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Game theory fans, meet comparative statics. This lesson from William Spaniel's Game Theory 101 series expands on the previous Soccer Penalty Kicks scenario to explore the world of comparative statics. Discover how a game's outputs change as a function of the game's inputs – in this case, a change in the probability of the kicker scoring a goal when he kicks in a certain direction. Learn and practice the four steps to calculating comparative statics.


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Why bend over backwards- or bend over at all- to pick up a tennis ball? Lock and Roll tennis teaches you how to perform Rafael Nadal's sweet trick for getting the tennis ball off the ground using just his feet. It's a stylish, hip, and effortless way to retrieve a ball, especially when you're practicing your tennis swings and have a lot of balls to collect!


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Want to get rid of dead skin and reveal smoother, softer, younger looking skin, but don't want to spend a fortune on beauty products? Taste4Beauty shows you how to make a DIY homemade sugar scrub that's cheap, quick, and easy to make- it only has two ingredients! This scrub will exfoliate and moisturize your skin, and improve blood circulation. You'll be revealing a glamorous new you in no time!


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Learn how not to write a subgame perfect equilibrium with this lesson from William Spaniel's Game Theory 101 series. Avoid the classic blunders that can trip you up and lose you points on an exam: remember that a subgame perfect equilibrium is a complete and contingent plan of action, and must state what happens on as well as off the equilibrium path of play. This lesson includes a handy trick to check your work by comparing the number of strategies you list with the number of game nodes.


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How do you take those black dots on the page and turn them into piano music? First you have to learn how to read music! Web Piano Teacher offers a series of lessons on sight reading music for beginners. Learn the names of notes and their positions on the keyboard. Figure out how to look at sheet music and tell the difference between a treble clef and bass clef. Get your eyes and your fingers in sync and start playing!


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Want to make a fun and colorful alcoholic drink? In this lesson, The Vegetarian Baker teaches you how to infuse Absolut Vodka with jelly beans, making the vodka colorful and sweet. Using mini vodka bottles and jelly beans, you can create a cheerful mini-fridge-sized drink with a kick. It's the perfect way to get a little of your inner child into your adult beverage!


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You know about backward induction in game theory, which assumes that all future play will be rational. But what about the opposite technique? In this lesson from William Spaniel's Game Theory 101 series, you'll be introduced to forward induction, which assumes that all past play was rational. Using a version of the Stag Hunt game, learn how Player 2 can look at payoffs and use forward induction to infer Player 1's move.


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Don’t think you’re cut out for playing guitar? Think again! Everyone gets frustrated. Even Jimi Hendrix wasn’t a rock god from day one. Check out this lesson for advice on learning how to play guitar and the encouragement to keep doing it. You’ll surely want to continue pickin’ after hearing these words of wisdom. Practice and persist!


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Ever wonder how so much rock ‘n roll can come from one tiny Fender guitar? Check out this lesson on the anatomy of an electric guitar. It’s very similar to that of an acoustic guitar, only with added amplification! You’ll learn the importance of pickups, knobs, switches, and extra electronics. Plug in and shred up and down the neck


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While diets may work to keep you healthy in the short term, the stress that they put on your mind and body sets you up for a big crash later. As Darya Rose, author and creator of Summer Tomato, explains, the secret is in taking small steps to build healthy habits instead of using up all of your hard-earned willpower. Start getting healthy for the long term today!


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Craving a down-home dish without the hassle? Ditch those russets and make some sweet potato fries. Not a huge fan of the sweet starchiness in dishes such as sweet potato pie or candied sweet potatoes? Girls Gone Sporty has a recipe for spicy sweet potato fries that is guaranteed to convert even the most adamant haters. Bake two batches in less than an hour with this tutorial.


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Game theory needn't mix you up! In this final lesson of William Spaniel's Game Theory 101 series, learn how to solve game theory scenarios with three possible strategies. Expand the mixed strategy algorithm and apply it to games with more than two strategies. Figure out the mixed strategy Nash equilibrium for a modified version of Rock, Paper, Scissors. Solve for a player's indifference and calculate expected utilities as a function of a given mixed strategy.


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Want to dominate game theory? Use this weak dominance trick: If your opponent is mixing among all of her pure strategies, then you should not play a weakly dominated strategy in equilibrium. Follow along with William as he illustrates this point using the "Take or Share" game—where players have the choice to divvy up $8,000 or take it all for themselves. Learn when it can be a bad idea to take your mom's advice on sharing.


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You and your best friend are offered free money, and so long as you both choose to accept it in a blind vote, you both get richer! What could go wrong? Learn about the Free Money game theory scenario, and why there's a possible outcome where everyone ends up poorer (but is still a Nash equilibrium). The Free Money game is an exception to the Odd Rule, which states that almost all games have an odd number of equilibria.


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Whether you are catering a swanky soiree or hosting your own celebration, learn how to create a festive blueberry dessert that looks much more difficult to make than it is! Your partygoers will be delighted with this chic Blueberry Dessert in a Martini Glass. In this lesson from The Aubergine Chef, you’ll learn how to make and combine the four components of this beautiful dessert recipe (cake, mousse, gelee, and Chantilly cream), and garnish each glass masterfully.


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Tackle the ‘Battle of the Sexes’ game from a new angle and learn to solve for pure and mixed strategy Nash equilibria using variables instead of numbers. This Game Theory 101 lesson explains how to find the expected payoff of certain strategies using the mixed strategy algorithm and probability distributions - even when some factors in the game are unknown. Use the approach covered in this lesson to understand and solve a variety of generalized games.


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Slice into the precarious world of knife-edge equilibria - a kind of game theory equilibrium that exists for a single and exact payoff value. If this value varies in even the slightest way, the game matrix equilibrium is destroyed. Follow along with William Spaniel and his Game Theory 101 lesson as he explores this rare occurrence that is frequently ignored in game theory studies.


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How does a game change when opponents make sequential rather than simultaneous moves? In this Game Theory 101 lesson, learn how subgame equilibrium plays into such a game: A firm must decide whether or not to enter a fictional market. If the firm enters, the current monopolist must - in turn - decide whether to accept the new firm or engage in a price war. To find the subgame perfect equilibrium, the first firm must determine the credibility of the monopolist’s threat of a price war.


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Are you a seasoned guitarist always on the lookout for advice? Or maybe you’re a frustrated beginner? Here’s a small tip that will last a lifetime of guitar playing: curl the last knuckle of each fretting finger. This helps you to strum chords efficiently and hit every necessary note. Check out this lesson to fully comprehend the importance of the curl.


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