Nash Equilibrium

Track 4: Nash Equilibrium*

 

Solitary sadness of my brain, solitary sadness of my brain

Solitary madness of my brain, solitary madness of my brain

Brain, brain, brain

Solitary sadness of my brain, solitary sadness of my brain

Solitary madness of my brain, solitary madness of my brain

Brain, brain, brain

Nash, Nash, Nash equilibrium[1]

If I play my best-response[2]

If you play your best-response

Play mine, play mine, play yours, play yours

If I play my best-response, if you play your best-response

Play mine, play mine, play yours, play yours

Play mine, play mine, play yours, play yours

Show me now your best-response, I will give my best-response

Nash, Nash, Nash equilibrium

If I play my best-response, if you play your best-response[3]

Nash, Nash, Nash equilibrium

Play mine, play mine, play yours, play yours

Play mine, play mine, play yours, play yours 

Nash, Nash, Nash equilibrium


*Text by Marco Marini. Music by Marco Marini, Elisa Pezzuto and Valter Sacripanti. All rights reserved.

Voice: Marco Marini, Elisa Pezzuto. Guitar: David Pieralisi, Marco Marini, Bass: David Pieralisi. Drum: Valter Sacripant, 

Production: Valter Sacripanti. Mastering: Fabrizio De Carolis.

 

[1] The Nash equilibrium is the most well-known equilibrium concept in game theory, due to John Forbes Nash Jr. (1928-2018). It is a strategy profile (i.e. one or more strategies for every player) such that no player has an incentive to deviate from the chosen strategy, given the strategies of other players. In simpler terms, it is a situation in which everyone is doing the best they can, given what everyone else is doing. Nash’s (1950) famous theorem proves that in any finite strategic form game at least one Nash equilibrium in pure or mixed strategies (in probabilities) always exists. 

[2] A best response for every player is a maximizing strategy in response to every rival player’s strategy.

[3] Among the available strategies, a Nash equilibrium has the relevant feature of being, for every player, a best-response to every other player’s strategies.



REFERENCES

 

Nash, John F.(1950). Equilibrium points in n-person games. Proceedings of the national academy of sciences, 36(1), 48-49. 

Nash, John F. (1953)."Two-Person Cooperative Games". Econometrica. 21 (1): 128–140.