Game theory analyzes competitive situations where one player’s actions affect the outcome for others. Dominant strategies give the greatest benefit regardless of others’ actions. Strategies can be weakly or strongly dominant, and identifying them requires understanding of math and economics. The Nash equilibrium predicts situations where players have no incentive to change their strategy. Dominant strategies are most common in zero-sum games.
In game theory, a dominant strategy is a series of maneuvers or decisions that give one player the greatest benefit, or “payoff,” regardless of what other players do. It is sometimes used intentionally by a calculating player, but often it is used more or less accidentally, with dominance appearing only at the end of the transaction. Game theory is a mathematical and economic way of understanding transactions involving thought and intentionality. It can be applied to traditional games and that’s where it gets its name from, but more often than not it is used to describe major economic, political or financial decisions. Here, the individual players are compared to the players and the transactions analogous to a game. There are different ways to classify strategies and the dominance is not always the same in every situation. Some moves can be seen as weakly dominant or strongly dominant, for example. A situation known as a Nash equilibrium can also be influential: in these scenarios, each player’s strategy is optimal, and as such, even if dominance is available, none of these strategies can be chosen or used. Identifying the dominant tactics that are available or used in any given scenario can be quite complex and usually requires a solid understanding of both mathematics and economics.
Game theory in general
Game theory is the branch of mathematics that analyzes the strategies used in competitive situations in which the outcome of one player’s actions depends on the actions of the other players. In these contexts, many scenarios can be thought of as “games”. Financial transactions are among the most common, but business decisions and even interpersonal relationships can be included. The theory usually has both mathematical and psychological components. Economists focus on things like probabilities and probable ramifications of particular moves and decisions, while the psychological aspect brings in things like a person’s potential response to pressured situations and how people typically react to feared or desired perceptions and outcomes . The idea of a dominant or winning strategy is primarily mathematical, but it has broader implications across many disciplines.
Regardless of the setting or game in question, some things stay the same. There must be at least two players in each game, for example, and their choices can be listed in a matrix showing how each of their strategies affects the other. Dominant strategies are most often found in so-called zero-sum games, where one player gains everything only at the expense of the other. For example, if the prize for winning is a predetermined amount of money, the only way for one player to win everything is for the other player to win nothing.
Different types of strategies
Strategies can be identified as strongly dominant or weakly dominant, depending on the difference between the maximum benefit that can be obtained and the minimum benefit or, alternatively, no benefit. If the advantage of a strategy produces only marginally better results, it is considered weakly dominant. Depending on the game, the dominant strategy is not always easy to identify due to the various effects other players’ choices can have on different strategies.
The domain and its results
Put simply, when there is one dominant or winning strategy, every other strategy is dominated. This type of strategy is one that will always earn the player a smaller payout, no matter what other players do. However, it is possible that there are dominated strategies without a single dominant strategy, which can make things even more complex.
Factoring in the Nash equilibrium
Even when there are dominant games available, the games can often end in a draw, with each player essentially finishing on an equal footing. Such situations are covered and often predicted by the Nash Equilibrium, which occurs when no player would make a different choice unless another player changed his strategy. When there is a Nash equilibrium, players have no desire to change their strategy because they would be worse off if another player also did not change their strategy.
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