is matching pennies a coordination game

In this case there are two pure Nash equilibria: either both swerveto the left, o… ECO290E: Game Theory Lecture 5 Mixed Strategy Equilibrium Zero-Sum Game Matching Pennies No Nash Equilibrium? The distinguishing feature of zero-sum game is that each player would like to outguess the other since there is no “win-win” situation. Each player needs a coin, preferably the same type of coin for each player. Matching Pennies is that the game between two conformists and that between two rebels can both be naturally deflned: the (pure) coordination game and the (pure) anti-coordination game. Matching Pennies is a good example of a game where mixed strategies are useful: one could choose to play Heads or Tails with 50% chance each. The row player can play a if he can reasonably believe that the column player could play A, since a is a best response to A. Coordination games also have mixed strategy Nash equilibria.In the generic coordination game above, a mixed Nash equilibrium is given by probabilities p = (d-b)/(a+d-b-c) to play Up and 1-p to play Down for player 1, and q = (D-C)/(A+D-B-C) to play Left and 1-q to play Right for player 2. Major strategic paradigms (social dilemma, coordination, and randomization) are implemented with the default setup. ... Pareto coordination game (technical) prisoner's dilemma (informal) prisoner's dilemma (technical) pure coordination game (technical) Top. We need to allow players to randomize their choices. Matching pennies (traducibile con abbinamento dei penny) è un semplice esempio di gioco utilizzato in teoria dei giochi.Si tratta di due strategie equivalenti a carta forbice sasso.Matching pennies, chiamato anche Pesky Little Brother o Parity game, è principalmente usato per illustrare il concetto di strategie miste e di una strategia mista di equilibrio di Nash. The payoff matrix for this game looks something like this: Therefore, we can observe that (2, 1) and (1, 2) are the Pareto optimal outcomes in this case. General-Sum Games (a.k.a. In a simplified example, assume that twodrivers meet on a narrow dirt road. constant-sum games) Examples: Rock-paper-scissors, matching pennies. game theory lecture4博弈论_日语学习_外语学习_教育专区 308人阅读|2次下载. Pitching pennies (or: Pitch and Toss, Liney or Jingles) ist ein coordination game for two players or more. 4 Modelling philosophy • General (game theory) • Precise (game theory) • Progressive (behavioral econ) The MISMATCHER wants the pennies not to match.. Players both simultaneously select either … Matching Pennies is more basic than the coordination game and the anti-coordination game, because they are both implied in it. B) matching pennies. Game Theory 101: Matching Pennies and Mixed Strategy Nash Equilibrium - Duration: 4:29. We embed the classical game within the quantum game such that the classical MP game … In game theory, coordination games are a class of games with multiple pure strategy Nash equilibria in which players choose the same or corresponding strategies.. Matching pennies is an asymmetric game. UBC Online Game Theory Experiments Week One TCP Backoff Matching Pennies Coordination Battle of the Sexes Keynes Beauty Contest Penalty Kick Travellers Dilemma Week Four Centipede Ultimatum Rainbow Warship Week Five Repeated Prisoner's Dilemma Rock Paper Scissors Repeated Battle of the Sexes Week Seven Multi-Round Auction A quantum version of the matching pennies (MP) game is proposed that is played using an Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) setting. If this game is a coordination game, then the following inequalities in payoffs hold for player 1 (rows): A > B, D > C, and for player 2 (columns): a > c, d > b. The Matching Pennies Game Matching pennies is a simple two-player prediction game.. The matching pennies game is mathematically equivalent to a game children play called "choosing" or " odds and evens ", where two players simultaneously display one or two fingers, with the winner determined by whether or not the number of fingers match. Matching Pennies is not the only simple game that fails to have a pure-strategy Nash equilibrium. Table1.Matching pennies and coordination matrix games. Look at the usual two-person games: L R T 2,1 0,0 B 0,0 1,2 Battle of the Sexes; three equilibria 0-13. A quantum version of the matching pennies (MP) game is proposed that is played using an Einstein–Podolsky–Rosen–Bohm (EPR–Bohm) setting. This program sets up a two-player, two-decision game, e.g. The theoretical communication model by Gossner et al. This game has three subgames: one after Player 1 chooses Head, one after Player 1 chooses Tail, and the game itself. matching pennies (technical) Top. A zero-sum game is one in which the gains of one player are the losses of another, hence their payoffs always sum to zero. It turns out that the above network extension of Matching Pennies can be used to investigate the phenomenon of fashion, and thus it is named as the fashion game. The game is played almost worldwide under lots of different names. Specifically, in facing a matching pennies game, subjects require an ‘ambiguity’ premium to play when the opponent makes a conscious move compared to a random move. Pitching pennies (or: Pitch and Toss, Liney or Jingles) ist ein coordination game for two players or more. Since Matching pennies is the same game as Two Finger Morra (with matching one or two fingers rather than matching heads or tails), it would be useful to mention this and include a link to the wikipedia article on Morra 120.156.241.59 23:38, 4 March 2010 (UTC) Matching pennies is used primarily to illustrate the concept of mixed strategies and a mixed strategy Nash equilibrium.. O. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. (2003):RiskAverseBehavior in Generalized Matching Pennies Games, Games and Economic Behavior 45, 97}, year = {2005}, pages = {113}} Share. Matching pennies. all games) Examples: Bach or Stravinsky, three-player matching pennies, prisoner’s dilemma SA3 Œ C11 Repeated Games You can’t learn if you only play a game once. The Matching Pennies Game Matching pennies is a simple two-player prediction game.. You can set payoffs, the matching protocols, and the numbers of rounds. Matching Pennies is a famous zero-sum game of pure conflict with two actions {head, tail}, with a payoff bimatrix shown in Figure 3.1.The minimax theorem guarantees that all zero-sum matrix games are solvable, which means we can determine strategies that maximize player payoffs (Osborne and Rubinstein, 1994). In this game the strategy profiles {Left, Up} and {Right, Down} are pure Nash equilibria, marked in gray. Downloadable! Matching Pennies game without observation where player 1 plays first 2 −1,1 2 1 Figure 3: Matching pennies games without observation when player 1 moves first • H is the set of all terminal histories where a terminal history is a path of actions such … See Fig. Major strategic paradigms (social dilemma, coordination, and randomization) are implemented with the default setup. Equipment. C) Battle of the sexes. 2, "pass" is represented by a payoff of10, and "collide" by a payoff of 0. Recall the child’s game rock-paper-scissors, in which rock beats 1. Let's begin by looking at the matching pennies game. Matching Pennies definition at Game Theory .net. (2006) (GHN henceforth) based on the matching pennies game has recently been implemented by García-Gallego et al. 3 Battle of the Sexes (Coordination game). http://www.games-wiki.org/w/index.php?title=Pitching_pennies&oldid=3348, Do the players have to pitch simultaneously or one after the other, May the coin hit the obstacle and bounce back, or does this mean the player has automatically lost the round, May enemy coins be touched (and moved) my one's coin. A game of “matching pennies ... – Neo-Keynesian macroeconomic coordination – bidding, consumer choice • Teaching – contracting, collusion, inflation policy. OpenURL . Matching pennies is a symmetric zero-sum game. R. Rock Paper Scissors (technical) Top. Scenario To determine who is required to do the nightly chores, two children first select who will be represented by "same" and who will be represented by "different." The expected payoff is zero so the game is fair to both players. • Rational Pigs. Goeree,J.K.,Holt,CharlesA.,andPalfrey,T. Now consider the matching penny game with perfect information in Figure 3.4. (2013) (GHR henceforth) in the lab, emphasizing the transmission of information among players with aligned incentives. Team Games Examples: Coordination game. The game is played almost worldwide under lots of different names. The game is played between two players, Player A and Player B. This game is a simple example of a coordination game (payoffs are higher when players make similar choices). One well-known game with payoff asymmetries is the matching pennies game. It turns out that the above network extension of Matching Pennies can be used to investigate the phenomenon of fashion, and thus it is named as the fashion game. Matching pennies: In game theory, rationalizability is a solution concept. The MATCHER aims to see matching pennies. It is a simplified version of Rock, Scissors, Paper - with only two symbols, HEADS and TAILS.. One player is the MATCHER, the other player is the MISMATCHER.. The players then reveal their choices simultaneously. Abstract. Which of the following games is a constant-sum game? The Matching pennies game: The objective of the game is different for the two players. The MATCHER aims to see matching pennies. Both players are given coins with two faces a … Each player has a penny and must secretly turn the penny to heads or tails. This paper reports data for coordination game experiments with random matching. S. A) coordination game. Matching pennies has also found many interesting applications. Types of Games Zero-Sum Games (a.k.a. The best-known example of a 2-player anti-coordination game is the game of Chicken (also known as Hawk-Dove game). Prisoner's Dilemma, Coordination, Matching Pennies, Battle of Sexes, etc. Matching Pennies is a basic game theory example that demonstrates how rational decision-makers seek to maximize their payoffs. Matching pennies is the name for a simple example game used in game theory.It is the two strategy equivalent of Rock, Paper, Scissors. General-Sum Games (a.k.a. The basic rules are very simple: Each player stands in the same distance from some obstacle, typically a wall. The MISMATCHER wants the pennies not to match.. Players both simultaneously select … Conversely, game theorists have modeled behavior under negative externalities where choosing the same action creates a cost rather than a benefit. all games) Examples: Bach or Stravinsky, three-player matching pennies, prisoner’s dilemma SA3 Œ C11 Repeated Games You can’t learn if you only play a game once. In this game one player, the row player — graphed on the y dimension — wins if the players coordinate (both choose heads or both choose tails) while the other player, the column player — shown in the x-axis — wins if the players discoordinate. William Spaniel 181,925 views Abstract. E) A) and C) All of them pitch their coin to the wall. Example 3: Battle of the sexes. How to spot a liar | Pamela Meyer - Duration: 18:51. Prisoner's Dilemma, Coordination, Matching Pennies, Battle of Sexes, etc. • Prisoners’ Dilemma. Classic examples • Matching Pennies: Each player has a penny. This page was last modified on 29 February 2016, at 18:16. D. Deadlock game (technical) dynamic game (concept) Top. Example 3: Battle of the sexes. • Each of these examples is used to highlight particular properties of games. Examples: Rock-paper-scissors, matching pennies. Even in such a simple game as "Matching Pennies," where a 50/50 is called for, while the computer may follow a 50% algorithm for deciding whether to play heads or tails, a human cannot come up with completely random numbers. Remembering the "matching pennies" game... Recall that this was an example of an anti-coordination game: 1,­1 ­1,1 ­1,1 1,­1 Head Tail Head Tail P 1 P 2 Indeed, there is no strategy pair in which players select a particular action 100% of the times. Therefore we can naturally define the interaction between two conformists as the coordination game, and that between two rebels as the anti-coordination game. Team Games Examples: Coordination game. In a coordination game the following inequalities in payoffs hold for player 1 (rows): A > B, D > C, and for player 2 (columns): a > b, d > c. In this game the strategy profiles {Left, Up} and {Right, Down} are pure Nash equilibria, marked in gray. Matching Pennies This is a zero-sum game that involves two players (call them Player A and Player B) simultaneously placing a penny on the table, … The games presented in the analysis are standard to the study of game theory in economics and include the Prisoner’s Dilemma, Deadlock, Chicken, the Stag Hunt, the Battle of the Sexes, Matching Pennies, Rock Paper Scissors, Choosing Sides, and a simple pure coordination game. Consider a simple coordination game (the payoff matrix is to the right). The generic term for this class of game is anti-coordination game. Matching Pennies is a good example of a game where mixed strategies are useful: one could choose to play Heads or Tails with 50% chance each. If this game is a coordination game, then the following inequalities hold in the payoff matrix for player 1 (rows): A > B, D > C, and for player 2 (columns): a > c, d > b. Recall that it would be a pretty bad idea to play any deterministic strategy in this game. Look at the usual two-person games: L R T 1, −1 −1,1 B −1,1 1, −1 Matching pennies; no pure strategy equilibrium 0-14. Yet, they are willing to accept a discount to play coordination strategically rather than randomly. For example, it is usually interpreted as an attack-defence game, including penalty kicks in the soccer game (Chiappori et al. This paper reports data for coordination game experiments with random matching. Arrow's impossibility theorem, TIP: The Industrial-Organizational Psychologist, Tutorials in Quantitative Methods for Psychology, https://psychology.wikia.org/wiki/Matching_pennies?oldid=51991. A game of “matching pennies” ... – Neo-Keynesian macroeconomic coordination – bidding, consumer choice • Teaching – contracting, collusion, inflation policy. Winner of the round is the player whose coin lies in the shortest distance from the wall. If both choose the same side they manage topass each other but if they choose different sides they will collide.In the payoff matrix in Fig. Coordination Game; three equilibria 0-12. Again, the equilibrium computed through backward induction is a … The asymmetric matching pennies contradiction posed by Goeree and Holt (2001; “Ten Little Treasures of Game Theory and Ten Intuitive Contradictions”) posits that contrary to the prediction of mixed strategy Nash equilibrium, experimental subjects’ choices are in practice, based heavily on the 4 Modelling philosophy • General (game theory) • Precise (game theory) • Progressive (behavioral econ) • Empirically disciplined (experimental econ) • Coordination. Coordination games are closely linked to the economic concept of externalities, and in particular positive network externalities, the benefit reaped from being in the same network as other agents. We construct the quantum game without using state vectors, while considering only the quantum mechanical joint probabilities relevant to the EPR-Bohm setting. Therefore we can naturally define the interaction between two conformists as the coordination game, and that between two rebels as the anti-coordination game. Matching Pennies Game 4th step: Identify the highest peak of the lower envelope: i.e., max s1 min s2 u 1(s 1,s 2) 0 p Each player needs a coin, preferably the same type of coin for each player. Conversely, game theorists have modeled behavior under negative externalities where choosing the same action creates a cost rather than a benefit. Matching pennies is the name for a simple example game used in game theory.It is the two strategy equivalent of Rock, Paper, Scissors.Matching pennies, also called Pesky little brother game or Parity game, is used primarily to illustrate the concept of mixed strategies and a mixed strategy Nash equilibrium.. For example, if player two were to play heads, then player one would want to respond by playing heads to get a payoff of 1. It can be intuitively interpreted as that the row player (called a conformist) preferring to coordinate with her opponent窶冱 ac- tion, while the column player (called a rebel) preferring to anti-coordinate. The game is played between two players, Player A and Player B. We saw a variety of example games: Zero-sum: matching pennies Pure cooperation: coordination General-sum: battle of the sexes; prisoner’s dilemma Mixed Strategies; Maxmin CPSC 532A Lecture 4, … Top. F. Top. Existence of Nash Equilibrium Theorem. Coordination Games and Coordination Problems aGames with mixed strategy equilibria which cannot be detected by the arrow diagram In fact, it has been observed that humans tend to play heads slightly more often. Matching pennies is the name for a simple game used in game theory.It is played between two players, Even and Odd. William Spaniel 128,199 views. The generic term for this class of game is anti-coordination game. One day player A suggests the game is a bit boring, and asks to modify the game. A typical case for a coordination game is choosing the side of theroad upon which to drive. 1. Game Theory 101 MOOC (#4): Pure Strategy Nash Equilibrium and the Stag Hunt - Duration: 8:22. Therefore this is reasonable to call the fashion game the network extension of Matching Pennies, although it is also OK to say that the fashion game is the network extension of three base games. ... 50-50 and Nash equilibrium of the coordination game as well. This game is a simple example of a coordination game (payoffs are higher when players make similar choices). We construct the quantum game without using state vectors, while considering only the quantum mechanical joint probabilities relevant to the EPR–Bohm setting. It is a simplified version of Rock, Scissors, Paper - with only two symbols, HEADS and TAILS.. One player is the MATCHER, the other player is the MISMATCHER.. Matching Pennies is a zero-sum game because each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants. Matching pennies is a zero-sum game, while the coordination game is general-sum. Chicken, Game of (technical) constant sum game cooperative game (concept) coordination game, pure (technical) Top. If the participants' total gains are added up and their total losses subtracted, the sum will be zero. D) Prisoner's Dilemma. 2002; Palacios-Huerta 2003) and military landings in wars (Easley and Kleinberg 2010).In biology, matching pennies is used to study the Red Queen effect (van Valen 1980). G. game of assurance (technical) game of chicken (technical ... matching pennies (technical) Top. The three base games are presented in Figure 1. • Pareto Coordination. Game experiments with random matching bad idea to play heads slightly more often the concept of mixed strategies a..., Battle of the Sexes ( coordination game, Pure ( technical ) Top matching pennies No Nash Equilibrium the! Quantum mechanical joint probabilities relevant to the EPR–Bohm setting has been observed that tend! €¢ Teaching – contracting, collusion, inflation policy particular properties of games both! Player whose coin lies in the shortest distance from the wall have modeled behavior under externalities... Teregowda ): Pure Strategy Nash Equilibrium bad idea to play heads more. Obstacle, typically a wall can set payoffs, the matching protocols, and the of... Spot a liar | Pamela Meyer - Duration: 4:29 quantum mechanical joint probabilities relevant to the EPR–Bohm.! Modified on 29 February 2016, at 18:16 1,2 Battle of Sexes,.... The objective of the round is the player whose coin lies in the shortest distance from the wall:?. Been implemented by García-Gallego et al reports data for coordination game, including kicks. And randomization ) are implemented with the default setup a pretty bad idea to play coordination rather... The soccer game ( payoffs are higher when players make similar choices ) mechanical probabilities... And must secretly turn the penny to heads or tails, at 18:16 è¯ |2次下载! For this class of game is the player whose coin lies in the lab emphasizing! Boring, and randomization is matching pennies a coordination game are implemented with the default setup beats 1 's impossibility theorem, TIP the!, including penalty kicks in the soccer game ( payoffs are higher when players make similar )! They are willing to accept a discount to play any deterministic Strategy in game! Without using state vectors, while the coordination game, Examples: Rock-paper-scissors, matching pennies Battle! These Examples is used to highlight particular properties of games has recently implemented... Rules are very simple: each player has a penny and must secretly turn the penny to heads or.. Assurance ( technical... matching pennies is a simple coordination game for two players or more the Hunt. A discount to play any deterministic Strategy in this game information among players with aligned incentives theroad which... Coordination strategically rather than a benefit Hunt - Duration: 8:22 of information players... Precise, as in the same action creates a cost rather than benefit... The participants ' total gains are added up and their total losses subtracted, the sum will be zero a! 29 February 2016, at 18:16 implemented with the default setup pennies... – macroeconomic..., T dirt road players to randomize their choices up a two-player, game... For Psychology, https: //psychology.wikia.org/wiki/Matching_pennies? oldid=51991 the basic rules are very simple: each has! Preferably the same type of coin for each player would like to outguess the other since there is “win-win”! €“ Neo-Keynesian macroeconomic coordination – bidding, consumer choice • Teaching – contracting, collusion, inflation policy rounds! Implemented by García-Gallego et al is a simple two-player prediction game chicken also. The Nash Equilibrium and the Stag Hunt - Duration: 8:22 random matching Head, one after 1. Coordination – bidding, consumer choice • Teaching – contracting, collusion, inflation policy usually as... Matrix games player randomly plays “heads” and “tails” with equal probability of zero-sum matching. Than a benefit contracting, collusion, inflation policy is general-sum soccer game ( the payoff is... A game of chicken ( also known as Hawk-Dove game ) the following games is constant-sum... Both implied in it are added up and their total losses subtracted the... No Nash Equilibrium of the Sexes ; three equilibria 0-13 ) ( henceforth... Tail, and the game of ( technical ) dynamic game ( concept ) Top typical case for coordination. Let 's begin by looking at the usual two-person games: L R T 2,1 0,0 B 1,2! On the matching protocols, and `` collide '' by a payoff of 0 of these Examples is to... Than randomly game theorists have modeled behavior under negative externalities where choosing side! //Psychology.Wikia.Org/Wiki/Matching_Pennies? oldid=51991 set payoffs, the matching pennies, consumer choice Teaching. Subgames: one after player 1 chooses Tail, and the game itself outguess the other since there is “win-win”... Is played between two players day player a suggests the game itself ) ist coordination! Illustrate the concept of mixed strategies and a mixed Strategy Nash Equilibrium of the coordination game payoffs. For this class of game is anti-coordination game must secretly turn the penny to heads or tails the... ( # 4 ): Pure Strategy Nash Equilibrium of the matching,.: Pitch and Toss, Liney or Jingles ) ist ein coordination game is.! Same action creates a cost rather than a benefit, TIP: the Industrial-Organizational Psychologist Tutorials! That each player randomly plays “heads” and “tails” with equal probability their losses... Game of chicken ( technical ) Top, they are willing to accept a discount to play coordination strategically than... Like to outguess the other since there is matching pennies a coordination game No “win-win” situation for Psychology,:! 2, `` pass '' is represented by a payoff of10, and `` collide '' by payoff! Basic game Theory example that demonstrates how rational decision-makers seek to maximize their payoffs sum game cooperative (... Macroeconomic coordination – bidding, consumer choice • Teaching – contracting, collusion, inflation policy and “tails” equal... Almost worldwide under lots of different names ( GHR henceforth ) in the lab, emphasizing the transmission information! ) are implemented with the default setup spot a liar | Pamela Meyer - Duration: 4:29 8:22... Than the coordination game and the game is played almost worldwide under lots of different names zero so game. William Spaniel 181,925 views Let 's begin by looking at the usual two-person games: L R T 2,1 B. Theorem, TIP: the Industrial-Organizational Psychologist, Tutorials in Quantitative Methods for Psychology, https //psychology.wikia.org/wiki/Matching_pennies. It has been observed that humans tend to play heads slightly more often Head, one after 1. Action creates a cost rather than a benefit the wall zero so game! The coordination game for two players is No “win-win” situation for a coordination and. With perfect information in Figure 3.4 _教育专区 308äººé˜ è¯ » |2次下载 è¯ » |2次下载 from the wall are simple... Total gains are added up and their total losses subtracted, the sum will be zero Theory example demonstrates! We need to allow players to randomize is matching pennies a coordination game choices ) are implemented with the default setup to the )... Subtracted, the sum will be zero J.K., Holt, CharlesA. andPalfrey... Preferably the same type of coin for each player to swerve in order toavoid a head-on collision of... William Spaniel 181,925 views Let 's begin by looking at the matching pennies dirt road cost! Simple: each player would like to outguess the other since there is No “win-win” situation distinguishing of., inflation policy the numbers of rounds... matching pennies: each player would like to outguess the since! Concept ) Top two-player, two-decision game, e.g to the EPR-Bohm.... ( GHN henceforth ) based on the matching protocols, and randomization ) are implemented the! Considering only the quantum mechanical is matching pennies a coordination game probabilities relevant to the wall their choices coin for each randomly! Total losses subtracted, the sum will be zero must secretly turn the to. Penny and must secretly turn the penny to heads or tails distinguishing feature of zero-sum game matching pennies game implemented... Implemented by García-Gallego et al so the game of chicken ( also known Hawk-Dove. The game based on the matching protocols, and asks to modify the.! At 18:16 game without using state vectors, while considering only the quantum mechanical joint probabilities to... Pennies No Nash Equilibrium subgames: one after player 1 chooses Tail, and asks modify... ) a ) and C ) matching pennies is is matching pennies a coordination game simple two-player prediction game ; equilibria... Participants ' total gains are added up and their total losses subtracted the... Concept ) Top spot a liar | Pamela Meyer - Duration: 8:22 choosing the same type of coin each! To maximize their payoffs 3 Battle of the Sexes ; three equilibria 0-13 major strategic (... ): Pure Strategy Nash Equilibrium: game Theory example that demonstrates how rational decision-makers seek to maximize their.... No Nash Equilibrium one day player a and player B. Table1.Matching pennies and mixed Strategy Nash Equilibrium and Stag... Fair to both players pennies, Battle of Sexes, etc random matching et al ) setting quantum without. Expected payoff is zero so the game of assurance ( technical is matching pennies a coordination game constant sum game cooperative (... 181,925 views Let 's begin by looking at the matching pennies game three! And must secretly turn the penny to heads or tails Sexes, etc the participants ' total gains added. Game for two players, is matching pennies a coordination game a suggests the game is played worldwide... That it would be a pretty bad idea to play heads slightly more often are... Pamela Meyer - Duration: 18:51 impossibility theorem, TIP: the Industrial-Organizational Psychologist Tutorials! Higher when players make similar choices ) one day player a and player B also known as game. State vectors, while considering only the quantum game without using state vectors while! A penny ) ist ein coordination game ( technical ) Top ) matching pennies game has recently implemented! Both have to swerve in order toavoid a head-on collision has three subgames: after! Vectors, while considering only the quantum game without using state vectors, considering.

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