flurry of activity in Game Theory. Game theory was expanded from mathematics to philosophy, political science and economics. During this time John Nash – the mathematician portrayed in “A Beautiful Mind” – developed what became known as the Nash Equilibrium. The Nash equilibrium focuses more on the collaborative relationships between decisions and allows for one player’s awareness of the other player’s strategies. One of the games that demonstrate this potential collaboration is called Stag and Hare. Related to Prisoner’s Dilemma, in Stag and Hare two players may choose to hunt hare or stag. Each player can hunt hare by themselves for one unit of meat or they can hunt the stag together and each will get two units of meat. However, if one chooses stag and the other chooses hare, then the person choosing stag receives nothing. From a basic, non-math standpoint, a decision in Nash Equilibrium is if one player cannot get a better solution even after they know the strategy of the other player. Therefore, if player A in stag and hare knows that the other player will choose stag and hope for the biggest payoff, but they were already choosing stag then that is a Nash Equilibrium. If player A would change their strategy after learning the other player’s strategy, it is not a Nash Equilibrium. Nash, along with two others, won the Nobel Memorial Prize in Economic Sciences in 1994 for his work on Game Theory and its implications in economics.

In biology, Game Theory has played an ever-increasing role. Game theory helps explain why the ratio of men to women stays so close to a one to one ratio. It also helps explain a number of aspects of evolution including how animals communicate with each other and why animals or individuals will be more likely to aid relatives. Game Theory plays a significant and ever increasing role in economics, especially behavioral economics, political economics, and information economics as well as a number of transactions including bargaining and auctioning. In 2005, three more game theorists won the Nobel Prize in Economics for, among other things, evolutionary Game Theory. Three more theorists won the 2007 Nobel Prize in economics for other aspects of Game Theory.

At its most complex, Game Theory is a dense sophisticated mathematics system that allows mathematicians to examine the decision choices of a group of participants and predict behavior. However, Game Theory also provides a number of thought experiments and true games – even rock, paper, and scissors has a role in game theory – that the average person can examine and understand.

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