Nash Equilibrium
   HOME
*



picture info

Nash Equilibrium
In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equilibrium strategies of the other players, and no one has anything to gain by changing only one's own strategy. The principle of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to competing firms choosing outputs. If each player has chosen a strategy an action plan based on what has happened so far in the game and no one can increase one's own expected payoff by changing one's strategy while the other players keep their's unchanged, then the current set of strategy choices constitutes a Nash equilibrium. If two players Alice and Bob choose strategies A and B, (A, B) is a Nash equilibrium if Alice has no other strategy available that does better than A at maximizing her payoff in response to Bob choosing B, and Bo ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  




Rationalizability
In game theory, rationalizability is a solution concept. The general idea is to provide the weakest constraints on players while still requiring that players are rational and this rationality is common knowledge among the players. It is more permissive than Nash equilibrium. Both require that players respond optimally to some belief about their opponents' actions, but Nash equilibrium requires that these beliefs be correct while rationalizability does not. Rationalizability was first defined, independently, by Bernheim (1984) and Pearce (1984). Definition Given a normal-form game, the rationalizable set of actions can be computed as follows: Start with the full action set for each player. Next, remove all actions which are never a best reply to any belief about the opponents' actions -- the motivation for this step is that no rational player could choose such actions. Next, remove all actions which are never a best reply to any belief about the opponents' remaining actions ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


Strategy
Strategy (from Greek στρατηγία ''stratēgia'', "art of troop leader; office of general, command, generalship") is a general plan to achieve one or more long-term or overall goals under conditions of uncertainty. In the sense of the "art of the general", which included several subsets of skills including military tactics, siegecraft, logistics etc., the term came into use in the 6th century C.E. in Eastern Roman terminology, and was translated into Western vernacular languages only in the 18th century. From then until the 20th century, the word "strategy" came to denote "a comprehensive way to try to pursue political ends, including the threat or actual use of force, in a dialectic of wills" in a military conflict, in which both adversaries interact. Strategy is important because the resources available to achieve goals are usually limited. Strategy generally involves setting goals and priorities, determining actions to achieve the goals, and mobilizing resources to e ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

Association Football
Association football, more commonly known as football or soccer, is a team sport played between two teams of 11 Football player, players who primarily use their feet to propel the Ball (association football), ball around a rectangular field called a Football pitch, pitch. The objective of the game is to Scoring in association football, score more goals than the opposition by moving the ball beyond the goal line into a rectangular framed Goal (sport), goal defended by the opposing side. Traditionally, the game has been played over two 45 minute halves, for a total match time of 90 minutes. With an estimated 250 million players active in over 200 countries, it is considered the world's most popular sport. The game of association football is played in accordance with the Laws of the Game (association football), Laws of the Game, a set of rules that has been in effect since 1863 with the International Football Association Board (IFAB) maintaining them since 1886. The game is p ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

Tragedy Of The Commons
Tragedy (from the grc-gre, τραγῳδία, ''tragōidia'', ''tragōidia'') is a genre of drama based on human suffering and, mainly, the terrible or sorrowful events that befall a main character. Traditionally, the intention of tragedy is to invoke an accompanying catharsis, or a "pain hatawakens pleasure", for the audience. While many cultures have developed forms that provoke this paradoxical response, the term ''tragedy'' often refers to a specific tradition of drama that has played a unique and important role historically in the self-definition of Western civilization. That tradition has been multiple and discontinuous, yet the term has often been used to invoke a powerful effect of cultural identity and historical continuity—"the Greeks and the Elizabethans, in one cultural form; Hellenes and Christians, in a common activity," as Raymond Williams puts it. From its origins in the theatre of ancient Greece 2500 years ago, from which there survives only a fra ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

Auction Theory
Auction theory is an applied branch of economics which deals with how bidders act in auction markets and researches how the features of auction markets incentivise predictable outcomes. Auction theory is a tool used to inform the design of real-world auctions. Sellers use auction theory to raise higher revenues while allowing buyers to procure at a lower cost. The conference of the price between the buyer and seller is an economic equilibrium. Auction theorists design rules for auctions to address issues which can lead to market failure. The design of these rulesets encourages optimal bidding strategies among a variety of informational settings. The 2020 Nobel Prize for Economics was awarded to Paul R. Milgrom and Robert B. Wilson “for improvements to auction theory and inventions of new auction formats.” Introduction Auctions facilitate transactions by enforcing a specific set of rules regarding the resource allocations of a group of bidders. Theorists consider auctions ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


Wardrop's Principle
John Glen Wardrop (1922–1989), born in Warwick, England, was an English mathematician and transport analyst who developed what became known as Wardrop's first and second principles of equilibrium in the field of traffic assignment. He studied at Downing College, Cambridge, and worked in Operational Research at British Bomber Command during the Second World War. He then helped to set up, and later headed, the Traffic Section of the Road Research Laboratory near Slough (Part of the Directorate of Scientific and Industrial Research within the UK Civil Service) where he published his work on equilibrium. He subsequently followed Dr Reuben Smeed to University College London, becoming Reader Emeritus in Traffic Studies. Wardrop equilibria In studies about traffic assignment, network equilibrium models are commonly used for the prediction of traffic patterns in transportation networks that are subject to congestion. The idea of traffic equilibrium originated as early as 1924, w ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

Coordination Game
A coordination game is a type of simultaneous game found in game theory. It describes the situation where a player will earn a higher payoff when they select the same course of action as another player. The game is not one of pure conflict, which results in multiple pure strategy Nash equilibria in which players choose matching strategies. Figure 1 shows a 2-player example. Both (Up, Left) and (Down, Right) are Nash equilibria. If the players expect (Up, Left) to be played, then player 1 thinks their payoff would fall from 2 to 1 if they deviated to Down, and player 2 thinks their payoff would fall from 4 to 3 if they chose Right. If the players expect (Down, Right), player 1 thinks their payoff would fall from 2 to 1 if they deviated to Up, and player 2 thinks their payoff would fall from 4 to 3 if they chose Left. A player's optimal move depends on what they expect the other player to do, and they both do better if they coordinate than if they played an off-equilibrium combina ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

Currency Crisis
A currency crisis is a type of financial crisis, and is often associated with a real economic crisis. A currency crisis raises the probability of a banking crisis or a default crisis. During a currency crisis the value of foreign denominated debt will rise drastically relative to the declining value of the home currency. Generally doubt exists as to whether a country's central bank has sufficient foreign exchange reserves to maintain the country's fixed exchange rate, if it has any. The crisis is often accompanied by a speculative attack in the foreign exchange market. A currency crisis results from chronic balance of payments deficits, and thus is also called a balance of payments crisis. Often such a crisis culminates in a devaluation of the currency. Financial institutions and the government will struggle to meet debt obligations and economic crisis may ensue. Causation also runs the other way. The probability of a currency crisis rises when a country is experiencing a ban ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

Bank Run
A bank run or run on the bank occurs when many clients withdraw their money from a bank, because they believe the bank may cease to function in the near future. In other words, it is when, in a fractional-reserve banking system (where banks normally only keep a small proportion of their assets as cash), numerous customers withdraw cash from deposit accounts with a financial institution at the same time because they believe that the financial institution is, or might become, insolvent; they keep the cash or transfer it into other assets, such as government bonds, precious metals or gemstones. When they transfer funds to another institution, it may be characterized as a capital flight. As a bank run progresses, it may become a self-fulfilling prophecy: as more people withdraw cash, the likelihood of default increases, triggering further withdrawals. This can destabilize the bank to the point where it runs out of cash and thus faces sudden bankruptcy. To combat a bank run, a ban ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


Technical Standard
A technical standard is an established norm or requirement for a repeatable technical task which is applied to a common and repeated use of rules, conditions, guidelines or characteristics for products or related processes and production methods, and related management systems practices. A technical standard includes definition of terms; classification of components; delineation of procedures; specification of dimensions, materials, performance, designs, or operations; measurement of quality and quantity in describing materials, processes, products, systems, services, or practices; test methods and sampling procedures; or descriptions of fit and measurements of size or strength. It is usually a formal document that establishes uniform engineering or technical criteria, methods, processes, and practices. In contrast, a custom, convention, company product, corporate standard, and so forth that becomes generally accepted and dominant is often called a ''de facto'' standard. A techn ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  




Stag Hunt
In game theory, the stag hunt, sometimes referred to as the assurance game, trust dilemma or common interest game, describes a conflict between safety and social cooperation. The stag hunt problem originated with philosopher Jean-Jacques Rousseau in his ''Discourse on Inequality''. In Rousseau's telling, two hunters must decide separately, and without the other knowing, whether to hunt a stag or a hare. However, both hunters know the only way to successfully hunt a stag is with the other's help. One hunter can catch a hare alone with less effort and less time, but it is worth far less than a stag and has much less meat. Rousseau therefore posits it would be much better for each hunter, acting individually, to give up total autonomy and minimal risk, which brings only the small reward of the hare. Instead, each hunter should separately choose the more ambitious and far more rewarding goal of getting the stag, thereby giving up some autonomy in exchange for the other hunter's cooper ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


Battle Of The Sexes (game Theory)
In game theory, the battle of the sexes is a two-player coordination game that also involves elements of conflict. The game was introduced in 1957 by R. Duncan Luce and Howard Raiffa in their classic book, ''Games and Decisions''. Some authors prefer to avoid assigning sexes to the players and instead use Players 1 and 2, and some refer to the game as Bach or Stravinsky, using two concerts as the two events. The game description here follows Luce and Raiffa's original story. Imagine that a man and a woman hope to meet this evening, but have a choice between two events to attend: a prize fight and a ballet. The man would prefer to go to prize fight. The woman would prefer the ballet. Both would prefer to go to the same event rather than different ones. If they cannot communicate, where should they go? The payoff matrix labeled "Battle of the Sexes (1)" shows the payoffs when the man chooses a row and the woman chooses a column. In each cell, the first number represents the ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]