# Do all finite games have a Nash equilibrium?

**Every game with a finite number of players and action pro- files has at least one Nash equilibrium**.

## Are there games with no Nash equilibrium?

In the game rock, scissors, paper, there is (with pure strategies) no Nash equilibrium. However, the strategies can be mixed.## 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.## Does every finite extensive form game have a subgame perfect equilibrium?

Theorem (Existence of subgame perfect equilibria) In a finite extensive form game with perfect information, there is always a subgame perfect equilibrium in pure strategies.## Can a game may have multiple Nash equilibria or none at all?

Under the Nash equilibrium, a player does not gain anything from deviating from their initially chosen strategy, assuming the other players also keep their strategies unchanged. A game may include multiple Nash equilibria or none of them. Nash equilibrium is one of the fundamental concepts in game theory.## 3. Finding Pure Strategy Nash Equilibrium in Finite Simultaneous-Move Games (Game Theory Playlist 3)

## What is an example of no Nash equilibrium?

If the pennies are matching heads or tails, then player A keeps both pennies. If the pennies don't match, player B keeps both pennies. This is an example of a game that has no Nash equilibrium, as the loss or gain of each player is directly correlated to the loss or gain of the other.## Can a game have a Nash equilibrium even though neither player has a dominated strategy?

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.## How many pure Nash equilibria does a finite strategic game have?

There are two pure-strategy Nash equilibria, (yes, yes) and (no, no), and no mixed strategy equilibria, because the strategy "yes" weakly dominates "no". "Yes" is as good as "no" regardless of the other player's action, but if there is any chance the other player chooses "yes" then "yes" is the best reply.## Is it possible to have no pure strategy Nash equilibrium?

Nash Equilibrium in Mixed StrategiesSome games, such as Rock-Paper-Scissors, don't have a pure strategy equilibrium. In this game, if Player 1 chooses R, Player 2 should choose p, but if Player 2 chooses p, Player 1 should choose S.