What I am taking about is life and dead
What I am taking about is life and dead
Life and dead, life and dead!
What I am talking about repeated game[1]
What I am talking about repeated game
Finite horizon, infinite horizon[2]
What I want to say now, if a Nash equilibrium
of the game exists, exists
What I want to say now, it’s a perfect equilibrium
of the game, in a finite horizon, finite horizon[3]
What I want to say now, cooperation equilibrium
of the game in an infinite horizon, infinite horizon[4]
It’s all about patience, it’s all about patience
What I am taking about repeated game
What I am taking about repeated game
Finite horizon, infinite horizon
What I want to say now, if a Nash equilibrium
of the game exists, exists
What I want to say now, it’s a perfect equilibrium
of the game in a finite horizon, finite horizon
What I want to say now, cooperation equilibrium
of the game, in an infinite horizon, infinite horizon
It’s all about patience, it’s all about patience.[5]
*Text by Marco Marini. Music by Marco Marini, Elisa Pezzuto and Valter Sacripanti. All rights reserved.
Voices: Marco Marini, Elisa Pezzuto. Guitars: David Pieralisi, Marco Marini, Bass: David Pieralisi. Drum: Valter Sacripanti,
Production: Valter Sacripanti. Mastering: Fabrizio De Carolis.
[1] A repeated game is a game where a certain constituent game (sometimes called stage game) is played multiple times. Players have the opportunity to observe the actions of other players in previous rounds and adjust their strategies accordingly.
[2] A repeated game is a finite (infinite) horizon when is played for a finite (infinite) number of times (periods).
[3] According to Reinhard Selten’s (1965) theorem, if the stage game possesses a unique Nash equilibrium, such equilibrium strategy repeated at each stage is the unique (subgame perfect Nash) equilibrium of the repeated game with finite horizon.
[4] In a repeated game with an infinite horizon a given cooperative payoff allocation among players can arise as a subgame perfect equilibrium of the entire game if players are sufficiently patient, namely their discount factor is sufficiently high and close to one, which basically means that they prefer more a balance payoff in every period rather than an immediate advantage but lower payoffs in the future.
[5] The so called Folk Theorem, (for instance, James Friedman, 1971) suggests that if players are patient enough and far-sighted, i.e. with a discount factor close to one, then the repeated interaction can result in virtually any average payoff feasible and individually rational at the subgame-perfect Nash equilibrium of the game,
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