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Pareto efficiency, also known as Pareto optimality, is an economic concept that describes a situation in which resources are allocated in a way that no reallocation can make one individual better off without making at least one other individual worse off. In simpler terms, an allocation is Pareto efficient if there are no possible changes that could improve someone's situation without harming someone else's situation.
Game design is the art and science of creating the content and rules of a game. It involves conceptualizing the game's mechanics, story, characters, environment, and aesthetics to create an engaging and interactive experience for players. Game design can encompass various genres and platforms, including video games, board games, card games, and more.
Fair division is a mathematical and economic concept that deals with dividing a set of resources or goods among individuals or parties in such a way that each participant believes they have received their fair share. This can involve tangible items, such as land or goods, as well as intangible resources, such as time or opportunities. The principles of fair division can be applied in various contexts, including: 1. **Dividing Chores or Tasks**: Splitting household responsibilities among family members or roommates.
Evolutionary game theory is a theoretical framework that combines concepts from evolutionary biology and game theory to study the strategic interactions among individuals (often referred to as "players") in a population. This approach aims to understand how certain behaviors or strategies evolve over time through the lens of natural selection and competitive interactions. Key components of evolutionary game theory include: 1. **Strategies**: In this context, a strategy is a specific behavior or action that an individual can adopt when interacting with others.
The "Tragedy of the Commons" is an economic concept and social theory that describes a situation in which individual users, acting independently according to their own self-interest, deplete or degrade a shared resource (the "commons") despite knowing that this depletion is contrary to the collective long-term interest of the group. The term was popularized by the ecologist Garrett Hardin in his 1968 essay.
Topological games are a branch of mathematics that blends concepts from topology and game theory. They typically involve players making moves within a topological space, and the outcomes often depend on the properties of the space and the strategies employed by the players. In general, a topological game involves two players, commonly referred to as Player 1 and Player 2. The game is played on a topological space, and players take turns choosing points from designated subsets of that space.
In game theory, a **strategy** refers to a comprehensive plan or set of actions that a player will follow in a game, which outlines the choices they will make in response to the actions of other players. The concept of strategy is central to understanding how players interact in various types of games, whether they are competitive, cooperative, or hybrid.
Non-cooperative games are a branch of game theory where players make decisions independently and strategically, without collaborating or forming binding agreements with each other. In these games, each player aims to maximize their own payoff, considering the potential actions of other players, but does not cooperate to achieve a collective goal. Key characteristics of non-cooperative games include: 1. **Individual Payoffs**: Each player’s strategy is aimed at maximizing their own payoff, which means they act in their own self-interest.
In game theory, inefficiency typically refers to a situation where resources are not allocated in the most effective way possible, leading to a loss of potential value or utility. This can occur in various forms, such as: 1. **Pareto Inefficiency**: A situation is said to be Pareto inefficient if there exists at least one alternative allocation of resources that would make at least one player better off without making any other player worse off.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.Figure 4. Visual Studio Code extension tree navigation.Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. - Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact





