# The Complete Idiot's Guide to Game Theory (Idiot's Guides)

Language: English

Pages: 384

ISBN: 161564055X

Format: PDF / Kindle (mobi) / ePub

**Gain some insight into the game of life... **

Game Theory means rigorous strategic thinking. It is based on the idea that everyone acts competitively and in his own best interest. With the help of mathematical models, it is possible to anticipate the actions of others in nearly all life's enterprises. This book includes down-to-earth examples and solutions, as well as charts and illustrations designed to help teach the concept. In *The Complete Idiot's Guide to Game Theory*, Dr. Edward C. Rosenthal makes it easy to understand game theory with insights into:

• The history of the discipline made popular by John Nash, the mathematician dramatized in the film *A Beautiful Mind*

• The role of social behavior and psychology in this amazing discipline

• How important game theory has become in our society and why

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pick a number from 0 to 100. The winner of the contest is the person who guesses the number that is ⅔ of the average number picked. • Step 0: The basic, gut response. At this level, you are not considering what others would do. Suppose you pick 50, just because it’s an average number. Let’s analyze this guess. The only way you could be the winner is if the average of the other responses was 75. Seeing this, I hope it makes sense that not only is 50 an unlikely winner, but that numbers above 50

similar to the one for strep, but with a prior probability of 1 percent rather than 40 percent. Also, to make the results clearer, I’ve changed the population to 100,000 people. Testing for HIV. Of the 1 percent (1,000 people) who actually had HIV, 990 of them received a positive test result. But 2 percent of the rest of the population also got a positive result, which amounts to 1,980 false positives. Given these results, the probability that someone with a positive test result did not have

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Consider the game represented in the following table. A zero sum game with a single dominant strategy. When Player 1 looks for row domination, he won’t find any: if Player 2 plays the first column, Player 1 is better off in the second row. But if Player 2 plays the second column, Player 1 is better off in the first row. Since neither row dominates the other, it is not obvious at this point what Player 1 should do. But what if Player 1 imagines himself in Player 2’s position? Looking at the

among the first three finishers. The votes are not recast. Rather, the exact same ballots are used but now the candidate ranked highest gets three points (instead of four), and so on. It is possible that the candidate who placed first when there were four of them will no longer be the winner when the last place finisher is removed from the ballots! BET ON IT Borda point-count tallies are used in a number of voting situations today. One example is the ranking of college basketball teams in