Game theory game classes

Repeated game

In game theory, a repeated game is an extensive form game that consists of a number of repetitions of some base game (called a stage game). The stage game is usually one of the well-studied 2-person games. Repeated games capture the idea that a player will have to take into account the impact of his or her current action on the future actions of other players; this impact is sometimes called his or her reputation. Single stage game or single shot game are names for non-repeated games. For the real-life example of a repeated game, consider two gas stations that are adjacent to one another. They compete by publicly posting pricing and have the same and constant marginal cost c (the wholesale price of gasoline). Assume that when they both charge p = 10, their joint profit is maximized, resulting in a high profit for everyone. Despite the fact that this is the best outcome for them, they are motivated to deviate. By modestly lowering the price, anyone can steal all of their competitors' consumers, doubling their revenues (nearly). P = c, where their profit is zero, is the only price without this profit deviation. In other words, in the pricing competition game, the only Nash equilibrium is inefficient (for gas stations) that both charge p = c. This is more of a rule than an exception: in a staged game, the Nash equilibrium is the only result that an agent can consistently acquire in an interaction, and it is usually inefficient for them. This is because the agents are just concerned with their own personal interests and are unconcerned about the benefits or costs that their actions bring to competitors. On the other hand, gas stations make a profit even if there is another gas station adjacent. One of the most crucial reasons is that their interaction is not one-off. This condition is portrayed by repeated games, in which two gas stations compete for pricing (stage games) across an indefinite time range t = 0, 1, 2,.... (Wikipedia).

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A07 Repeated real eigenvalues

What the the eigenvalues repeat? There are two possibilities. In one there is only a single eigenvector and in the other there are more than one. Each scenario leads to a different set of solutions.

From playlist A Second Course in Differential Equations

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This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.

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A08 Example problem of repeated real eigenvalues

Here is an example problem with repeated eigenvalues.

From playlist A Second Course in Differential Equations

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21. Repeated games: cooperation vs. the end game

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Recurring Decimals | Number | Maths | FuseSchool

In this video we look at what recurring decimals are, and how to write them as fractions. Recurring decimals repeat forever. To save us having to write all of the repeating numbers, we can place a dot above the number or numbers that repeat. If all the decimal places don’t repeat, just put

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Parallel Repetition of Two Prover Games: A Survey - Ran Raz

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C56 Continuation of previous problem

Adding a bit more depth to the previous problem.

From playlist Differential Equations

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This mathematics video tutorial provides a basic introduction into addition, multiplication, exponents, and tetration. Addition can be thought of as repeat counting. Multiplication is repeat addition and exponentiation is repeat multiplication. Tetration is repeat exponentiation. This

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Nash equilibrium | Backward induction | Chainstore paradox | Linear algebra | Folk theorem (game theory) | Trigger strategy | List of games in game theory | Game theory | Public goods game | Minimax | Fictitious play