This video explains how dominant strategies work, and how to reach a Nash equilibrium. We start by analysing dominant strategies, then explain what the Nash equilibrium is. Finally, we show an example of elimination of dominated strategies.
Nash equilibria are defined as the combination of strategies in a game in such a way, that there is no incentive for players to deviate from their choice. This is the best option a player can make, taking into account the other players’ decision and where a change in a player’s decision will only lead to a worse result if the other players stick to their strategy. One of the best known Nash equilibria can be found in the prisoner’s dilemma. This concept belongs to game theory, specifically to non-cooperative games, and was named after John Nash who developed it.
There are a few consistency requirements that must be taken into account when dealing with Nash equilibria. One of them is known as common knowledge, which extends the necessity of complete information. Therefore, expectations about other player’s strategies must be rational.
A Nash equilibrium is therefore a combination of beliefs about probabilities over strategies and the choices of the other player.
Nash equilibria can be used to predict the outcome of finite games, whenever such equilibrium exists. Furthermore, the best equilibrium outcome can be found by using the method of elimination of dominated strategies, which will help us find the best Nash equilibrium by excluding ‘unreasonable’ Nash equilibria.
Learn more by reading the dictionary entry.