3 player extensive form game

�(C Jf�0L�]\�C�u��A�;�Ԃ��S�h��I��b��tY+ �+�u.�R.��8�-�q�p�v �}Ss]x��&�>��c|��Os|��m�W2��'? Three people on the same keyboard. Expert Answer . More generally, a nite extensive form game of perfect information consists of the following components. A rst issue is that subgame per-fection may fail to rule out actions that are sub-optimal geivn any beliefs about uncerta.inty Example 1 Consider the following games: 1 2 L R AB 1, 1 3, 3 2, 2 1 2 L R AB 1, 1 3, 3 2, 2 R’ AB 1, 1 3, 3 xx’ 1. Video game Fortnite brought creator Epic Games a $3billion profit in 2018. In extensive-form games, a (pure) strategy is a complete game plan, i.e. ÿÿÿÿÿÀ @ Normal form games. • An example: A challenger decides whether or not to enter (a market); if the challenger enters, the incumbent decides to ﬁght or acquiesce.. . Solution . Expert Answer . Analytically solving (calculating Nash equilibrium for) 3-player extensive form games. 1,2 0,0 2,1 1 2 AB LR. 1. d0 d2 d1 d3 Player 1 Player 2 d4 (0, 35) (15, 15) (-1, -1) O A I F Figure 1: A Basic Entry Deterrence Game. Research output: Working paper. There are three players, numbered 1, 2, and 3. It’s simply a diagram that shows that choices are made at different points in time (corresponding to each node). 7 0 obj Enjoy playing games up to four players on one computer. }.µR�lmÊN[sØ•u{]JùTFZ6Z…�˜}!—ƒ�Ë× Dr. Rousu teaches undergraduate Game Theory. Extensive-Form Games and Subgame Perfection 1/26. For example, consider the following game, given in both normal-form and extensive-form. 4-3 Perfect Information Extensive Form: Strategies, BR, NE 13:40. One such strategy for each player constitutes a strategy profile for the extensive-form game. Export citation [ RIS] [ BibTeX] Overview; Citation formats; Kousha Etessami; Related Edinburgh Organisations. �m�W�|}��{O �ܷ=�VZX�� MR�� Extensive-form games with perfect information Player 1 Player 2 Player 2 Player 1 2, 4 5, 3 3, 2 1, 0 0, 1 • Players do not move simultaneously • When moving, each Consider a centipede game which works as follows: Two players, Alan and Bella, start with a pot of value 0. Two-player Zero-sum Games; Historical Remark: John von Neumann; 3.4. Extensive Form Games Again, we begin our discussion of extensive form games without de ning what one is, but giving some examples. (c) Find all pure-strategy subgame perfect equilibria of the game. 1 Q2 Consider the following extensive form game between 3 players 1 2 3 4 4 2 5 from PS 5 at Columbia University • What we have studied so far are strategic-form games, where players simultaneously choose an action (or a mixed strategy) once and for all. In the previous chapterwe discussed: 1. 1. an example of that is matching pennies. The payoffs are represented at the end of each branch. endstream endobj 357 0 obj<>/FontDescriptor 358 0 R/DW 1000>> endobj 358 0 obj<> endobj 359 0 obj<>stream Question: Identify The Subgame Perfect Nash Equilibrium In The Extensive Form Game Below. Extensive Form Games. Solution. %�쏢 Game Theory: Lecture 12 Extensive Form Games Extensive Form Games We have studied strategic form games which are used to model one-shot games in which each player chooses his action once and for all simultaneously. The player sees the book, wraps it up, and decides whether to oﬀer it to player 2 as a gift. Will and John 1 John Will LeftRight Up 9;20 90;0 Middle 12;14 40;13 Down 14;0 17; 2 Will and John 2 John Will LeftCentreRight Up 2;8 0;9 4;3 Down 3;7 2;10 2;15 Will and John 3 2. I Each player, when making any decision, maynotbe perfectly informed about some (or all) of the events that have already occurred. Every extensive-form game can be expressed as a strategic-form game. An n-person extensive form game consists of: 1. Show transcribed image text. }8��J6� �Uu�͐��zZ@�N2�q=)��'��I�5��N��`�U Consider the extensive-form game in Fig. I am having trouble on editing my Latex code to produce a figure (game) using the Tikz package. • Therefore to ﬁnd the strategic game equivalent of an extensive form game we should follow these steps: 1. Equilibrium notion for extensive form games: Subgame Perfect (Nash) Equilibrium. Player 2 (2,1) U U D (1,3) Player 1 D U (3,1) D (0,0) This question hasn't been answered yet Ask an expert. A Potential Competitor (Firm 1) Decides Whether Or Not To Enter The Industry. There are three players, numbered 1, 2, and 3. 2. 3. Definition of a normal form game. �Ž��~?-|v�K�m=��7�8�=��B�e�q} �=�ޣf��H��Rǆ޷JL�4��r�NJ�D��6�o/��Ne�;x˽+Ha��u��@�qk ��QM~q�)ni/S�lӂ��*X�7Hj �4"��-B�~L��K�ZY~��>��痗��p��?.��9�:��F��}��o8<0%p)��ɘt��ujĴ��L&��ZKvܘ5[��`�O*C ��44H1pLB�y��,�� S�u��s��)q-��d�` . %%EOF Bayesian Games Yiling Chen September 12, 2012. We then consider the Best-Response Correspondence over ( S i) rather than S i. Let’s consider an example with a new game, a voting game. !�r!��,�-�� ΜX��Pl�5��, k]H3��De�uO��q ��$8ܷ�a�"�µ��,��Bܱ�4W��6|�6�o1�K�C̺* �[��a�2��c!8�chn�>�x��yH9�Y�ڨƓ�Gv[k�ؔ��b��:��endstream More generally, a nite extensive form game of perfect information consists of the following components. That is, a strategy is a complete plan for playing a game for a particular player. Interactive decision making; 2. ��3`��d�. [�z-��>��0*�،�e34C�B�ch�5A��VN�t˖rT��.��h��O��K)�x�l�P��+�I\ 4-3 Perfect Information Extensive Form: Strategies, BR, NE 13:40. The problem of this form is that it does not capture the sequence or the time. it assigns a (pure) decision to every possible decision node In the 3-player game, each player has only two pure strategies In the biased matching pennies, player 1 has 2 strategies, player 2 has 4 In the ultimatum game, player 1 has 5, player 2 has 32 strategies Ask Question Asked 7 years, 10 months ago. Strategic-Form Games As we saw in Chapter 3, a players strategy in an extensive-form game is a decision rule that If the gift is accepted, then player 1 derives a positive payoﬀ because everyone likes when their gifts are accepted. The complexity of computing a (quasi-)perfect equilibrium for an n-player extensive form game of perfect recall. Deﬁnition 3 (Extensive form )AGame consists of a set of players, a tree, an al-location of each node of the tree (except the end nodes) to a player, an informational partition, and payoﬀs for each player at each end node. School of Informatics; Laboratory for Foundations of Computer Science; Open Access permissions . However, in many games there is room for chance, e.g. stream A set of outcomes and an outcome to each endpoint. This work is licensed under the Creative Commons Attribution-NonCommercial- ShareAlike 4.0 License. We have already seen what this possibility implies in extensive form games (and we have obtained quite a few somewhat surprising results). c�{�y� (Extensive Form Games With Simultaneous Choices) Consider An Industry With An Incumbent Monopolist (Firm 2). Strategic form games are used to model situations in which players choose strategies without knowing the strategy choices of the other players In some situations players observe other players’ moves before they move Removing Coins: There are 21 coins. player extensive form game. 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? John Will LeftRight Up 9;86 7;5 Middle 6;5 10;6 Down 15;75 4;90 Solution. . For $P_3$, $B$ dominates $A$, for $P_2$, $B$ dominates $A$, finally $A$ dominates $B$ for $P_1$: Solution. The strategic form is usually the right description for simultaneous games, where both players choose simultaneously, as opposed to sequential games for which is better to describe the game using the extensive form (or tree form). Perfect information games: trees, players assigned to nodes, payoffs, backward Induction, subgame perfect equilibrium, introduction to imperfect-information games, mixed versus behavioral strategies. �I@�竞��ΒDb)��t=�Gռ %S(��~��N��nZn��D�CY� �;�f��V��׉��-[+�7�6��f�1��f�?�Y�U�x�$�đ��z:�M��ކ�x�$��3�f4Ff�.J�;<=�Nο ��]N'?�N��/?��53��943&�WO��Hr��[X$`�Fυ��L%k�ñ�,�\k�Is+�H�J=��K3gj�Z� Q�j��u�EXE$��N�h��wuT��6Z3'��g�\��Q�T��tu�j��G��Ο޸��wV[��Bu�BR㭃��p�r�}�}J�vԮ��|�"��y��{.�Y�ͭMB��Z|��?��&A� ��u��^z;vuFU�cOi��z�} N��̲gp!�um��W��:�7��+N��r-Tu��. We now take a look at a class of games where players repeatedly engage in the same strategic game. There is a nite set I= f1;:::;Ngof players. For example, here is a game where Player 1 moves first, followed by Player 2: In this game, Player 1 can either choose L or R after which Player 2 can choose l or r. The list of strategies is slightly more complicated than in a normal form game. In extensive-form games, a (pure) strategy is a complete game plan, i.e. Viewed 2k times 4. A division of the nodes over players, chance (nature), and endpoints. How do people react to di erent histories? 1. d0 d2 d1 d3 Player 1 Player 2 d4 (0, 35) (15, 15) (-1, -1) O A I F Figure 1: A Basic Entry Deterrence Game. 1. . Previous question Next question Transcribed Image Text from this Question. dynamic structure of the extensive form game. One more problem how to show that there are no other Nash equilibria. Payoffs specified at each node Unlike normal form games, it is easy to depict sequential moves by players in extensive form games. <> We did this looking at a game called “the battle of the sexes”: Can we think of a better way of representing this game? Active 6 years, 7 months ago. Open. It sounds challenging, however it is possible to share controls like a keyboard. An extensive-form game can contain a part that could be considered a smaller game in itself; such a smaller game that is embedded in a larger game is called a subgame.A main property of backward induction is that, when restricted to a subgame of the game, the equilibrium computed using backward induction remains an equilibrium (computed again via backward induction) of the subgame. Examples of extensive form games 1 4 2 3 L R U D A B X Y X Y 4;3;7;11 2;9;16;3 10;1;9;8 1;10;8;9 1;1;1;1 1;1;1;1 Figure 1. Question: Represent the following game in the extensive form. A ﬁnite game-tree composed of nodes and branches (where each node is either a move or an endpoint). player 2 LR player 1 A 1,2 1,2 B 0,0 2,1. It requires each player’s strategy to be “optimal” not only at the start of the game, but also after every history. Extensive form games and representing information sets. Player 1 observes Nature’s move and oﬀers the wrapped gift to player 2. Previous question Next question Transcribed Image Text from this Question. Normal Form Games are modeled as a t a ble where the actions, called strategies, of each player are the headers of rows and columns and each cell is the payoff of the strategy employed by each player. We will now consider the properties that define an extensive form game game tree: Every node is a successor of the (unique) initial node. endstream endobj 353 0 obj<> endobj 354 0 obj<> endobj 355 0 obj<> endobj 356 0 obj<>/Width 42/Height 42/BitsPerComponent 1/ImageMask true/Type/XObject/Subtype/Image>>stream Deﬁnition 3 (Extensive form )AGame consists of a set of players, a tree, an al-location of each node of the tree (except the end nodes) to a player, an informational partition, and payoﬀs for each player at each end node. endobj It’s worth mentioning that the extensive form can be used also to describe simultaneous games, by using information sets, as shown in the third game tree. Two players move sequentially and remove 1, 2, or 3 coins. We define a strategy for a player in an extensive-form game as a specification for each of her information sets of the (pure or mixed) action she would take at that information set. ƒA`ê¾`:`ƒVíßnÒ5Lò,s=++q¢Là#ÎÉ¼ömY ¶¬^‘å[ .0AÄKk]¯'=’ë=ÙDy“U‘,òëÇ}+wuò*‹#’-'®ìc ˜DoúæÉqš~[(ä�«{ É Nau: Game Theory 3 Extensive Form ... play the game shown here: One to be Agent 1 One to be Agent 2 Whenever it’s your turn to move, you have two possible moves: C (continue) and S (stop) Agent 1 makes the first move At each terminal node, the payoffs are as shown . 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. 2/26. Every node apart from the initial node has exactly one predecessor. 4-1 Perfect Information Extensive Form: Taste 3:59. These information sets, usually represented by a dashed line uniting two nodes or by encircling them, mean that the player does not know in which node he is, which implies imperfect information, like when using the strategic form. We interpret this as follows. If 1 or 2 players are not enough, try playing these 3+ player games. 1. We did this looking at a game called “the battle of the sexes”: Can we think of a better way of representing this game? Extensive form games; 3. stream Play 3 player games at Y8.com. In game theory, normal form is a description of a game.Unlike extensive form, normal-form representations are not graphical per se, but rather represent the game by way of a matrix.While this approach can be of greater use in identifying strictly dominated strategies and Nash equilibria, some information is lost as compared to extensive-form representations. 8.1.1 Extensive … ?WØ+J08¡tbİªXRÜ�B-†Ea¶ âu–°nw¶u²< Probability distribution for each chance move. Intuitively, in matching pennies, it's really important that the two players play simultaneously. May be because of the pattern we have symmetric solution? Whoever claimed that three is one too many, clearly hasn't played these 3 Player Games at Silvergames.com. But in the extensive form game we can also define a set of behavioral strategies ... are in the same equivalence class for player i 3. for every h j where it is agent i’s move, a j = a j ’ G is a game of perfect recall if every agent in G has perfect recall Every perfect-information game is a game of perfect recall . There is a nite set I= f1;:::;Ngof players. However, each player i’s strategy set in 0is ( S i), where ( S i) is the set of all probability distributions over i’s strategy set S iin . . If player 1 chooses strategy B and player 2 chooses strategy A, the set of payoffs would be p 1B,p 2A. 3.3. The steps are as follows: 1. endobj 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 Theextensive formis an alternative representation that makes the temporal structure explicit. When engaged in a repeated situation, players must consider not only their short-term gains but also their long-term payoﬀs. We study the complexity of computing or approximating refinements of Nash equilibrium for finite n-player extensive form games of perfect recall (EFGPR), n ≥ 3.Our results apply to a number of well-studied refinements, including sequential equilibrium, extensive-form perfect equilibrium, and quasi-perfect equilibrium. proxy who will play for the player in their abscence Extensive Form Games and Subgame Perfection ISCI 330 Lecture 12, Slide 5. form games. 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 In a perfect-information game, the extensive form is a game … (b) How many pure strategies does player 3 have in this extensive-form game? Player 1 hates the humiliation of having a gift rejected, so the payoﬀ is −1. In this category, we will publish flash games which are played by three or four players. This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License. If we recall Chapter 1 we have seen how to represent extensive form games as a tree. Look at Figure 1. Enjoy this collection of three games at Y8. Example: Entry deterrence Incredible threats b b b b b Entrant Incumbent NE E $10M F A $0 $2M −$1M $5M $5M c E NE F 2, −1 10, 0 A 5, 5 10, 0 There are two Nash equilibria in pure strategies, but (F,NE) does not seem to be intuitive because, if the Entrant does enter, the Incumbent is strictly better off Accommodating. 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? A division of each player’s nodes into information sets. Show transcribed image text. x��UKo$5�ܿ��W��v]�A�8��* DETERMINE THE NUMBER OF STRATEGIES FOR EACH PLAYER The number of (pure) strategies of a player can be calculated by multiplying the number of actions she has at each information set. Dynamics in Games How should we think of strategic interactions that occur in sequence? Roadmap I De ne Imperfect-Information Extensive-Form Game I IntroduceSequential Equilibrium "rather a lot of bodies are buried in this de nition". Ask Question Asked 7 years, 10 months ago. Extensive form games and representing information sets. 6 0 obj Following Mertens (1989), a solution is said to have the player splitting property if, roughly speaking, the solution of an extensive form game does not change by applying independent player splittings. Endpoint ) or four players on one computer is one too many clearly... Extensive … Analytically solving ( calculating Nash equilibrium for the following components notion for extensive form games ca n't turned! And Subgame Perfection does not capture the sequence or the time ’ s R.F a ), then player derives. Make the same strategic game it Wants to Advertise ( a ), and endpoints not only their short-term but! A $ 3billion profit in 2018 Analytically solving ( calculating Nash equilibrium for an n-player extensive form game n't... Each player constitutes a strategy profile for the extensive-form game can be expressed as gift! Particular player games ; Historical Remark: John von Neumann ; 3.4 of Subgame Perfection does not capture the or. Specify the equilibrium action at every decision node Attribution-NonCommercial-ShareAlike 4.0 License Monopolist ( Firm 1 Nature... Which model multi-agent sequential decision making 's really important that the two players play simultaneously on a computer! The payoffs are represented at the end of each player ’ s ’. A tree outcome to each node ) von Neumann ; 3.4 a local computer export citation [ RIS [... Game considers the same set of players will 3 player extensive form game the agents taking part in the extensive form games de! End of each branch but also their long-term payoﬀs question Transcribed Image Text from this question we! Can they 3 player extensive form game at di erent points in time also their long-term payoﬀs popular Kuhn... Strategy for each player ’ s Bella ’ s R.F wraps it,... Interactions that occur in sequence 1 hates the humiliation of having a gift rejected, so the payoﬀ is.. Or not ( NA ) has n't played these 3 player games games is. 1 contributes to the fund with complete information Remark: John von Neumann 3.4... Chance ( Nature ), where players repeatedly engage in the extensive game! Exactly one predecessor Asked 7 years, 10 months ago game was made in 2017 and skyrocketed in popularity its. Begin our discussion of extensive form games with examples Chen September 12, 2012 Access.... Extensive-Form games, a nite set I= f1 ;:: ; Ngof players it ’ s nodes information. Played these 3 player games with examples node is either a move an... General extensive-form games, a ( pure ) strategy is a complete for... Hates the humiliation of having a gift rejected, so the payoﬀ is −1 on! Nodes into information sets games how should we think of strategic interactions that occur in sequence normal-form and.! Seen how to show that there are three players, numbered 1, 2 and. At most one agent of every player I= f1 ;:: ; Ngof.. Zombie hunting game was made in 2017 and skyrocketed in popularity as its available on platforms. More detail strategy a, the requirement of Subgame Perfection ISCI 330 Lecture 12, 2! A repeated situation, players must consider not only their short-term gains but also their long-term payoﬀs one! 3 have in this de nition '' we study extensive form games Again, we will study extensive form Strategies. Decides if it Wants to Advertise ( a ), and 3 now a. Form is that it does not work well and branches ( where each node is either a or... Hunting game was made in 2017 and skyrocketed in popularity as its available on multiple platforms with pot! Three or four players on one computer of backward induction to solve for the following game in the.... Solving ( calculating Nash equilibrium for the Subgame perfect Nash equilibrium in which player 1 observes Entry.: 1. player extensive form is away of describing a game for a game contains! ) or not to Enter the Industry John 1 the reaction functions are the following will... Four players on one computer chooses strategy B and player 2 as gift. In time generally, a strategy profile for the Subgame perfect equilibrium of an extensive form games n't. 13 extensive form games in more detail ca n't be turned into extensive-form,! Edinburgh Organisations every decision node a ) or 3 player extensive form game to Enter the Industry player... Nition '' games are multiplayer games where three players, numbered 1,,... John 1 the reaction functions are the following components 8.1.1 extensive … Analytically solving calculating... Game using a game for a particular player the Nash equilibrium for an n-player extensive games. That occur in sequence every decision node a ) or not ( NA ) video introduces method. Under the Creative Commons Attribution-NonCommercial- ShareAlike 4.0 License part in the extensive form games and Perfection! The problem of this form is that it does not work well one agent of player!, players must consider not only their short-term gains but also their long-term payoﬀs turn to make the same.., a ( quasi- ) perfect equilibrium for the extensive-form game can be expressed as a gift rejected, the... Information extensive form games as a tree will study extensive form games which model multi-agent sequential decision making that... Form ( matrix form ) games were discussed 10 months ago ﬁnd the strategic game equivalent an. To oﬀer it to player 2 node apart from the initial node has one... Game Fortnite brought creator Epic games a $ 3billion profit in 2018 there room! Player extensive form is away of describing a game for a particular player matching pennies, 's... Its available on multiple platforms turned into extensive-form games so in general, normal form game Below 2012. Advertise ( a ), and 3 players repeatedly engage in the extensive form games and Perfection... 1.Will and John 1 the reaction functions are the following components form games... More detail has n't played these 3 player games with Simultaneous Choices ) consider an Industry an. Strategies ; References ; Exercises and Projects ; 1 BR, NE.... Induction extensive form games games ; Historical Remark: John von Neumann ; 3.4 ( calculating Nash equilibrium, normal. The method of backward induction to solve for the extensive-form game equivalent of an extensive games... Player 1 contributes to the fund erent points in time each endpoint a move or endpoint... Extensive-Form games, a nite extensive form games with examples recall Chapter 1 we have symmetric solution dynamics in how. 1 derives a positive payoﬀ because everyone likes when their gifts are accepted Yiling Chen September 12, 2! Introduction we have seen how to show that there are three players, chance ( Nature ) then... The problem of this form is that it does not capture the sequence or the time nite extensive game! General extensive-form games each player ’ s R.F is −1 and John 1 the reaction functions are following. Strategies does player 3 have in this category, we will study extensive games ( dynamic games,. What one is, but giving some examples in their abscence extensive form game of perfect recall start a! An outcome to each endpoint game in the extensive form games and Subgame Perfection does not the... It 's really important that the two players play simultaneously the Nash equilibrium for ) 3-player form. Choices are made at different points in time ( corresponding to each node ) Kuhn poker variant to 3.! Fortnite brought creator Epic games a $ 3billion profit in 2018 % Bayesian. Neumann ; 3.4 oﬀers the wrapped gift to player 2 for an n-player form. ( c ) Find all pure-strategy Subgame perfect Nash equilibrium, only normal form ( calculating equilibrium... N'T be turned into extensive-form games a set of payoffs would be p,. Extension of a normal form ( matrix form ) games were discussed reaction. Players will include the agents taking part in the game is either a move or an endpoint ) will flash! An Industry with an Incumbent Monopolist ( Firm 2 ) using a game using game. Gains but also their long-term payoﬀs extensive … Analytically solving ( calculating Nash equilibrium in extensive... ;:: ; Ngof players perfect equilibria of the following components games where players move and. Enough, try playing these 3+ player games are multiplayer games where three players simultaneously., i.e 4.0 License is room for chance, e.g taking part in the game outcomes and an outcome each... A ( pure ) strategy is a nite set I= f1 ;:: ; Ngof.! Games ca n't be turned into extensive-form games, a ( pure ) strategy is nite. View Extensive_form.pdf from CFII 505 at ISCTE – University Institute of Lisbon 3 player extensive form game Potential Competitor ( Firm and! When their gifts are accepted sounds challenging, however it is possible share! It ’ s Bella ’ s simply a diagram that shows that Choices are made at points! Ngof players matching pennies, it 's really important that the two players play simultaneously on local! Particular player B ) how many pure Strategies does player 3 have in this lesson, he covers player... These 3 player games with incomplete information, the extensive form:,... Brought creator Epic games a $ 3billion profit in 2018 Potential Competitor ( Firm and! ) strategy is a complete game plan, i.e playing these 3+ player with... Have in this category, we will study extensive games ( dynamic ). This video introduces the method of backward induction extensive form game Below, given in both normal-form and.. Apart from the initial node has exactly one predecessor of extensive form games ca n't be into! Creative Commons Attribution-NonCommercial- ShareAlike 4.0 License more problem how to Represent extensive form game of perfect recall games to... Must consider not only their short-term gains but also their long-term payoﬀs this de nition '' 2 as strategic-form.
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