The Gift-exchange game is a concept used in economics and social science to study the dynamics of reciprocity, trust, and social norms within interactions between individuals. It is typically framed as a specific type of game in experimental economics, where participants make decisions involving gifts or resources to one another. Here’s a basic outline of how the Gift-exchange game typically works: 1. **Players**: There are generally two players involved: a "giver" and a "receiver.
A finite game is a concept chiefly derived from game theory and is often contrasted with infinite games. Finite games have specific characteristics: 1. **Defined Rules:** Finite games have clear and fixed rules that determine how the game is played. 2. **Clear Objectives:** Players in a finite game have specific goals that they strive to achieve, such as winning or reaching a certain score.
An extensive-form game is a type of game used in game theory to model situations where players make decisions sequentially over time. It represents the structure of a game in a tree-like format, illustrating the various possible moves, strategies, and outcomes that can arise in the game. Each node of the tree represents a decision point for a player, and branches represent the possible actions that can be taken from that point.
A continuous game, in the context of game theory, refers to a type of game in which players choose strategies from a continuous set of options, rather than from a discrete set. This can involve decisions regarding quantities, prices, or strategies that are represented by real numbers or continuous intervals. ### Key Features of Continuous Games: 1. **Continuous Strategy Space**: Players' choices can take any value within a given range.
A **congestion game** is a type of game in game theory that models scenarios where multiple players (or agents) choose from a set of shared resources, which can become congested as more players use them. In these games, players do not have direct control over resources, but their choices affect the availability and efficiency of those resources. ### Key Characteristics of Congestion Games: 1. **Players**: A finite set of players who independently choose resources.
The CC–PP game likely refers to a concept within game theory or a specific type of strategic interaction involving two players, commonly denoted as "CC" for "Cooperate-Cooperate" and "PP" for "Play-Play" (often used in the context of cooperative vs. non-cooperative scenarios). However, the specific acronym can sometimes vary in meaning depending on the context in which it is used.
A bimatrix game is a type of game in game theory that involves two players, each of whom has a finite set of strategies. The outcomes of their choices are represented in the form of a matrix (or two matrices) that captures the payoffs for each combination of strategies chosen by the players. In a bimatrix game, the strategies of the two players can be represented as follows: - Player 1's strategies are represented in one matrix (let's call it Matrix A).
A Bayesian game is a type of game in game theory that incorporates incomplete information about certain aspects of the game, particularly the preferences or types of the players. In a Bayesian game, players have private information that is not known to the other players, and this information can affect their strategies and payoffs. Key features of Bayesian games include: 1. **Types**: Each player has a type, typically representing their preferences or payoffs.
The Bandwidth-sharing game is a concept used in the field of networking and resource allocation, and it often appears within the context of game theory. In this scenario, a number of users or agents compete for limited bandwidth resources in a network. The central idea is that each user must decide how much of the available bandwidth to utilize, with each user’s decision affecting not only their own performance but also the overall performance of others in the network.
In game theory, an aggregative game is a type of game where each player's payoff is determined not only by their own strategy but also by the aggregate actions or strategies of all players in the game. This means that the players' decisions affect each other through their collective outcomes. ### Key Features of Aggregative Games: 1. **Aggregate Function**: The payoff for each player is a function that can be expressed in terms of the total (or aggregate) action taken by all players.
Symmetric equilibrium is a concept often used in game theory and economics. It refers to a situation in which all players in a game or economic model choose the same strategy, leading to an equilibrium where no player has an incentive to deviate unilaterally from that strategy. In symmetric equilibrium: 1. **Identical Strategies**: All players have access to the same strategies, and they choose the same one.
Subgame Perfect Equilibrium (SPE) is a refinement of Nash Equilibrium used in game theory, specifically in the context of extensive-form games, which can be represented by a tree-like structure. In an SPE, the strategy profile is not only a Nash Equilibrium in the game as a whole but also remains a Nash Equilibrium in every subgame of that game.
A Strong Nash Equilibrium is a concept in game theory that extends the traditional notion of Nash equilibrium. In a typical Nash equilibrium, a set of strategies is considered stable if no single player can unilaterally change their strategy to achieve a better payoff, given the strategies of the other players. In contrast, a Strong Nash Equilibrium requires that no group of players can improve their payoff by jointly deviating from their current strategies.
Stochastically stable equilibrium is a concept used in the field of evolutionary game theory and dynamic systems to describe a state of a system that remains stable over time under stochastic (random) influences. It represents an equilibrium point that is not only stable in a deterministic sense but also resilient to small random fluctuations or perturbations that may occur in the system.
Sequential equilibrium is a concept from game theory, particularly in the context of dynamic games, which are games where players make decisions at various points in time, and the decisions can depend on past actions. A sequential equilibrium is an extension of the Nash equilibrium that takes into account the order of moves and the information available to players at each decision point. It considers both the strategies of players and their beliefs about the game's state.
Separating equilibrium is a concept used in game theory and economics, particularly in the context of signaling games. It refers to a situation where different types of players (often with private information) choose distinct actions or strategies that reveal their type to other players. In a separating equilibrium, the actions taken by each type of player provide clear signals that allow other players to infer the type of the signaling player accurately.
A self-enforcing agreement is a type of contract or arrangement in which the terms and conditions are designed to be automatically upheld or enforced without the need for external intervention, such as a court or a regulatory agency. In other words, the agreement contains built-in mechanisms that incentivize the parties to comply voluntarily, as the consequences of non-compliance are sufficiently significant to deter breaches.
A self-confirming equilibrium is a concept in game theory that refers to a type of equilibrium in which players' beliefs about the strategies and types of other players are consistent with the observed actions of those players, but not necessarily with the entire strategy profile of the game. This means that players form beliefs based on the limited information they have observed, which influences their strategic choices. In a typical Nash equilibrium, all players' strategies are mutual best responses, given their beliefs about the other players' strategies.
"Satisfaction equilibrium" is not a widely recognized term in mainstream economics or psychology, but it can be interpreted in a few different ways depending on the context. 1. **In Economics**: It might refer to a state where individuals or firms derive a level of satisfaction from their consumption or production that is balanced with their constraints (like budget or resources). This concept could be related to the idea of utility maximization, where consumers are satisfied with their choices given their income and the prices of goods.

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!
We have two killer features:
  1. 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-calculus
    Articles 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/derivative
  2. 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.
    Figure 5. . 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.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
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