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Dominant Strategy in Game Theory: Definition & Examples

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  • 0:04 Game Theory & Dominant…
  • 2:01 Examples
  • 5:03 Lesson Summary
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Lesson Transcript
Instructor: Michael Quist

Michael has taught college-level mathematics and sociology; high school math, history, science, and speech/drama; and has a doctorate in education.

There are many ways to approach game-like challenges, especially those that involve unknowns or other human players. In this lesson, we'll discuss the 'dominant' strategy and look at examples of how you can use it.

Game Theory & Dominant Strategy

Most people like games. Whether it's chess, football, or Jeopardy, it's fun to participate in a simulated event where the excitement is real, yet the risk is limited. Game theory is the science of strategy, the study of math and logic behind conflict and cooperation. Everyone uses some sort of strategy (the algorithm, or logical set of steps, that determines how they make their choices) to approach life. Some strategies are effective for winning, others for maintaining an equilibrium where no one gets ahead, and some create losses.

For example, every move you make on a chessboard carries consequences and opportunities. If you advance your king's pawn two squares, you have also created a set of risks and possibilities for your opponent. His strategy will determine what he does with those risks and possibilities. Game theory is especially applicable in situations where models can be useful, such as economics or politics, and it can be helpful in games like poker or bridge.

A dominant strategy is one that will have the absolute best effects, no matter what your opponents or partners do. It's a set of choices that creates the highest balance of reward/risk ratios. Sometimes, there is no truly dominant strategy, which leaves you in an intransitive situation, where your strategy must adapt to the actions of others. For example, chess is an extremely complex game and is purely adversarial (one player must lose for the other to win), so it's almost impossible to create a dominant strategy. You and your opponent are constantly adapting using intransitive strategies.

The dominated strategy produces the absolute worst result, regardless of the choices made by the other players. Going back to our chess example, some players will randomly advance their pieces, heedless of the risks or disadvantages they create for themselves. This strategy causes the players to lose, regardless of how any normal opponent plays.

Examples

Most people are familiar with the rock-paper-scissors game. You and your opponent each hide one of your hands and then form scissors, rock, or paper with the other. Each choice wins against one of the others, loses against another, and ties if the opponent makes the same choice. Rock wins over scissors (smashes them), scissors wins over paper (cuts it), and paper wins over rock (covers it).

At first glance, this game would seem to be fairly intransitive. No matter what choice you make, there is a choice your opponent can make that will defeat you and another choice that will cause you to win. Is there a dominant strategy for this simple game? People who study game theory would say that there is a dominant strategy against a certain opponent given the moves he or she historically tends to make. The following steps might be part of your analysis and strategy:

  1. If you know that almost every time you begin a rock-paper-scissors game with a certain person, he starts with rock, then your dominant strategy would include using the correct counter-move and throw paper.
  2. If you observe that whenever your opponent loses a turn, he tends to pick the choice that defeated him for the next turn, then your dominant strategy can include a counter for that move.
  3. If you observe that your opponent tends to play the same move over and over again, you can counter that in your strategy until he chooses to change.

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