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For finitely repeated games, if a stage game has only one unique Nash equilibrium, the subgame perfect equilibrium is to play without considering past actions, treating the current subgame as a one-shot game. An example of this is a finitely repeated Prisoner's dilemma game. The Prisoner's dilemma gets its name from a situation that contains ...
Strict stationary subgame-perfect equilibria: [6] An outcome is attainable in strict-stationary-subgame-perfect-equilibrium, if for every player the outcome is strictly better than the player's minimax outcome (note that this is not an "if-and-only-if" result). To achieve subgame-perfect equilibrium with the overtaking criterion, it is required ...
This would have two subgame perfect equilibria: (Proposer: S=0, Accepter: Accept), which is a weak equilibrium because the acceptor would be indifferent between their two possible strategies; and the strong (Proposer: S=1, Accepter: Accept if S>=1 and Reject if S=0). [3] The ultimatum game is also often modelled using a continuous strategy set.
The Stackelberg model can be solved to find the subgame perfect Nash equilibrium or equilibria (SPNE), i.e. the strategy profile that serves best each player, given the strategies of the other player and that entails every player playing in a Nash equilibrium in every subgame.
In the subgame where player 1 did offer x 2 ' where x 2 > x 2 ' > d x 2, clearly player 2's best response is to accept. To derive a sufficient condition for subgame perfect equilibrium, let x = (x 1, x 2) and y = (y 1, y 2) be two divisions of the pie with the following property: x 2 = d y 2, and; y 1 = d x 1, i.e. x = (x 1, x 2), and
If a node is contained in the subgame then so are all of its successors. If a node in a particular information set is in the subgame then all members of that information set belong to the subgame. It is a notion used in the solution concept of subgame perfect Nash equilibrium, a refinement of the Nash equilibrium that eliminates non-credible ...
In game theory, the one-shot deviation principle (also known as the single-deviation property [1]) is a principle used to determine whether a strategy in a sequential game constitutes a subgame perfect equilibrium [2]. An SPE is a Nash equilibrium where no player has an incentive to deviate in any
The "deterrence strategy" is not a Subgame perfect equilibrium: It relies on the non-credible threat of responding to in with aggressive. A rational player will not carry out a non-credible threat, but the paradox is that it nevertheless seems to benefit Player A to carry out the threat.