Have you ever heard the term ‘dominance’ in game theory? It refers to a strategy that always yields a better outcome than any other strategy, regardless of what the other players choose. In simpler words, it means that one player has an advantage over the others.
Finding dominance is crucial in game theory as it helps players determine the best course of action to take. To find dominance, you need to follow a few steps:
Step 1: Identify the Players and Their Strategies
The first step is to identify all the players involved in the game and their respective strategies. For example, let’s consider a simple game of rock-paper-scissors between two players – Player A and Player B. The strategies for both players are as follows:
– Player A: Rock, Paper, Scissors
– Player B: Rock, Paper, Scissors
Step 2: Create a Matrix
Next, create a matrix that shows all possible outcomes for each combination of strategies. In this case, there are nine possible outcomes:
- A plays Rock and B plays Rock – Tie
- A plays Rock and B plays Paper – B wins
- A plays Rock and B plays Scissors – A wins
- A plays Paper and B plays Rock – A wins
- A plays Paper and B plays Paper – Tie
- A plays Paper and B plays Scissors – B wins
- A plays Scissors and B plays Rock – B wins
- A plays Scissors and B plays Paper – A wins
- A plays Scissors and B plays Scissors – Tie
Step 3: Identify Dominant Strategies for Each Player
Now, to find the dominant strategy for each player, we need to consider each strategy and compare the outcomes with the other strategies. If a particular strategy yields a better outcome regardless of what the other player chooses, then it is considered a dominant strategy.
Looking at the matrix above, we can see that there is no dominant strategy for either player. Each strategy results in a win, loss or tie depending on what the other player chooses.
Step 4: Identify Dominant Strategy Equilibrium
If there are no dominant strategies for either player, we need to look for a Nash equilibrium. A Nash equilibrium is a situation where neither player has an incentive to change their strategy if they know what the other player is doing.
In our example above, the Nash equilibrium is when both players choose their strategies randomly since there is no dominant strategy for either of them.
In conclusion, finding dominance in game theory involves identifying all players and their respective strategies, creating a matrix to show all possible outcomes, and determining whether there are any dominant strategies or finding Nash equilibrium if there aren’t any. By understanding this concept, players can make informed decisions and increase their chances of winning in any game or competition.