What is Game Theory?
Game theory is a well-developed field of mathematics and economics used to:
- Predict the behavior of people and organizations in situations of parallel and conflicting goals.
- Assist management in making better decisions in those situations.
History of Game Theory
The origins of game theory go far back in time. Recent work suggests that the division of an inheritance described in the Talmud (in the early years of the first millennium) predicts the modern theory of cooperative games.
People have studied the mathematics of gambling games from the moment they were invented. However, the book The Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern (published in 1944) is usually credited as the origin of the formal study of game theory.
The Golden Age of game theory occurred in the 1950s. Starting with the concepts of rationality explored by John Nash, who was later made famous in the movie A Beautiful Mind, and culminating with Luce and Raiffa's book, Games and Decisions. During this decade, all of the basic ideas of game theory were developed. The Prisoner's Dilemma, very familiar to any MBA student, is a product of the thinking of this period.
Following the 1950s, game theory receded from public consciousness. However, the cold war motivated continued work in this field, not only by mathematicians but also by political scientists. Although progress was slower, the concepts developed in the 50s spread to other fields and matured.
The 1990s saw a visible resurgence of general interest in game theory. The 1994 Nobel Prize for Economics was awarded to John Nash (for his seminal work in the 50s), John Harsanyi (for formalizing Nash's work), and Reinhard Selten (for extending Nash's work). Also around the same time, the US Federal Communications Commission used game theory approaches to structure the auction of underused radio spectra, resulting in unexpectedly large amounts of revenue for the FCC. These two high-profile milestone events helped motivate applications of game theory to business problems, including our very own Open Options process.
The "Prisoner's Dilemma" Problem
The Prisoners' Dilemma is a classic problem in game theory that highlights the distinction between individual rationality and joint efficiency.
The story is that two suspects are picked up for a robbery. They are placed in separate cells and are individually offered the following deal (the specific number of years are arbitrary):
- If the suspect confesses, he or she will be freed but the partner will go to jail for 10 years
- If both suspects confess, both will go to jail for 4 years
- If neither suspect confesses, both will go to jail for 2 years (because less evidence will be available to justify a longer sentence).
What should each suspect do, confess or deny?
| Prisoner 2 | |||
|---|---|---|---|
| Deny | Confess | ||
| Prisoner 1 | Deny | P1: 2 years P2: 2 years |
P1: 10 years P2: 0 years |
| Confess | P1: 0 years P2: 10 years |
P1: 4 years P2: 4 years | |
The problem can be diagrammed as shown in Figure 1 as a 2x2 game, which means that there are two players, each with two possible strategies.
Note that for Prisoner 1 (P1), no matter what Prisoner 2 (P2) does, P1 is better off confessing: If P2 denies, P1 will get 2 years in jail for denying, 0 years for confessing. If P2 confesses, P1 will get 10 years for denying and 4 years for confessing. So P1, by the principle of individual rationality, is better off confessing. Since the same choices are available to P2, the natural result is that both players will confess and go to jail for four years each.
| Prisoner 2 | |||
|---|---|---|---|
| Deny | Confess | ||
| Prisoner 1 | Deny | P1: 2 years P2: 2 years |
P1: 10 years P2: 0 years |
| Confess | P1: 0 years P2: 10 years |
P1: 4 years P2: 4 years | |
On the other hand, if both prisoners deny (Figure 2), they are both better off by going to jail for two years each. By the principle of joint efficiency, a better outcome is attainable. This may require coordination between the players, or else the ability of one player with a clear vision to constrain or motivate the actions of the other.
When applying the Open Options process, individual rationality generally points to the Natural Outcome, while joint efficiency points to the Best Attainable OutcomeTM.
Game Theory and Open Options
Open Options uses ordinal, non-cooperative game theory. Our focus is on following a series of steps to achieve certain stable outcomes, rather than on finding a quantitative equilibrium. To find out more about Open Options' technical foundation, you may reference Dr. Niall Fraser's academic papers or contact us to request more technical information.
