# subgame game theory

In the game on the previous slide, only (A;R) is subgame perfect. A subgame on a strictly smaller set of nodes is called a proper subgame. For example, the above game has the following equilibrium: Player 1 plays in the beginning, and they would have played ( ) in the proper subgame, as In game theory, a subgame perfect equilibrium (or subgame perfect Nash equilibrium) is a refinement of a Nash equilibrium used in dynamic games.A strategy profile is a subgame perfect equilibrium if it represents a Nash equilibrium of every subgame of the original game. THEORY: SUBGAME PERFECT EQUILIBRIUM 1. A subgame-perfect Nash equilibrium is a Nash equilibrium because the entire game is also a subgame. The first game involves players’ trusting that others will not make mistakes. In game theory, a subgame is a subset of any game that includes an initial node (which has to be independent from any information set) and all its successor nodes.It’s quite easy to understand how subgames work using the extensive form when describing the game. A subgame perfect Nash equilibrium is a Nash equilibrium in every induced subgame of the original game. Extensive Form Games • Strategic (or normal) Form G ames – Time is absent • Extensive Form Games – Capture time – With the introduction of time, players can adopt strategies contingent ... • The subgame of game G that follows history h is the following game … The second game involves a matchmaker sending a couple on a date. There is a unique subgame perfect equilibrium,where each competitor chooses inand the chain store always chooses C. For K=1, subgame perfection eliminates the bad NE. In game theory, a subgame is any part (a subset) of a game that meets the following criteria (the following terms allude to a game described in extensive form):. It has three Nash equilibria but only one is consistent with backward induction. In the following game tree there are six separate subgames other than the game itself, two of them containing two subgames each. We show the other two Nash equilibria are not subgame perfect: each fails to induce Nash in a subgame. Each game is a subgame of itself. ; If a node is contained in the subgame then so are all of its successors. Subgame game definition at Game Theory .net. Every path of the game in which the outcome in any period is either outor (in,C) is a Nash equilibrium outcome. There can be a Nash Equilibrium that is not subgame-perfect. the initial node is in a singleton information set). It has a single initial node that is the only member of that node's information set (i.e. Note that this includes subgames that … ” These are the games that constitute the rest of play from any of the game’s information sets. is called a subgame. Subgame perfect equilibria discovered by backward induction are Nash equilibria of every subgame.. updated: 15 August 2005 A subgame perfect Nash equilibrium is a Nash equilibrium in which the strategy profiles specify Nash equilibria for every subgame of the game. For large K, isn’t it more reasonable to think that the A subset or piece of a sequential game beginning at some node such that each player knows every action of the players that moved before him at every point. Subgames • A subgame is a part of an extensive form game that constitutes a valid extensive form game on its own Deﬁnition A node x initiates a subgame if all the information sets that contain either x or a successor of x contain only nodes that are successors of x. 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