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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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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Life's full of tough choices, and sometimes there's not just one right answer: there are infinitely many. In this Game Theory 101 lesson by William Spaniel, learn about scenarios in which a set of mixed strategies can lead to an infinite number of Nash equilibria. Review concepts like strict dominance, pure strategy Nash equilibria, and partially mixed strategies - and discover how one player's pure strategy can result in another player's indifference.

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Want to learn a programming language that will do a lot of the work for you? Check out Professor Paul Krause's introduction to Ruby on Rails, a highly dynamic and fully object-oriented framework for creating websites. In this first of a series of lessons on Ruby, hear the history of Ruby on Rails and why it's useful, and find out how Ruby can cope with problems that would leave Javascript reeling.

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We use fonts every time we type, but do we really understand them? In this first in a series of typography lessons from Yes I'm a Designer, get an introduction to the wonderful world of fonts. You'll learn how to use InDesign to view the full range of glyphs in a font (beyond the characters you're used to seeing on your keyboard), discover how fonts are stored on your computer, and unravel the mystery of unicode.

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Have you ever lost points on a game theory assignment or test because you came to a slightly wrong conclusion? In this installment of his series on Game Theory, William Spaniel reveals one of the most frequent mistakes game theory students make: expressing mixed strategy Nash equilibria as decimals, not fractions. William demonstrates why 1/3 is not the same as .33, supporting his claim that when solving game theory equations, its always safe to stick with fractions.

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You've tackled Game Theory 101, so what's next? William Spaniel gives you a sneak preview of more advanced Game Theory concepts such as repeated games and incomplete information. What the heck is a Bayesian Nash equilibrium? Who gets a better deal in a negotiation, and why? How and when is war inefficient? Why do people vote? All these questions and more can be answered with the magic—um, science—of game theory!

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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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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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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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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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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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Mixed strategies, pure strategies, Nash equilibria... why can't they all get along? In this lesson from William Spaniel's Game Theory 101 series, learn the rules to determine if a pure strategy is in support of a mixed strategy Nash equilibrium. You’ll work on calculating probability and expected utility, but this time will apply your skills to a 3 by 3 rather than the usual 2 by 2 game.

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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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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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War: what is it good for? Find out using backward induction to solve the Escalation Game, courtesy of William Spaniel's Game Theory 101 lesson. Should State 1 accept the status quo, or threaten State 2? If threatened, should State 2 concede, or escalate to war? Learn how each state can work backward to determine its opponent's optimal strategies, figure out its maximum payoff at each decision point, and discover why peace really is the answer.

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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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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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