Table of Contents
Can there be two weakly dominant strategy?
No. If si and si were both weakly dominant, si = si, then you would have ui(si,s−i) > ui(si,s−i) for some s−i and also ui(si,s−i) ≥ ui(si,s−i) which is impossible.
Do both players need a dominant strategy for Nash equilibrium?
Yes, a game can have a Nash equilibrium even though neither player has a dominant or dominated strategy. In fact, every game has a Nash equilibrium, possibly in mixed strategies. The game of Chicken is an example of a game with no dominant or dominated strategies but which has a Nash equilibrium.
Can a weakly dominated action be used with a strictly positive probability in a mixed strategy Nash equilibrium?
Remarks: Strictly dominated strategies are never used with positive probability in a mixed strategy Nash Equilibrium. However, as we have seen in the Second Price Auction, weakly dominated strategies can be used in a Nash Equilibrium.
Can a dominant strategy be a Nash equilibrium?
A dominant strategy solution may also be in Nash equilibrium, although the underlying principles of a dominant strategy render Nash analysis somewhat superfluous.
Can a weakly dominated strategy be a best response?
Here no strategy is strictly or weakly dominated. On the other hand C is a never best response, that is, it is not a best response to any strategy of the opponent.
Which choice is both a Nash equilibrium and dominant strategy for the two prisoners players?
Because defection always results in a better payoff than cooperation regardless of the other player’s choice, it is a strictly dominant strategy for both A and B. Mutual defection is the only strong Nash equilibrium in the game (i.e. the only outcome from which each player could only do worse by unilaterally changing …
What is weakly dominant strategy?
-a weakly dominant strategy is that strategy that provides at least the same utility for all the other player’s strategies, and strictly greater for some strategy. The elimination of dominated strategies is commonly used to simplify the analysis of any game.
Can evolutionary stable strategy be weakly dominated?
Suppose that the pure strategy s∗ is evolutionarily stable. Is it possible that there is some other pure strategy that weakly dominates s∗? Answer: No. It is sufficient to write down the definition of weak domination for a strage s and to show that this contradicts the fact that s∗ is ES.
Which player 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.
Which game strategy prevents rivals from easily predicting a player’s actions?
which game strategy prevents rivals from easily predicting a player’s actions? – know when their rivals deviate from a collusive agreement.