- e the do
- ant strategy in game theory refers to a situation where one player has superior tactics regardless of how their opponent may play. Holding all factors constant, that player enjoys an upper hand in the game over the opposition
- ant strat-egy for ROW. If you circled ROWchooses N inboth trees, then N is a do
- ant strategy is a choice that is preferable for one player no matter what their opponent chooses to do. To deter
- ant strategy for Firm A involves the following steps: Select the first strategy of the opponent i.e. Firm B i.e. hiring a lawyer. Look inside the 'Hire a Lawyer' column for Firm A's payoff and see which row has the higher payoff. In this example, it is 45 (as 45 is greater than 25)
- ant and Do

-a strictly dominant strategy is that strategy that always provides greater utility to a the player, no matter what the other player's strategy is; -a weakly dominant strategy is that strategy that provides at least the same utility for all the other player's strategies, and strictly greater for some strategy Only one player has a dominant strategy: In the given game, Player 1 has the dominant strategy a because strategy a gives the best outcome for Player 1 regardless of the actions of Player 2. Therefore, Player 1 has the dominant strategy If you observe that whenever your opponent loses a turn, he tends to pick the choice that defeated him for the next turn, then your dominant strategy can include a counter for that move. If you.. In order to identify the dominated strategy, we need to find if a row exists which corresponds to the lowest Firm A payoffs in all columns. The lowest red values all occur in the highlighted row in the payoff matrix shown above. Hence, cutting advertising is the dominated strategy for Firm A A dominant strategy is a strategy that leads to better outcomes for a player than other available strategies (while taking into account the strategies that other players can use). Dominant strategies can be strictly dominant or weakly dominant: A strategy is strictly (or strongly) dominant if it leads to better outcomes than alternative strategies

One key consideration is that a strategy can be strictly dominated by mixed strategies as well. In other words, if we can assign a probability distribution of two actions such that they do strictly better than a particular strategy in expectation, than that strategy is strictly dominated Let's find the dominant strategies. The first strategy that is dominated, is Right. Player 2 will always be better off by playing Middle, so Right is dominated by Middle. At this point the column under Right can be eliminated since Right is no longer an option

Takeaway Points. If a mixture of two strategies strictly dominates a third strategy, you may eliminate the third strategy. Procede with iterated elimination of strictly dominated strategies as usual, if possible. (Note that there are no other strictly dominated strategies in the game in the video.) Back to Game Theory 101 Weakly Dominant Equilibrium Call the strategy pro le sW 2S aweakly dominant strategy equilibrium if sW i 2S i is a weakly dominant strategy for all i 2N. That is, if sW i ˜ W i s 0 i for all s 0 i 2S i, for all i 2N. Obviously BoS is an example of a game with no weakly dominant strategy equilibrium. EC202, University of Warwick, Term 2 17 of 3 How to find dominant strategy and nash equilibrium The dominant strategy in game theory refers to a situation where one player has superior tactics regardless of how their opponent may play. Holding all factors constant, that player enjoys an upper hand in the game over the opposition. It means, regardless of the strategies employed by the. Where **To** **Find** A Submissive or **Dominant** Partner Sep 10, 2007 Master Arcane All Lessons A-Z , BDSM Play , D/s Training , **Dominant** , Relationships , Submissive 3 A Dom-Dom couple (both people are **Dominant**; neither is submissive) wrote to me asking **how** and where they could **find** a submissive for the two of them to Co-Top

With dominant strategy, each player is unaware of the other's optimal strategy. Each player chooses the best strategy among all options. Nash equilibrium occurs when each player knows the strategy.. Strategies 3. Nash Equilibrium Dominant Strategies • Astrategyisadominant strategy for a player if it yields the best payoﬀ (for that player) no matter what strategies the other players choose. • If all players have a dominant strategy, then it is natural for them to choose the dominant strategies and we reach a dominant strategy equilibrium Here is my 60 second explanation of how to identify the dominant strategy with game theory payoff matrix. The numbers in the left of each square are for the.

Dominant strategy is an action that gives the upper hand to the decision-maker in a game and it will have direct consequences for the other players. The other players may, however, adopt the same strategy to cope with the move and that will result in no gain no loss outcome for both of the players Summary (dominant strategy method): Check each column for Row player's highest payoff, this is their best choice given Column player's choice. (if there are two high choices, then the result will be a mixed strategy outcome). Now check to see if Row's choice for 1) would also be their choice given any choice by Column player ** Learn more: http://www**.policonomics.com/nash-equilibrium/This video explains how dominant strategies work, and how to reach a Nash equilibrium. We start by a.. http://economicsdetective.com/Game theory is the study of human behaviour in strategic settings. It is used to solve some of the harder problems in economic.. Dominant strategy equilibrium: A set of strategies (s 1, , s n) such that each s i is dominant for agent i Thus agent i will do best by using s i rather than a different strategy, regardless of what strategies the other players use In the prisoner's dilemma, there is one dominant strategy equilibrium: both players defec

Week 1: Introduction and Overview. Introduction, overview, uses of game theory, some applications and examples, and formal definitions of: the normal form, payoffs, strategies, pure strategy Nash equilibrium, dominant strategies. Introductory Video 8:20. 1-1 Game Theory Intro - TCP Backoff 11:23. 1-2 Self-Interested Agents and Utility Theory 3:53 player had a dominant strategy; the Prisoner's Dilemma game was one example. In many games, however, one or more players do not have dominant strategies. This chapter explores two solution concepts that we can use to analyze such games. The ﬁrst solution concept, iterated dominance, is a reﬁnement of the domi Dominant Strategy Equilibrium An action pro le a is a dominant strategy equilibrium if a i is an optimal action independent of the other players' choice for every i. Dominant Strategy Equilibrium a 2A is a dominant strategy equilibrium if for every i 2N, u i(a;a i) u i(a i;a i) 8a i 2A i; 8a i 2A i: Note: When a is a dominant strategy. A Dominated Strategy is a strategy that is always worse than some other strategy no matter what other players do. While Player 2 does not have a dominant strategy in the game above (there is no one strategy that is always best), Player 2 does have a strategy that doesn't seem very useful. Consider the strategy W

Dominant Strategy Rules (Dominance Principle) If all the elements of a column (say i th column) are greater than or equal to the corresponding elements of any other column (say j th column), then the i th column is dominated by the j th column and can be deleted from the matrix.; If all the elements of a row (say i th row) are less than or equal to the corresponding elements of any other row. Understanding How to Find a Dominant Online. Answered by dating expert Alex Reddle. If you're serious about finding a dominant online, it's worth the expense of joining a specialist site and meeting people who enjoy a submissive/dominant relationship. Even then, a personal is not enough. So a site with a busy chat room is a good place to start set. That is, a strategy is a complete plan for playing a game for a particular player. • Therefore to ﬁnd the strategic game equivalent of an extensive form game we should follow these steps: 1. First we need to ﬁnd all strategies for every player. To do that ﬁrst we ﬁnd all information sets for every player (including th Where All The Dominants Are and How to Find Them. Written by lunaKM. from the Submissive Guide Newsletter 8-8-15. Finding a partner is hard. We all know that dating is difficult in the best of times and adding in D/s or BDSM needs or desires just makes it harder still. But there are people out there and they are looking for you * Where To Find A Submissive or Dominant Partner Sep 10*, 2007 Master Arcane All Lessons A-Z , BDSM Play , D/s Training , Dominant , Relationships , Submissive 3 A Dom-Dom couple (both people are Dominant; neither is submissive) wrote to me asking how and where they could find a submissive for the two of them to Co-Top

A strictly dominant strategy for i uniquely maximizes her payoﬀ for any strategy proﬁle of all other players. If such a strategy exists, it is highly reasonable to expect a player to play it. In a sense, this is a consequence of a player's rationality * We say sD is a strict dominant strategy equilibrium if sD i 2Si is a strictly dominant strategy for all i2N (set of all players)*. In other words, a strictly dominant strategy equilibrium is a strategy pro le that consists of each player's strictly dominant strategy. We may manage to nd a plausible equilibrium using the concept of \weak.

** Dominant-strategy equilibrium Definition: A strategy si* is a dominant strategy iff si* weakly dominates every other strategy si**. Definition: A strategy profile s* is a dominant-strategy equilibrium iff si* is a dominant strategy for each player i. If there is a dominant strategy, then it will be played, so long as the players are How to Find a Dominant Men. The first, and most crucial aspect to finding a dominant man, is to go where dominant men are. Off the top of my head: Gyms with lots of power-lifters. MMA and boxing gyms (more of the meatheads type of dominance) Bars where policemen hang out after work

* Handout on Mixed Strategies Ben Polak, Econ 159a/MGT522a October 4, 2007 The main lesson of the last class was the following: Main Lesson If a mixed strategy is a best response then each of the pure strategies involved in the mix must itself be a best response*. In particular, each must yield the same expected payo inant strategy equilibria. Furthermore, there can be at most one dominant strategy equilibrium, but as the Battle of the Sexes shows, Nash equilibrium is not unique in general. There can also be a other Nash equilibria when there is a dominant strategy equilib-rium. For an example, consider the game 1 A dominant strategy is the one that is best for an organization (player) and is not influenced by the strategies of other organizations (players). Let us understand the dominant strategy with the help of the example given in Table-1. Suppose organizations ABC or XYZ adopt a dominant strategy A strategy is dominant if, regardless of what any other players do, the strategy earns a player a larger payoff than any other. Hence, a strategy is dominant if it is always better than any other strategy, for any profile of other players' actions. Depending on whether better is defined with weak or strict inequalities, the strategy is termed strictly dominant or weakly dominant

The dominant strategy is an action that a player must take, regardless of what other players do. The such strategy is found through an exhaustive examination of all scenarios. In contrast, a Nash equilibrium is the optimal strategy if a player believes that others will act according to their dominant strategies. It would result in a balance of. selected a dominant strategy. Solution: False. A dominant strategy is one that is a best response no matter what the other player does. A Nash equilibrium is one in which both player play the optimal strategy, given the other player's strategy. If both players are playing a dominant strategy, this must be a Nash Equilibrium, but not vice. Ruisheng Li, in Distributed Power Resources, 2019. 3.6.2.1 Dominant strategy Dominant strategy is a term in game theory that refers to the optimal option for a player among all the competitive strategy set, no matter how that player's opponents may play, and the opposite strategy is called inferior strategy. The AC&DC hybrid microgrid has two buses with different types of power. * After constructing the table you realize that player 2 has a weakly dominant strategy (L)*. You have to go back and forth between the two tables (for type A and B) and the third table for player 2 to find all the fixed points. For this game, there are several equilibria; so maybe that is throwing you off

Dominant strategy asserts that a player will choose a strategy that will lead to the best outcome regardless of the strategies that other plays have chosen. Dominant strategy can be included in. ** ADVERTISEMENTS: The definition of Nash equilibrium lacks the ∀ s-i of dominant strategy equilibrium**. The Nash equilibrium strategy need only be a best response to the other Nash strategies not to all possible strategies. Although, we deal with best responses and the moves are actually simultaneous. Therefore the players are predicting each other moves. The [

* Transcribed image text: 1*. Find the dominant strategy of each player (if any) and Nash equilibrium (if any) in the following games. (a) Game 1: Battle of Sexes: Player 2 Opera (0) Boxing (B) 3,2 1,1 0.0 2,3 Player 1 Opera (O) Boxing (B) (b) Game 2: Prisoner's Dilemma Player 2 Confess (C) Deny (D) Confess (C) -3,-3 0,-6 Player 1 Deny (D) -6,0 -1,-1 (c) Game 3 t Player 2 L M R 16,4 8,16 3,8 4,2. In decision theory and game theory, an alternative or **strategy** (2) that, in every contingency that might arise, yields a payoff at least as good as the payoff from any other available alternative or **strategy** and a strictly better payoff in at least one. A **dominant** **strategy** is strongly **dominant** if it yields a strictly better payoff than any other alternative or **strategy** in every possible. Twenty five million times a month a woman somewhere on the planet googles, How do I find a Dom?. Women want to be in a Dom and submissive style relationship. They are already in the process of find a Dom. These repressed women want to be subs for doms. Surprise! Sub women want to wea

- ant Strategy Equilibria A strategy is strictly (resp., weakly, very weakly) do
- A Nash equilibrium is a profile of strategies $(s_1,s_2)$ such that the strategies are best responses to each other, i.e., no player can do strictly better by deviating. This helps us to find the (pure strategy) Nash equilibria. To start, we find the best response for player 1 for each of the strategies player 2 can play
- Here we have covered some forex entry strategies to find out the perfect forex entry point for you. These are the scanners of your identified potential trade areas for searching forex confirmation entry. A good entry confirmation strategy or entry technique can boost your overall trading strategy & take it to the next level
- ant strategy equilibrium, then in the IESDS process at stage 1 would eli
- ant strategy if that strategy is superior independent of the other player's action. Another important concept is the concept of a Nash equilibrium : A pair of strategies (a*, b*) such that a* is an optimal strategy for Player 1 if Player 2 plays b*, and b* is an optimal strategy for Player 2 if Player 1 plays a*
- ates strategy D. Eli
- ant strategy, if it exists. c. Find the Nash equilibrium (or equilibria) of.

- ant Strategy, since it is the best choice given any of the strategies selected by the other player. Similarly, \(\text{CONFESS}\) is the do
- ant, do
- ant strategy exists for one player in a game, that player will play that strategy in each of the game's Nash equilibria. If both players have a strictly do
- In fact, the conditional strategy proved to be 10 percent more reliable for winning than did the Nash Equilibrium. From this, you should definitely be more cautious in using the Nash Equilibrium. Of course, we did find the Nash Equilibrium for Rock, Paper, and Scissors but we cannot say that will be the best strategy

The new year is an opportunity to rewrite the rules and stop settling for less in your business. It is the opportunity to cast a strategic vision that is different from the past and to create more. For example, each firm has two strategies in this example: either start a campaign or not. Dominant strategy for firm A would be to start a campaign as its payoffs are 10 and 15 (compared to 6 and 10 if they don't). For firm b, choosing to start a campaign is also the dominant strategy as payoffs are 5 and 8 (compared to 0 and 2 if they don't)

- ant strategy is to play invest regardless of P1 strategy, they will play the strategy Invest. The payoff in this situation will be $15 to P1 and P2. The new equilibrium is P1 playing Don't invest and P2 playing invest. As we can see, from pursuing the strategy of Maxi
- ant for each player, meaning that whatever the other player does, defecting yields an outcome at least as good and possibly better than remaining in solidarity would. Note that if the bottom right cell payoffs were (2,2) instead of (1,1), then defecting would be strictly do
- ant strategy is ___ high price __ (low price, high price, it has no do
- ant strategy Nash Outline Lab evidence 1. Do
- ant eye looks at the same object at a slight angle. Depth perception is the result between the two. The small angular difference between the do

- ant market bias, your probabilities of making money decrease dramatically
- ant BR titles which emphasize fighting skills, Minecraft inclines towards inventory and strategic features. Together with its increasing popularity, there are a variety of ga
- ant strategies should make it easy to predict the outcome of a game, but there can sometimes be complications even then. The Prisoner's Dilemma is a two-player game, where each player has a do

- ant strategy equilibrium is the outcome in which each player plays his/her do
- ant strategy NE, that the mixed strategy NE will agree with it
- ant force that is strategically ready, globally relevant, and flexibly sustainable. The cornerstone to this vision is achievin
- ant strategy remains. This is done through backward induction. Backward Induction. In this process, the game tree is essentially flipped. Working backwards from the payoff, the decision-maker begins to eli
- Conducting a high-level competitive analysis is crucial to your online success. Often, your most significant opportunities come from your competitors' data. Keeping up with your competitors' marketing strategies is a great way to identify their strengths and weaknesses. Which you can use for your marketing strategy. The first step into developing a competitive analysis strategy is.

However, one dominant person out of 100 can blow an organization to smithereens. Most People Will Avoid a Person Who I Domineering. Here are some basic facts: Most people will avoid a dominant, overbearing, personality at all costs. In avoiding a dominant personality, most people hope that they will go away To put it simple, consider dominant strategy equilibrium as a strategy which will make each trader better off no matter what other players choose. For example, if I find a buck on a road, it is a dominant strategy to pick it up no matter what othe..

- Find a venue that provides these learners with large spaces so they can write and draw. Encourage them to draw diagrams, graphs and maps. Get them to interact with physical objects or solve puzzles. Role-playing. Provide real life examples, such as, case studies. Suggest reviewing their notes whilst they engage in physical activity
- ant strategy which is to set a Low Price. Hence, the Nash Equilibrium is (Low Price , Low Price) A Nash Equilibrium represents a situation where every player is choosing his/her best response, given what the other player is doing. A Nash Equilibrium is identified when there are 2 circled responses in a cell
- ated strategies cannot be played in equilibrium, and you will note that the calculator says that is the PSNE. The reason it lists strictly do
- pure strategies +1, -1-1, +1-1, +1 +1, -1 Heads Tails Heads Tails Player 2 Player 1 All Best Responses are underlined. 5 Computing Mixed Strategy Equilibria in 2×2 Games aSolution criterion: each pure strategy in a mixed strategy equilibrium pays the same at equilibrium aEach pure strategy not in a mixed strategy equilibrium pays les
- ant strategy. The question #8 below is for graduate students only. 8. You are a duopolist producer of a homogeneous good. Both you and your competitor have zero marginal costs. The market demand curve is P = 30 - Q where Q = Q 1 + Q 2. Q

The most important personality characteristic is a high level of self-confidence and self-esteem. This is really the core of what it means to be an alpha male. Other important personality traits of alpha males are determination, decisiveness, purposefulness, persistence, and being naturally charismatic Many people with dominant personalities enjoy being challenged at work, so try to find projects that will test their skills and abilities. Recognize their work 1. Don't try to fix the difficult person. Accept them exactly as they are. (This applies to all difficult people, not just family.) It's tempting to try to help someone you want to care about.

- ant) Wing. It's best to look at it this way: Your main type reflects the pattern (or strategy) you use most often in life, that you rely on the most and that has the greatest influence on your personality
- ant position by finding flaws in the PC to contrast with Mac computers' simplicity to steal significant market share by enticing frustrated PC consumers to buy a Mac. 2) Apple will launch a full assault against the entire music industry.
- ant strategy. Your business tactic has to evolve and improve according to the environment of your market. The most adjusting and the most effective - the two-folds here - will win the game, or in essence of the business, get more sales. 2. Be Active In Social Networks & Be Goo

We extend the equivalence between Bayesian and dominant strategy implementation (Manelli and Vincent in Econometrica 78:1905-1938, 2010; Gershkov et al. in Econometrica 81: 197-220, 2013) to environments with nonlinear utilities satisfying a property of increasing differences over distributions and a convex-valued assumption. The new equivalence result produces novel implications to the. Dominant. This is the level with the most visual weight and the one that gets the most emphasis. Your dominant level will usually consist of a single element in the foreground. Sub-dominant. This is the level of focal points, with the exception of the dominant element or dominant focal point. It gets secondary emphasis 3.1 What A Woman Truthfully Wants. 3.2 Women's Desire To Find A Better, More Dominant Man. 4 If You DON'T Dominate Your Wife, Hypergamy Kicks In. 5 How To Dominate Your Wife. 5.1 Dread Game. 5.2 Planting Dread Inside Your Wife's Mind. 6 Why You Need To Totally Fuck With Her Mind Many of those who need to apply motivational strategies to their work and lives also come to similar conclusions. Teachers tend to have much better success in motivating their students to read when they take the time to transform the lesson plan into activities that children find to be interesting, curiosity-provoking, and personally inspiring

Global E-cigarettes Market to Reach $28.3 Billion by 2027. Amid the COVID-19 crisis, the global market for E-cigarettes estimated at US$16.6 Billion in the year 2020, is projected to reach a revised size of US$28.3 Billion by 2027, growing at a CAGR of 7.9% over the analysis period 2020-2027. Modular, one of the segments analyzed in the report. Gibbard and Satterthwaite show that when there are three or more alternatives, sincere voting is always the voter's dominant strategy only if it is dictatorial.This result is well known as the Gibbard-Satterthwaite theorem. Footnote 1 This theorem implies that it is hard to make a voting rule that is not dictatorial and any voters always sincerely vote The CCI indicator strategy was really designed to find cyclical trends in the market and to be used as a bearish or bullish filter. The CCI is simply an oscillator indicator that moves the majority of the time between +100 and -100. Technically, the way to interpret the Commodity Channel indicator is that a positive reading above +100 is a bullish signal and a start of an uptrend, while a. The Dominant Growth Model for the Decade • Part 1: An Introduction to Data Dominance • Part 2: The Digital Data-Centric Enterprise. A Data Strategy for Revenue Growth • Part 3: The Product Strategy • Part 4: The Data Strategy. Designing, Building, and Optimizing • Part 5: Organizing the Data Ecosyste

If the dominant person is going off on a tangent, or speaking for so long that the body language of your colleagues indicates they're getting antsy, find a way to cut the speaker off politely. One technique is to use something they've said as a jumping off point and spin it positively. For example, cut in and say, Matt, I like what you. More clients, revenue, and profit. There are five critical areas every small business owner MUST address in order to attract new clients, generate more revenue, and increase profitability. This video will teach you my business-changing formula, give you the ability to immediately double your profits, and create exponential growth for your business One way to choose is to amalgamate a core ability, knowledge, and value. A client today should be instructive. I change irrelevant details to protect the client's anonymity. He was interested in.

This game has two pure strategy equilibria: (Swerve, Don't) and (Don't, Swerve). In addition, it has a mixed strategy. Suppose that Column swerves with probability p.Then Row gets 0p + -1(1 - p) from swerving, 1p + (-4)(1 - p) from not swerving, and Row will randomize if these are equal, which requires p = ¾. That is, the probability that Column swerves in a mixed strategy. Kagi Chart Major Trend Changes. In your trading strategy, you'd need to see a couple of reversals where the line remains thin before accepting that the dominant trend has changed, since as you know prices usually go through a consolidation period before definitively changing direction.. These consolidations show up clearly on a Kagi bar as a succession of short thick and thin lines Formally, a dominant strategy for some player iis a strategy si∈Sisuch that for all s−i∈S−iand all ˜si∈Si vi(s i,s−i) ≥v i(˜s i,s−i) When both players in the game have a dominant strategy we know what will happen: each player plays his dominant strategy and we can describe the outcome. We call this an equilibrium in dominant. Try to be realistic here, and keep in mind that even a number like 25% might be a dominant share. Next, break down your business's plan for positioning, which relates to the market niche your. 1) Check each column to find the one where player 1 has maximum payout. 2) Check if the choice of 1 tends to always be the same, whatever the choice of player 2 (dominant strategy) 3) Repeat for the same player the same procedure. 4) The Nash equilibrium is reached where the dominant strategies intersect

- The realm of Strategy, more than any other discipline, must be learned by watching and learning from the decisions of others. In 1962, President Kennedy was confronted with the greatest decision of his era. Intelligence-gathering aircraft over Cuba confirmed the presence of missiles there that meant Cuba would soon have capability for launching.
- ant paradigm in strategy remains Michael Porter's 1985 competitive advantage theory encouraging companies.
- ant strategy equilibria can result in negative consequences in real life when: it is in the best interest of a firm to not clean up its pollution providing its competitor does. A zero-sum game means it ___________ possible for both players to find an optimal strategy with a given move; therefore, a Nash equilibrium ____________ exist
- ant parent is a party.
- We spoke to Haas F1 Team's Mike Caulfield to find out what a Strategy Engineer does, how to become one, and what skills you need for the job. Strategists in Formula 1 are responsible for creating.

It is not something we talk about often, but the dominant strategic approach in Australian education - and in many countries around the world - is fundamentally flawed. Once the policy making wheels get in motion, we somehow find ourselves drifting further and further away from classrooms. This strategic approach means that system leaders, school leaders and teachers keep working harder. Tyler Duffey, MIN - 483 ADP (24 IP, 1 W, 31 K, 1.88 ERA, 0.79 WHIP) The forgotten man in the Twins bullpen that now includes Alex Colome, Duffey has now given us two elite reliever seasons in a. So if you're moving super slowly, it's less stress through the joint, they move faster, it's more stress to the joint. There's so many ways to do this from a program perspective. What we're trying to do is manipulate some of the stress in whatever way you'd like, low speed, movement, whatever. There's a lot of options When students read against the grain, they learn to push back against the foregrounding and privileging of a dominant point of view (often heterosexual, non-disabled, Christian, white, or male). This strategy adds the experiences of less represented individuals and groups into the textual discourse. Reading against the grain combines analysis. a. All firms have a dominant strategy and each firm chooses its dominant strategy. b. All firms have a dominant strategy, but only some choose to follow it. c. All firms have a dominant strategy, and none choose it. d. None of the above is correct

Matt is a Certified Financial Planner based in South Carolina who has been writing for The Motley Fool since 2012. Matt specializes in writing about bank stocks, REITs, and personal finance, but.

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