The subgame initialized at x is the extensive form game … Levent Koc¸kesen (Koc¸ University) Extensive Form Games II 10 / 51 Subgame Perfect Equilibrium Proposition Let Γ be an extensive form game with perfect information and s∗ be a subgame perfect equilibrium of Γ. It requires each player’s strategy to be “optimal” not only at the start … I player 1: 3; player 2: 8 I Overall, a pure strategy for a player in a perfect-information game is a complete specification of which deterministic action I A sequential equilibrium is a Nash equilibrium. extensive form to strategic form as well. has the two extensive form game representations shown. However, subgame perfection takes care of this issue by requiring a form of sequential rationality, even offthe equilibrium path. It requires each player’s strategy to be “optimal” not only at the start of the game, but also after every history. To find SPE 1. Subgame Perfect Equilibrium Extensive form game strategies A pure strategy of a player specifies an action choice at each information set of that player Definition A strategy profile in an extensive form game is a subgame perfect equilibrium (SPE) if it induces a Nash equilibrium in every subgame of the game. Equilibrium notion for extensive form games: Subgame Perfect (Nash) Equilibrium. I Thm: Every nite extensive-form game with perfect recall has a sequential equilibrium. For finite horizon games, found by backward induction. A Nash equilibrium of a finite extensive-form game Γ is a Nash equilibrium Centipede, normal form: The equilibrium 1, 0 1, 0 0, 4 Take the money Wait Player 2 2, 2 Player 1 Split the money Take the money 24 Look Ahead and Reason Back aThis is also called Backward Induction aBackward induction in a game tree leads to a subgame perfect equilibrium aIn a subgame perfect equilibrium, best … extensive-form game with perfect recall if it issequentially rationalandconsistent. In the following game tree there are six separate … For infinite horizon games, characterization in terms of one … In extensive games with perfect information, there is the possibility that a player will face a situation that is in-consistent with the presumed equilibrium being played. Subgame Perfect Nash Equilibrium is a re nement of Nash Equilibrium It rules out equilibria that rely on incredible threats in a dynamic environment All SPNE are identi ed by backward induction 26/26. Clearly every SPE is a NE but not conversely. Equilibrium notion for extensive form games: Subgame Perfect (Nash) Equilibrium. I With perfect information, a subgame perfect equilibrium is a sequential equilibrium. Subgames Definition of a subgame. Then s∗ is a backward induction equilibrium of Γ. Definition 1. The solution concept we now define ignores the sequential nature of the extensive form and treats strategies as choices to be made by players before all play begins (i.e. Title: Game Theory 2: Extensive-Form Games and Subgame Perfection Created Date: In that … 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. These requirements eliminate the bad subgame-perfect equilibria by requiring players to have beliefs, at each information set, about which node of the information set she has reached, conditional on being … just like in strategic games). Definition of subgame perfect equilibrium. The concept of perfect Bayesian equilibrium for extensive-form games is defined by four Bayes Requirements. 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. Game Theory: Lecture 13 Extensive Form Games Introduction We have studied extensive form games which model sequential decision making. Recap Perfect-Information Extensive-Form Games Subgame Perfection Pure Strategies I In the sharing game (splitting 2 coins) how many pure strategies does each player have? In an extensive form game, a node \(x\) is said to initiate a subgame if and only if \(x\) and all successors of \(x\) are in information sets containing only successors of \(x\).
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