10 Questions
What is the principle of Nash equilibrium?
Each player has no incentive to unilaterally change their strategy
Who is the mathematician after whom the Nash equilibrium is named?
John Nash
How is a Nash equilibrium defined in a non-cooperative game?
Each player knows the equilibrium strategies of the other players and has nothing to gain by changing their own strategy
What constitutes a Nash equilibrium in a game?
When no player can increase their own expected payoff by changing their strategy while the other players keep theirs unchanged
When did the principle of Nash equilibrium originate?
The principle of Nash equilibrium dates back to the time of Cournot in 1838
Who is the mathematician after whom the Nash equilibrium is named?
John Nash
What is the principle of Nash equilibrium based on?
Each player's assumption of the equilibrium strategies of the other players and no player having anything to gain by changing only one's own strategy
When does a set of strategy choices constitute a Nash equilibrium?
When no player can increase their expected payoff by changing their strategy while the other players keep theirs unchanged
How did Cournot contribute to the principle of Nash equilibrium?
Cournot applied the principle of Nash equilibrium to competing firms choosing outputs in 1838
What defines a Nash equilibrium for two players Alice and Bob and their strategies A and B?
If Alice has no other strategy available that does better than A at maximizing her payoff in response to Bob choosing B, and Bob has no other strategy available that does better than B at maximizing his payoff in response to Alice choosing A
Study Notes
Nash Equilibrium
- The Nash equilibrium is a concept in game theory that describes a state where no player can improve their outcome by unilaterally changing their strategy, assuming all other players keep their strategies unchanged.
Origin and Namesake
- The Nash equilibrium is named after John Nash, an American mathematician who introduced the concept in the 1950s.
Definition in Non-Cooperative Games
- In a non-cooperative game, a Nash equilibrium is defined as a set of strategies, one for each player, where no player can improve their payoff by changing their strategy, assuming all other players keep their strategies unchanged.
Constituents of a Nash Equilibrium
- A set of strategies constitutes a Nash equilibrium if no player has an incentive to deviate from their chosen strategy, given the strategies of all other players.
History of the Principle
- The principle of Nash equilibrium originated in the 1950s, introduced by John Nash.
Principles and Assumptions
- The Nash equilibrium is based on the assumption that all players are rational and act in their own self-interest.
Conditions for a Nash Equilibrium
- A set of strategy choices constitutes a Nash equilibrium if no player can improve their payoff by unilaterally changing their strategy, assuming all other players keep their strategies unchanged.
Contributions to the Principle
- Antoine Augustin Cournot, a French mathematician, laid the groundwork for the concept of Nash equilibrium through his work on oligopoly, which was later developed by John Nash.
Nash Equilibrium for Two Players
- For two players, Alice and Bob, with strategies A and B, a Nash equilibrium is defined as a pair of strategies (A, B) where neither player can improve their payoff by unilaterally changing their strategy, assuming the other player keeps their strategy unchanged.
Test your knowledge of game theory with this quiz on Nash equilibrium. See how well you understand the concept and its application in non-cooperative games involving multiple players.
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