Backward Induction and Subgame Perfection In extensive-form games, we can have a Nash equilibrium profile of strategies where player 2’s strategy is a best response to player 1’s strategy, but where she will not want to carry out her plan at some nodes of the game tree. There are two different, but equivalent, ways of defining a game tree. 5. Connection between extensive and normal form games. Let’s introduce a way of incorporating the timing of actions into the game explicitly Use a game tree to represent the sequential aspect of choices 11/26. What is backward induction? But First! The first, used by Kuhn, defined a game tree as a finite acyclic connected graph with a distinguished initial node or root. Extensive form games: notation and basic results. 4-1 Perfect Information Extensive Form: Taste 3:59 ... Game Theory 2: Extensive-Form Games and Subgame Perfection Created Date: 3 Backward Induction Extensive Form Games Lecture 7, Slide 2. Lecture 6: Dynamic Games/Extensive-form Games Backward Induction and Sequential Rationality Applying common knowledge of sequential rationality justi–es solving games by backwards induction Players at the last stage will take the optimal action if they ever reach those nodes Players at the penultimate stage know that this is how Perfect information games: trees, players assigned to nodes, payoffs, backward Induction, subgame perfect equilibrium, introduction to imperfect-information games, mixed versus behavioral strategies. Extensive-Form Games Backward Induction • The easiest way of approaching any extensive-form game is to use backward induction, which is the procedure of solving an extensive-form game by first considering the last mover’s decision. Extensive Games Subgame Perfect Equilibrium Backward Induction Illustrations Extensions and Controversies Finding SPNE in finite horizen games: backward induction (逆向归纳) • An extensive game is finite if it has finite horizon (i.e., the length of the longest terminal history is finite), and the number of terminal histories is finite. Then, the optimal action of the next-to-last moving … A definition of an extensive form game Γ starts with the notion of a game tree. Rollback (often called backward induction) is an iterative process for solving finite extensive form or sequential games.First, one determines the optimal strategy of the player who makes the last move of the game. In this Chapter we will take a look at another important aspect of extensive form games. Perfect-Information Extensive-Form GamesSubgame PerfectionBackward Induction Introduction The normal form game representation does not incorporate any notion of sequence, or time, of the actions of the players Nau: Game Theory 3 Extensive Form The sharing game is a game in extensive form A game representation that makes the temporal structure explicit Doesn’t assume agents act simultaneously Extensive form can be converted to normal form, so previous results carry over But there are additional results that depend on the temporal structure Investigated an analysis technique for extensive form games called backwards induction. In the of, The first mover to act in a sequential game gets a … Extensive form games. Backward Induction 10/26. When can backward induction be used to arrive at the equilibrium for a game? The procedure of solving an extensive-form game by first considering the last mover's decision. It should be relatively straightforward to see that we can represent any extensive form game in normal form.
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