background preloader

Nash equilibrium

Nash equilibrium
In game theory, the Nash equilibrium is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.[1] If each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitutes a Nash equilibrium. The reality of the Nash equilibrium of a game can be tested using experimental economics method. Stated simply, Amy and Will are in Nash equilibrium if Amy is making the best decision she can, taking into account Will's decision while Will's decision remains unchanged, and Will is making the best decision he can, taking into account Amy's decision while Amy's decision remains unchanged. Applications[edit] History[edit] The Nash equilibrium was named after John Forbes Nash, Jr. Let .

Game theory Game theory is the study of strategic decision making. Specifically, it is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers."[1] An alternative term suggested "as a more descriptive name for the discipline" is interactive decision theory.[2] Game theory is mainly used in economics, political science, and psychology, as well as logic, computer science, and biology. The subject first addressed zero-sum games, such that one person's gains exactly equal net losses of the other participant or participants. Modern game theory began with the idea regarding the existence of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. This theory was developed extensively in the 1950s by many scholars. Representation of games[edit] Most cooperative games are presented in the characteristic function form, while the extensive and the normal forms are used to define noncooperative games. Extensive form[edit] [edit]

Bankruptcy Notice of closure attached to the door of a Computer Shop outlet the day after its parent company declared "bankruptcy" (strictly, put into administration) in the United Kingdom Bankruptcy is a legal status of a person or other entity that cannot repay the debts it owes to creditors. In most jurisdictions, bankruptcy is imposed by a court order, often initiated by the debtor. Etymology[edit] The word bankruptcy is derived from Italian banca rotta, meaning "broken bench", which may stem from a custom of breaking a moneychanger's bench or counter to signify his insolvency, or which may be only a figure of speech.[1][2][3][4][5] History[edit] In Ancient Greece, bankruptcy did not exist. In Islamic teaching, according to the Qur'an, an insolvent person was deemed to be allowed time to be able to pay out his debt. The Statute of Bankrupts of 1542 was the first statute under English law dealing with bankruptcy or insolvency.[8] Bankruptcy is also documented in East Asia. Fraud[edit] Brazil[edit]

Science Magazine: Sign In Theoretical work suggests that structural properties of naturally occurring networks are important in shaping behavior and dynamics. However, the relationships between structure and behavior are difficult to establish through empirical studies, because the networks in such studies are typically fixed. We studied More Theoretical work suggests that structural properties of naturally occurring networks are important in shaping behavior and dynamics. Demand deposit Demand deposits, bank money or scriptural money[1] are funds held in demand deposit accounts in commercial banks.[2] These account balances are usually considered money and form the greater part of the narrowly defined money supply of a country.[3] History[edit] In the United States, demand deposits arose following the 1865 tax of 10% on the issuance of state bank notes; see history of banking in the USA. In the U.S., demand deposits only refer to funds held in checking accounts (or cheque offering accounts) other than NOW accounts; however, in a 1970s and 1980s response to the 1933 promulgation of Regulation Q in the U.S., demand deposits in some cases came to allow easier access to funds from other types of accounts (e.g. savings accounts and money market accounts). Money supply[edit] Demand deposits are usually considered part of the narrowly defined money supply, as they can be used, via checks and drafts, as a means of payment for goods and services and to settle debts. See also[edit]

Behavioral dynamics and influence in networked coloring and consensus Author Affiliations Edited by Brian Skyrms, University of California, Irvine, CA, and approved July 16, 2010 (received for review February 3, 2010) A correction has been published Abstract We report on human-subject experiments on the problems of coloring (a social differentiation task) and consensus (a social agreement task) in a networked setting. Social organizations often need to perform coordination tasks in a networked and decentralized fashion. We describe human-subject experiments in which decentralized coordination is modeled as the problems of coloring and consensus on a parametrized family of networks. The (behavioral) coloring problem (1) requires each player in a network to choose a color from a fixed set that differs from the choice of all of their network neighbors, while consensus requires selecting a color that agrees with all network neighbors. Related Work Decentralized coordination is a problem of long standing interest. Experimental Methodology Fig. 1. Fig. 2. Fig. 3.

Systemic risk In finance, systemic risk is the risk of collapse of an entire financial system or entire market, as opposed to risk associated with any one individual entity, group or component of a system, that can be contained therein without harming the entire system.[1][2][3] It can be defined as "financial system instability, potentially catastrophic, caused or exacerbated by idiosyncratic events or conditions in financial intermediaries".[4] It refers to the risks imposed by interlinkages and interdependencies in a system or market, where the failure of a single entity or cluster of entities can cause a cascading failure, which could potentially bankrupt or bring down the entire system or market.[5] It is also sometimes erroneously referred to as "systematic risk". Explanation[edit] Systemic risk has been associated with a bank run which has a cascading effect on other banks which are owed money by the first bank in trouble, causing a cascading failure. Measurement of systemic risk[edit]

PageRank Algorithm used by Google Search to rank web pages PageRank (PR) is an algorithm used by Google Search to rank web pages in their search engine results. It is named after both the term "web page" and co-founder Larry Page. PageRank is a way of measuring the importance of website pages. PageRank works by counting the number and quality of links to a page to determine a rough estimate of how important the website is. Currently, PageRank is not the only algorithm used by Google to order search results, but it is the first algorithm that was used by the company, and it is the best known.[2][3] As of September 24, 2019, all patents associated with PageRank have expired.[4] Description[edit] A PageRank results from a mathematical algorithm based on the webgraph, created by all World Wide Web pages as nodes and hyperlinks as edges, taking into consideration authority hubs such as cnn.com or mayoclinic.org. History[edit] Algorithm[edit] A probability is expressed as a numeric value between 0 and 1.

Cascading failure An animation demonstrating how a single failure may result in other failures throughout a network. A cascading failure is a failure in a system of interconnected parts in which the failure of a part can trigger the failure of successive parts. Such a failure may happen in many types of systems, including power transmission, computer networking, finance and bridges. Cascading failures usually begin when one part of the system fails. Cascading failure in power transmission[edit] Cascading failure is common in power grids when one of the elements fails (completely or partially) and shifts its load to nearby elements in the system. This failure process cascades through the elements of the system like a ripple on a pond and continues until substantially all of the elements in the system are compromised and/or the system becomes functionally disconnected from the source of its load. Examples[edit] Cascading failure caused the following power outages: Cascading failure in computer networks[edit]

Behavioral experiments on biased voting in networks Author Affiliations Edited by Ronald L. Graham, University of California at San Diego, La Jolla, CA, and approved December 5, 2008 (received for review August 19, 2008) Abstract Many distributed collective decision-making processes must balance diverse individual preferences with a desire for collective unity. We report here on an extensive session of behavioral experiments on biased voting in networks of individuals. Keywords: The tension between the expression of individual preferences and the desire for collective unity appears in decision-making and voting processes in politics, business, and many other arenas. The 2008 Democratic National Primary race offers a recent, if approximate, example of this phenomenon. Although there is now a significant literature on the diffusion of opinion in social networks (2–4), the topic is typically studied in the absence of any incentives toward collective unity. Fig. 1. Screenshot of the user interface for a typical experiment. Experimental Design

Fractional reserve banking Fractional-reserve banking is the practice whereby a bank holds reserves in an amount equal to only a portion of the amount of its customers' deposits to satisfy potential demands for withdrawals. Reserves are held at the bank as currency, or as deposits reflected in the bank's accounts at the central bank. Because bank deposits are usually considered money in their own right, fractional-reserve banking permits the money supply to grow to a multiple (called the money multiplier) of the underlying reserves of base money originally created by the central bank.[1][2] Fractional-reserve banking is the current form of banking in all countries worldwide.[3] History[edit] Fractional-reserve banking predates the existence of governmental monetary authorities and originated many centuries ago in bankers' realization that generally not all depositors demand payment at the same time.[4] How it works[edit] In most legal systems, a bank deposit is not a bailment. Economic function[edit] Formula[edit]

Exclusive: How Google's Algorithm Rules the Web | Wired Magazine Want to know how Google is about to change your life? Stop by the Ouagadougou conference room on a Thursday morning. It is here, at the Mountain View, California, headquarters of the world’s most powerful Internet company, that a room filled with three dozen engineers, product managers, and executives figure out how to make their search engine even smarter. This year, Google will introduce 550 or so improvements to its fabled algorithm, and each will be determined at a gathering just like this one. The decisions made at the weekly Search Quality Launch Meeting will wind up affecting the results you get when you use Google’s search engine to look for anything — “Samsung SF-755p printer,” “Ed Hardy MySpace layouts,” or maybe even “capital Burkina Faso,” which just happens to share its name with this conference room. You might think that after a solid decade of search-market dominance, Google could relax. Still, the biggest threat to Google can be found 850 miles to the north: Bing.

Margin (finance) Margin buying refers to the buying of securities with cash borrowed from a broker, using other securities as collateral. This has the effect of magnifying any profit or loss made on the securities. The securities serve as collateral for the loan. The variation margin or mark to market is not collateral, but a daily payment of profits and losses. The seller of an option has the obligation to deliver the underlying of the option if it is exercised. Additional margin is intended to cover a potential fall in the value of the position on the following trading day. SMA and portfolio margins offer alternative rules for U.S. and NYSE regulatory margin requirements. Enhanced leverage is a strategy offered by some brokers that provides 4:1 or 6:1+ leverage. Example 1 An investor sells a call option, where the buyer has the right to buy 100 shares in Universal Widgets S.A. at 90¢. Example 2 Futures contracts on sweet crude oil closed the day at $65. Example 3 (ROM + 1)(1/trade duration in years) - 1

The Small-World Phenomenon: An Algorithmic Perspective 1 Jon Kleinberg 2 Abstract: Long a matter of folklore, the ``small-world phenomenon'' -- the principle that we are all linked by short chains of acquaintances -- was inaugurated as an area of experimental study in the social sciences through the pioneering work of Stanley Milgram in the 1960's. This work was among the first to make the phenomenon quantitative, allowing people to speak of the ``six degrees of separation'' between any two people in the United States. Since then, a number of network models have been proposed as frameworks in which to study the problem analytically. One of the most refined of these models was formulated in recent work of Watts and Strogatz; their framework provided compelling evidence that the small-world phenomenon is pervasive in a range of networks arising in nature and technology, and a fundamental ingredient in the evolution of the World Wide Web. The Small-World Phenomenon. Modeling the Phenomenon. The Present Work. Let us return to Milgram's experiment. and

Related: