In any strategic situation, from a business negotiation to a simple board game, we’re always looking for an edge. We know who the players are and what the payoffs could be, but how do we decide on a course of action? The simplest starting point is to search for a move that is best, no matter what the other player does. This is the core idea of a dominant strategy.

A strategy is strictly dominant if it yields a better payoff than any other strategy you could choose, for every possible move your opponent makes. It’s the slam-dunk, no-brainer choice. To see this in action, let's look at the most famous example in game theory: the Prisoner's Dilemma-.

Imagine two partners in crime are arrested and held in separate interrogation rooms. The police don't have enough evidence for a major conviction unless one of them confesses. They offer each prisoner a deal, and neither knows what the other will choose.

Here are the options:

1. If you confess (Defect) and your partner stays silent (Cooperates), you go free, and your partner gets 10 years.
2. If you both stay silent (Cooperate), you both get a minor charge with a 1-year sentence.
3. If you both confess (Defect), you both get 5 years.

Let's analyze this from Prisoner A's perspective.

• If Prisoner B stays silent, Prisoner A gets 1 year for staying silent but goes free for confessing. Confessing is better.
• If Prisoner B confesses, Prisoner A gets 10 years for staying silent but only 5 for confessing. Confessing is better again.

No matter what Prisoner B does, confessing (Defecting) is always the better option for Prisoner A. Since the game is symmetrical, the same logic applies to Prisoner B. Confessing is a strictly dominant strategy for both. The outcome is that both confess and serve 5 years, even though they would have been better off if they had both cooperated.

When you identify a strictly dominated strategy, you can confidently assume a rational player will never use it. This allows us to simplify complex games by removing these inferior options. This process is called the Iterated Elimination of Strictly Dominated Strategies (IESDS).

The idea is simple: find a strictly dominated strategy for any player and remove it from the game. This creates a smaller, simpler game. Now, look at this new game. Are there any new strictly dominated strategies that have appeared? If so, remove them. You repeat this process until no more strategies can be eliminated.

For IESDS to work, we must rely on a powerful assumption: Common Knowledge of Rationality-. This means that not only is every player rational, but every player knows that every other player is rational. And every player knows that every other player knows that everyone is rational, and so on, infinitely.

Why is this necessary? When you eliminate a strategy for Player 1, you're assuming Player 1 is rational. When you then use that simplified game to eliminate a strategy for Player 2, you're assuming Player 2 is rational and that Player 2 knows Player 1 is rational and would have never played their dominated strategy. Each step of elimination requires another layer of this shared knowledge.

By identifying and eliminating dominated strategies, we can often cut through the complexity of a game to find a clear path forward. This process of strategic reduction is a key step before we explore more complex scenarios where no such obvious choices exist.