Game Theory: Definition, Prisoner's Dilemma and Business Use

Playing games to win is the goal behind game theory.

Game theory is one of the more useful tools available to economists, mathematicians and business leaders to get a competitive leg up on what decisions competitors and organizations are making - and why they're making them.

Game theory is all about recognizing how others may react to a specific situation then acting on that knowledge to better the chances of winning the game yourself.

That scenario plays out in economics or business just as it would in outlasting game combatants on a desert island, just like the CBS reality show "Survivor," or in more real-world scenarios like high-level poker or when law enforcement uses game theory to solve big crimes.

So how do you play the game? It's all about applying theory to actual strategy, game-wise, and using the knowledge of your opponent to up your chances of coming out on top - no matter what competition you're engaged in.

What Is Game Theory?

In essence, game theory is a strategic tool that is used to reveal behavior and tendencies from other "game" participants, and to leverage that knowledge to produce an optimal outcome in any competitive scenario.

Winning at game theory means recognizing the choices available, by analyzing the possible choices an opponent has at his or her disposal and choosing the options that upgrade your chances of victory.

Game theory dates back to 1944, when John von Neumann and Oskar Morgenstern used the term to explain a mathematical theory that sought to define and explain the strategic behavior of game participants who know that decisions made in the competition impacts all game participants - good or bad.

While the term game theory had been used in a roundabout way among mathematicians and economists to define decision making, a book formalized the term and brought it into the public domain. That occurred in 1944, when "The Theory of Games and Economic Behaviorwas published by Neumann and Morgenstern, and soon came to be known as the "bible" of game theory analysis.

The application and analysis of game theory evolved over the next 50 years culminating in a Nobel Prize for economics for three economists - John Nash, John Harsanyi, and Reinhard Selten. The highly-coveted prize recognized their work in advancing the practical use of game theory in the field of economics.

Examples of Game Theory

Game theory operates in a wide variety of fields, including economics, business, mathematics, psychology, political science, biology and zoology, and ecology. In all of the above fields, examples of how game theory is used abound:

  • As a metaphor for decision theory. Economists often equate game theory with decision theory. Under that theory, each competitor in a game actually owns the tools (or "utilities") linked to a competition's outcomes. That's not exactly the same as game theory, however, as a game competitor needs to understand that opponents have those utilities and tools, too, and the competitor has weighed how opponents will use those tools to increase their odds of victory.
  • Links to the minimax theorem. One example of game theory is known as minimax theorem. Here, game competitors know that a resolution to a game or competition between two parties often depends on knowing a competitor's opposite goals and interests.
  • As a mathematical equation. The cultural term "tit for tat" derives from game theory. It's a gaming concept where one competitor reacts to another competitor's move or strategy by responding with the same move or strategy.
  • Leveraging "common knowledge." Hiding secrets from competitors is a big part of game theory. That's also known as common knowledge in game theory parlance. Under that scenario, game theory participants learn key information that could sway the competition's outcome, but don't know if other competitors possess the same information.

What Is the Prisoner's Dilemma?

One widely used example of the game theory is the "Prisoner's Dilemma."

The term is derived from a scenario where two prisoners accused of a crime, separated from one another, don't know if the other will confess or not confess to the accused crime, and have to act accordingly.

Having known the other accused prisoner, the other prisoner must rely on tendencies and tactics they know the other prisoner used in the past, and must base their own decision to confess or not based on that knowledge.

Here's a real-world scenario of the Prisoner's Dilemma.

Let's say the accused were cited for simple assault and battery, for example, but the officers suspected they were linked to higher crimes, like an armed bank robbery. At that point, to gain more information from the accused, law enforcement officers will place each of the accused in different cells, ensuring they have no way to communicate with one  another.

Each of the accused criminals is told they are suspected of also being armed robbers linked to a recent bank heist. Under the original crime of assault and battery, which may carry a one-year prison sentence, the law enforcement officials will up the ante and accuse each of armed bank robbery, too. That crime could carry a heavy term of five-to-10 years in prison - depending on how well the accused know game theory.

Under the Prisoners Dilemma theory, law enforcement officers will play each of the accused off of the other, promising a lighter prison sentence for the one who confesses to both crimes (say, two years), and a heavier prison sentence (say, seven years) to the accused who does not confess to both crimes. Or, they'll offer the same sentence (say, three years) if they both confess to both of the crimes (although they won't tell the prisoners that.)

Now the game theory gets interesting. Each of the accused, completely walled off from the other, has two options:

  1. Confess to the bank robbery and hope for the lighter sentence.
  2. Or, deny any involvement in the bank robbery and hope the other accused does the same.

If prisoner "one" denies the allegations, but prisoner "two" confesses, that would result in an outcome where prisoner one faces seven years in prison, while prisoner two gets off easier, likely only facing two years in prison.

Yet if both of the accused match up and deny the charges outright (and let the justice system roll on with the presumption of innocence) or both confess to the crime, only the two-to-three years in prison are on the table for both of the accused.

The optimal outcome for both of the accused under interrogation?

Denying the charges and hoping for an "innocent" declaration in a court of law is the best outcome. Yet the more sensible path, especially if the accused parties don't know each other very well, is to confess to the crime, and face the two years in jail.

That way, the heavier seven-year sentence is eliminated.

How Does Game Theory Apply in Business and Economics?

Economists often use game theory in real-world applications - think of a Middle Eastern oil cartel engaging in price fixing and competitive espionage. Knowing the cartel's options can help companies or countries who may be negatively impacted by the cartel's decision making to better understand their options, and ideally change those negative outcomes and turn them into positive outcomes.

Businesses also regularly apply game theory, as well.

Let's say that Ford (F) and General Motors (GM) both wish to advertise their vehicles on the open market, on broadcast channels, digitally, and even in small-town newspapers.

Both have significant budgets to advertise their cars and trucks to earn more visibility with the auto-buying public, yet both wish to minimize advertising spending, to save on bottom line costs.

Under the game theory, the objective would be for Ford and General Motors to accurately gauge how much money the other is spending on vehicle advertising, and match that spending in the most efficient, effective and economical way.

If one knows what the other is spending they can spend a little more - but not the entire budget - and increase market share while keeping a sharp eye on the bottom line at the same time. Consequently, by playing the game theory well, or at least better than their competitor, a company can gain a financial benefit by applying game theory skills and analysis to business decisions.

Improving decision making, after all, is the bottom line with game theory - a game more and more companies are playing on a regular basis.

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