This lecture shows how games can sometimes have multiple subgame perfect equilibria. Most games have only one subgame perfect equilibrium, but not all. When players receive the same payoff for two different strategies, they are indifferent and therefore may select either. This causes multiple SPE.
What is a strategy in a repeated game?
2. The definition of a strategy in a repeated game determines player’s choice for each history, in particular for histories that cannot be outcomes of the repeated game. As a result the joint strategy from item (i) is not a unique Nash equilibrium of G(k) when players have two or more strategies in the stage game.
How do you find the Subgame perfect equilibrium?
Finding subgame-perfect equilibria The subgame-perfect Nash equilibrium is normally deduced by “backward induction” from the various ultimate outcomes of the game, eliminating branches which would involve any player making a move that is not credible (because it is not optimal) from that node.
What is the important distinction for a game to be considered an infinitely repeated game?
Finitely vs infinitely repeated games Infinite games are those in which the game is being played an infinite number of times. A game with an infinite number of rounds is also equivalent (in terms of strategies to play) to a game in which the players in the game do not know for how many rounds the game is being played.
What is SPNE game theory?
In game theory, a subgame perfect equilibrium (or subgame perfect Nash equilibrium) is a refinement of a Nash equilibrium used in dynamic games. Here one first considers the last actions of the game and determines which actions the final mover should take in each possible circumstance to maximize his/her utility.
Are all subgame perfect equilibria Nash equilibria?
Here one first considers the last actions of the game and determines which actions the final mover should take in each possible circumstance to maximize his/her utility. The set of subgame perfect equilibria for a given game is always a subset of the set of Nash equilibria for that game.
Is a grim trigger Nash equilibrium a Subgame perfect Nash equilibrium?
, and this is true for every subgame. Therefore, the strategy for the infinitely repeated prisoners’ dilemma game is a Subgame Perfect Nash equilibrium….The infinitely repeated prisoners’ dilemma.
| Prisoner B Prisoner A | Stays Silent (Cooperate) | Betray (Defect) |
|---|---|---|
| Betray (Defect) | 2, -1 | 0, 0 |
Are all Subgame perfect equilibria Nash equilibria?
How do you find the perfect equilibrium of a subgame?
The subgame perfect equilibria are computed as follows. First compute a Nash equilibrium of the subgame, then fixing the equilibrium actions as they are (in this subgame), and taking the equilibrium payoffsinthissubgame as the payoffs for entering the subgame, compute a Nash equilibrium in the remaining game.
Can a finitely repeated game have multiple Nash equilibria?
If a simultaneous move game has multiple Nash equilibria, then there are many subgame perfect equilibria of the finitely repeated game. Some of these involve the play of strategies that are collectively more profitable for players than the one-shot stage game Nash equilibria, (e.g. Aa, Ba, Ab in the last game studied).
Do players know when to stop repeating a game?
Infinitely repeated games also model a long-term relationship in which the playersdo not know a priori when they will stop repeating the game: there is nopre-ordained number of repetitions.
