Game theory is a theoretical framework that analyzes decision-making in social situations involving competing players. In such scenarios, game theory dominated strategy helps individuals and businesses make optimal decisions to compete effectively against others. Understanding the basics of game theory and the role of strategy is crucial in navigating competitive situations and achieving desired outcomes.
Game theory is a theoretical framework that analyzes decision-making in social situations involving competing players. In such scenarios, game theory dominated strategy helps individuals and businesses make optimal decisions to compete effectively against others. Understanding the basics of game theory and the role of strategy is crucial in navigating competitive situations and achieving desired outcomes.
What Is Game Theory Dominated Strategy?
Game theory dominated strategy is a concept in game theory, which focuses on the optimal decision-making of independent and competing actors in a strategic setting. A strategy is dominant in game theory if it leads a player to better outcomes than alternative strategies, i.e., it dominates the alternative strategies. On the other hand, a strategy is said to be dominated if another strategy always leads to better outcomes for that player, regardless of what the other players do.
Unlike dominant strategies, dominated strategies in game theory are never used by rational players. For example, in a two-player game, if both players are rational and apply dominant strategies, there will always be a unique outcome (Nash equilibrium). However, if either or both players choose dominated strategies, the outcome may vary and not result in a Nash equilibrium.
The Nash Equilibrium
The Nash Equilibrium is a concept in game theory that determines the optimal outcome for a game in which two or more players are involved. In this equilibrium, each player’s strategy is the best response to the strategies chosen by the other players. In simpler terms, no player has anything to gain from changing their strategy, given the strategies of the other players.
In game theory dominated strategy, finding the Nash Equilibrium is crucial in decision-making as it leads to a better chance of achieving the desired outcome. However, this is not always attainable, especially in situations where players are not aware of the other players’ strategies or when there are numerous possible outcomes that make it impossible to identify the Nash Equilibrium.
Identifying Dominant Strategies
In game theory, a dominant strategy is a strategy that always leads to the best outcome for a player, regardless of the strategies chosen by their opponents. To identify dominant strategies, the first step is to create a payoff matrix that outlines the potential outcomes of the game for each player based on their possible strategies.
The payoff matrix will typically include the strategies available to each player and the payoffs associated with each combination of strategies. It is important to note that the payoffs represent the outcomes for each player, and that a higher payoff indicates a better outcome.
Once the payoff matrix has been created, the next step is to analyze the matrix to identify any dominant strategies. The dominant strategy for each player is the strategy that leads to the highest payoff for that player, regardless of the strategies chosen by their opponents.
For example, suppose two players are playing a game in which each player can choose to cooperate or defect, and the payoff matrix is as follows:
| Player 2 | ||
| Player 1 | (5, 5) | (0, 10) |
| (10, 0) | (1, 1) | |
In this game, each player’s dominant strategy is to choose to defect, regardless of the strategy chosen by their opponent. Choosing to defect will always result in a higher payoff for each player than choosing to cooperate, regardless of the other player’s choice.
Overall, identifying dominant strategies is an important aspect of game theory, as it allows players to make optimal decisions in strategic settings where they are competing against one another.
Types of Dominated Strategies
In game theory, dominated strategies are those that lead to worse outcomes for the player, regardless of what their opponent does. These can be classified into two types: strongly dominated strategies and weakly dominated strategies.
Strongly Dominated Strategies
A strictly dominated strategy is a strategy that always leads to a worse outcome than some other strategy, regardless of what the opponent does. In other words, it is always inferior to one or more other available strategies. For example, in the “prisoner’s dilemma” game, confessing is a strictly dominated strategy because it always results in a worse outcome than remaining silent, no matter what the opponent does.
Weakly Dominated Strategies
A weakly dominated strategy is a strategy that may lead to an equal or worse outcome than some other strategy, depending on what the opponent does. In other words, it is not always inferior to other available strategies, but it can be inferior under certain circumstances. For example, in the “battle of the sexes” game, going to the opera is a weakly dominated strategy because it can result in an equal or worse outcome than going to the football game, depending on what the opponent does.
Understanding the concept of dominated strategies is important in game theory as it helps players identify strategies that should be avoided or eliminated from consideration, allowing them to focus on the strategies that are more likely to yield a better outcome.
Examples of Dominated and Dominant Strategies
In game theory, dominated strategies refer to tactics that always result in worse outcomes compared to alternative strategies, regardless of the opponent’s move. Whereas, dominant strategies refer to tactics that lead to superior outcomes regardless of how the opponent chooses to act. Below are some real-world examples of dominant and dominated strategies:
Dominated Strategies
- Prisoner’s Dilemma: In this game, two criminals are arrested and put into separate jail cells. If one criminal confesses and the other doesn’t, the confessor is rewarded with a reduced sentence while the other receives a harsher sentence. If both confess, both receive a lesser sentence. If neither confesses, both receive the same sentence. The dominated strategy is to confess since it always results in a worse outcome than staying silent.
- Tragedy of the Commons: This game involves a shared resource where anyone can use it. Each person can choose to use the resource more or less sparingly, but if everyone uses it too much, the resource will become depleted, and everyone loses. The dominated strategy is to overuse the resource since it ultimately harms everyone in the end.
- Pricing War: In this game, two companies are trying to sell similar products. If one company lowers its price, its competitor will have to do the same to keep up. This continues until the products are being sold at cut-throat prices, leaving both companies with small profits. The dominated strategy is to keep lowering the price until it results in no profit.
Dominant Strategies
- Battle of the Sexes: This game involves a couple deciding which movie to watch. If they cannot agree, they will watch separate movies, which they both view as a worse outcome. However, they have different preferences: the man prefers to watch a boxing game, while the woman prefers to watch a ballet. In this particular game, the woman’s dominant strategy is to guess that the man will choose the boxing game and choose the same, while the man’s dominant strategy is to choose the boxing game regardless of his guess.
- Rock-Paper-Scissors: This game involves two players choosing one of the three options. Rock beats scissors, scissors beats paper, and paper beats rock. In this game, there is no dominant strategy as each option has a chance of winning, resulting in a Nash equilibrium.
- Chicken Game: This game involves two drivers racing toward each other. If one driver swerves, they are viewed as weak or a “chicken”, while if both drivers swerve, they are both viewed as cowards. If both drivers choose not to swerve, there will be a head-on collision resulting in a catastrophic outcome. The dominant strategy here is to swerve since it results in the best possible outcome regardless of the other player’s move.
Strictly Dominated Strategies
In game theory, a strategy is considered strictly dominated if there is another strategy that yields a better outcome regardless of which strategy the opponent chooses. In other words, a strictly dominated strategy is dominated by another strategy in terms of payoff. This type of strategy always delivers a worse outcome than any other strategy, hence it is inferior even if the opponent does not know about the existence of the superior strategy.
One example of a strictly dominated strategy is in the prisoner’s dilemma game. If both players confess, they will both face prison sentences, albeit for a shorter period. However, if one player remains silent while the other confesses, the former will receive a longer sentence, while the latter will go free. In this scenario, remaining silent is a strictly dominated strategy because confessing guarantees a better outcome, regardless of what the opponent does.
The Iterated Deletion of Strictly Dominated Strategies
In game theory, the iterated deletion of strictly dominated strategies is a process of iteratively removing strategies one by one that are strictly dominated. This process can help identify the Nash Equilibrium, which is reached when no player has any incentive to change their strategy.
To identify the strictly dominated strategies, a player must first determine their best responses to the other players’ strategies. If a player has a strategy that always delivers a worse outcome than an alternative strategy, regardless of what strategy the opponent chooses, then that strategy is strictly dominated and can be eliminated.
The process of iteratively deleting strictly dominated strategies can be repeated until no strictly dominated strategies remain. The final outcome is the Nash Equilibrium, where every player’s strategy is their best response to the strategies of the other players.
Disadvantages of Dominated Strategies Method
The dominated strategies method is a popular technique in solving games, but it also comes with some disadvantages.
One disadvantage of the dominated strategies method is that it may not narrow down all possible outcomes that could happen in the game. The method only eliminates dominated strategies, but it does not guarantee that the best strategy will be chosen.
Another disadvantage of the dominated strategies method is that it assumes rationality among players. This may not always be the case in real-life situations, as emotions and other factors can affect decision-making.
Furthermore, the dominated strategies method only works on finite games. For infinite games, where the number of moves is not predetermined, it is difficult to identify dominated strategies which can lead to an incorrect solution.
Overall, while the dominated strategies method is a useful tool in solving games, it is important to understand its limitations and potential pitfalls in order to make the best decisions.
Applications of Game Theory Dominated Strategy
Game theory dominated strategy has many applications in various fields, including business, politics, and sociology.
Business
In business, understanding game theory dominated strategy can help a company gain a competitive advantage over its rivals. By analyzing the strategies of its competitors, a company can identify the dominant strategy and use it to its advantage. For example, a dominant strategy for a company selling a product might be to lower its price to match or beat its competitors.
Politics
Game theory is also important in politics, especially in election campaigns. Understanding the dominant strategy can help a candidate develop a winning campaign strategy. For instance, knowing that voters in a particular region have a certain preference can help a candidate formulate a strategy that caters to those preferences to win their votes.
Sociology
Game theory can also be applied to sociology to better understand human behavior in various social situations, such as conflict resolution or bargaining. A dominant strategy can help individuals or groups involved in these situations to identify the optimal outcome and work towards achieving it.
Other Applications
Besides the fields mentioned above, game theory dominated strategy also has applications in fields such as economics, psychology, and even sports. For instance, in sports, understanding the dominant strategies of opponents can help teams develop winning game plans.
Related Concepts
Game theory dominated strategy can be related to various concepts, such as Pareto efficiency, zero-sum games, and the prisoner’s dilemma. In terms of Pareto efficiency, a strategy is considered dominant if it leads to a Pareto improvement, which means that at least one player can benefit without harming the others. A zero-sum game is a type of game where the sum of the payoffs of one player is equal to the sum of the payoffs of the other player, and the dominant strategy can be used to optimize one’s payoff. The prisoner’s dilemma is a scenario where two individuals have to choose between cooperation and defection, and while the dominant strategy may seem to be defection, it may result in a lower payoff for both individuals in the long run.
Counterarguments and Criticisms
Despite its usefulness in strategy-making and decision-making, game theory is not without its criticisms and counterarguments. The most common criticism is the assumption of rational decision-making, which may not always be the case in real-world situations. In reality, emotions, biases, and incomplete information can affect the decision-making process of players. Thus, game theory may not always accurately predict outcomes or strategies.
Another criticism is the potential for unequal power dynamics among players, especially in games involving institutions or groups. Some players may have more resources, information, or leverage than others, giving them an unfair advantage in the game. This can lead to outcomes that do not necessarily align with the best interests of all players or the society as a whole. Critics argue that game theory should take into account these power imbalances and address them in the decision-making process.
Despite these criticisms, game theory remains a valuable tool in various fields, including economics, political science, and psychology. By understanding the basic principles of game theory, players can make more informed decisions and strategies, and institutions can design more effective policies and regulations.
Conclusion
In conclusion, game theory dominated strategy refers to the superior tactics used by a player that outweigh those of their opponents. It is important to note that game theory is a vital tool in the decision-making process, as it provides a theoretical framework for conceiving social situations among competing players. The understanding of dominant and dominated strategies, as well as the Nash equilibrium, can help decision-makers to make optimal decisions in strategic settings. In any decision-making process, it’s crucial to consider the interdependent nature of the players’ identities, preferences, and available strategies, as these strategies affect the outcomes. Thus, understanding game theory dominated strategies could lead to better outcomes and an upper hand in the game over the opposition.
References
Here are some trusted references for further reading on game theory and dominant strategies:
