# Is there always a dominant strategy in game theory? ### Is there always a dominant strategy in game theory?

0:543:59Intro to Game Theory and the Dominant Strategy EquilibriumYouTubeStart of suggested clipEnd of suggested clipOne strategy strictly dominates another strategy if the player is always better off under thatMoreOne strategy strictly dominates another strategy if the player is always better off under that strategy no matter what other players do.

### What if there is no dominant strategy in game theory?

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).Raj. 20, 1440 AH

### What is a dominant strategy in a game?

According to game theory, the dominant strategy is the optimal move for an individual regardless of how other players act. A Nash equilibrium describes the optimal state of the game where both players make optimal moves but now consider the moves of their opponent.

### How do you determine if there is a dominant strategy?

0:051:31Finding a Dominant Strategy - YouTubeYouTubeStart of suggested clipEnd of suggested clipBut what about if player. 1 were to play B. So let's now fix player 1 at playing strategy B. Let'sMoreBut what about if player. 1 were to play B. So let's now fix player 1 at playing strategy B. Let's just cover up strategy a and what do we see player 2 we need to get to or zero.

### Can there be two dominant strategies?

Can a player have two strictly dominant strategies? Give an example or prove that this is impossible. No. If si and si were both strictly dominant, si = si, then you would have ui(si,s−i) > ui(si,s−i) > ui(si,s−i) for all s−i, which is impossible.

### Is there always a Nash equilibrium?

There does not always exist a pure Nash equilibrium. Theorem 1 (Nash, 1951) There exists a mixed Nash equilibrium. ... for every i, hence must have pi(s, α) ≤ 0 for every i and every s ∈ Si, hence must be a Nash equilibrium. This concludes the proof of the existence of a Nash equilibrium.

### Can there be no Nash equilibrium?

It is also possible that there are no Nash equilibria, but, fortunately, by allowing randomized strategies, a randomized Nash equilibrium is always guaranteed to exist.

### Is dominant strategy always a Nash equilibrium?

A Nash equilibrium is always a dominant strategy equilibrium. If a player's optimal strategy depends on the behavior of rival players, then that player must have a dominant strategy. The prisoners' dilemma provides an explanation for price wars among oligopolists.

### What is dominant strategy example?

Hiring a lawyer is a dominant strategy for Firm A because if Firm B hires a lawyer, it is better to hire a lawyer and get \$45 million instead of not hiring and getting only \$25 million. If Firm B doesn't hire a lawyer, it is better for Firm A to hire a lawyer and get \$70 million instead of only \$25 million.Raj. 4, 1440 AH

### What is dominant and dominated strategy?

Strategic dominance is a state in game theory that occurs when a strategy that a player can use leads to better outcomes for them than alternative strategies. A strategy is dominant if it leads to better outcomes than alternative strategies, and dominated if it leads to worse outcomes than alternative strategies.

### What is the dominant strategy in game theory?

• Dominant Strategy. 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.

### What is dominated strategy game theory?

• In game theory, a dominant strategy is a series of maneuvers or decisions that gives a player the most benefit, or “gain,” no matter what the other players do. Sometimes it’s used intentionally by a calculating player, but it’s often used more or less accidentally, with the dominance only appearing...

### What is dominant strategy equilibrium?

• A dominant strategy is a type of Nash equilibrium. 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.