Contents

- 1 What happens if there is no dominant strategy?
- 2 Is it possible to not have a dominant strategy?
- 3 What is the solution in dominant strategies?
- 4 Do not play a strictly dominated strategy?
- 5 Can there be two dominant strategies?
- 6 What is a strictly dominated strategy?
- 7 Does each firm have a dominant strategy and if so what is it?
- 8 How do you know if there is no Nash equilibrium?
- 9 Who has a dominant strategy?
- 10 What is a weakly dominant strategy?
- 11 Do all games have dominant strategies?
- 12 What is a dominant strategy in game theory?

## What happens if there is no dominant strategy?

A dominant strategy is a strategy which results in the best payoff for a player no matter what the other firm does but a Nash equilibrium represents a strategy which maximizes payoff given what the other player would do. A game has a Nash equilibrium even if there is no dominant strategy (see example below).

## Is it possible to not have a dominant strategy?

It must be noted that any dominant strategy equilibrium is always a Nash equilibrium. However, not all Nash equilibria are dominant strategy equilibria. Since only one of them has a dominant strategy, there is no dominant strategy equilibrium.

## What is the solution in dominant strategies?

The solution in dominant strategies is when both players have chosen the best strategy and those choices are unaffected or not influenced by the choice of the opposing party.

## Do not play a strictly dominated strategy?

A rational player will never play a strictly dominated strategy. Proof. No dominated strategy can ever be optimal because, by definition of strict dominance, there is another dominating strategy yielding a higher payoff regardless of the other players’ strategies.

## Can there be two dominant strategies?

A game can only have more than one dominant strategy per player, if the strategies are only weakly dominant (meaning it always does at least as well as every other strategy, but in some cases it may only tie other strategies, not beat them), and have the same payoffs for their player.

## What is a strictly dominated strategy?

A strategy is strictly (or strongly) dominated if it leads to worse outcomes than alternative strategies. A strategy is weakly dominated if it leads to equal or worse outcomes than alternative strategies.

## Does each firm have a dominant strategy and if so what is it?

2d A game is a prisoner’s dilemma if: each player has a dominant strategy, and when both players choose their dominant strategy, each gets a lower payoff than if each had chosen their dominated strategy. No, Firm 1 does not have a dominant strategy in this game.

## How do you know if there is no Nash equilibrium?

To quickly find the Nash equilibrium or see if it even exists, reveal each player’s strategy to the other players. If no one changes their strategy, then the Nash equilibrium is proven.

## Who has a dominant strategy?

The dominant strategy in game theory refers to a situation where one player has a superior tactic regardless of how the other players act. The Nash Equilibrium is an optimal state of the game, where each opponent makes optimal moves while considering the other player’s optimal strategies.

## What is a weakly dominant strategy?

A strategy is weakly dominant if, regardless of what any other players do, the strategy earns a player a payoff at least as high as any other strategy, and, the strategy earns a strictly higher payoff for some profile of other players’ strategies.

## Do all games have dominant strategies?

In game theory, a dominant strategy is the course of action that results in the highest payoff for a player regardless of what the other player does. Not all players in all games have dominant strategies; but when they do, they can blindly follow them.

## What is a dominant strategy in game theory?

3.6. “Dominant strategy” is a term in game theory that refers to the optimal option for a player among all the competitive strategy set, no matter how that player’s opponents may play, and the opposite strategy is called “inferior strategy.”