What is a Strictly Dominated Strategy in Game Theory?

This article provides a clear explanation of what a strictly dominated strategy is in game theory, how it influences decision-making, and why it is a fundamental concept for analyzing strategic interactions. By understanding this concept, you will learn how rational players eliminate worst-case options to simplify complex games and identify optimal outcomes.

In game theory, a strategy is defined as strictly dominated when there is another strategy available to a player that always yields a strictly higher payoff, regardless of the decisions made by the opponents. In simpler terms, no matter what the other players do, choosing the strictly dominated strategy will always result in a worse outcome than choosing the dominating alternative.

Mathematically, if a player has two strategies, Strategy A and Strategy B, Strategy A is strictly dominated by Strategy B if the payoff from choosing Strategy B is always greater than the payoff from choosing Strategy A for every possible combination of strategies chosen by the other players.

Because rational players aim to maximize their own payoffs, a basic assumption in game theory is that a rational player will never choose a strictly dominated strategy. Since these strategies are guaranteed to produce suboptimal results, they can be completely eliminated from the analysis of the game.

The Process of Iterated Elimination

Identifying and removing these strategies is a common method used to solve games, known as the Iterated Elimination of Strictly Dominated Strategies (IESDS). The process works as follows:

1. Identify any strictly dominated strategies for all players in the game.
2. Eliminate those strategies from the game matrix, as rational players will never use them.
3. Repeat the process for the remaining strategies. Since the elimination of one player’s strategy changes the game, it may cause a previously viable strategy for another player to now become strictly dominated.
4. Continue this process until no more strictly dominated strategies can be found.

In some games, this process of elimination leads to a single, unique outcome, which represents the Nash equilibrium of the game.

A Practical Example: The Prisoner’s Dilemma

The classic Prisoner’s Dilemma is a perfect illustration of strictly dominated strategies. In this game, two suspects are arrested and placed in separate rooms. Each has two choices: “Cooperate” (remain silent) or “Defect” (confess and testify against the other).

• If Player 1 suspects Player 2 will Cooperate, Player 1 gets a better outcome by Defecting (going free instead of serving a minor sentence).
• If Player 1 suspects Player 2 will Defect, Player 1 still gets a better outcome by Defecting (serving a moderate sentence instead of the maximum sentence for staying silent).

In this scenario, “Cooperate” is a strictly dominated strategy for both players because “Defect” always yields a better individual payoff, regardless of the other player’s choice. Consequently, both rational players will choose to defect, leading to the Nash equilibrium where both confess.