In a non-Bayesian game, a strategy profile is a Nash equilibrium if every strategy in that profile is a best response to every other strategy in the profile, i.e. there is no strategy that a player could play that would yield a higher payoff, given all the strategies played by the other players. In a Bayesian game (where players are modelled as risk-neutral), rational players are seeking to maximise their expected payoff, given their beliefs about the other players. A Bayesian Nash equilibrium is defined as a strategy profile and beliefs ...

See also:

Bayesian game, Bayesian game - Specification of games, Bayesian game - A signalling example, Bayesian game - Bayesian Nash equilibrium, Bayesian game - Perfect Bayesian equilibrium, Bayesian game - Belief systems, Bayesian game - Sequential rationality, Bayesian game - Definition, Bayesian game - An example

Read more here: » Bayesian game: Encyclopedia II - Bayesian game - Bayesian Nash equilibrium

Some authors have interpreted Marx's law of value as a theory of market equilibrium. However, Marx offered no theory of market equilibrium, only a dynamic theory of economic reproduction. In reality, markets were rarely in equilibrium anyway (that was more a hypothesis used by economists), and what explained the market behaviour of individuals and groups was precisely the imbalances between supply and demand. Under capitalist conditions, balancing output and market demand depended on capital accumulation occurring. A capitalist ...

See also:

Law of value, Law of value - Economic value as such, Law of value - Is it an equilibrium theory?, Law of value - Factors counteracting the law of value, Law of value - Law of value in capitalism, Law of value - Smith's hidden hand, Law of value - Modification of the law of value in the world market, Law of value - A comment by Marx on the law of value, Law of value - A comment by Frederick Engels on the law of value, Law of value - The law of value in non-capitalist societies, Law of value - Post-modern thinking about the topic, Law of value - Criticism, Law of value - A Californian perspective: Jim Devine on the LoV, Law of value - Steve Keen and the machine

Read more here: » Law of value: Encyclopedia II - Law of value - Is it an equilibrium theory?

To resolve this difficulty, first we make use of the nodal equilibrium equations in order to reduce the number of independent unknown member forces. The nodal equilibrium equation for the system has the form: where : The resulting nodal equilibrium matrix : The vector of forces arising from loading on the members. In the case of determinate systems, matrix b is square and the solution for Q can ...

See also:

Flexibility method, Flexibility method - Member flexibility, Flexibility method - Nodal equilibrium equations, Flexibility method - The primary system, Flexibility method - Compatibility equation and solution, Flexibility method - Advantages and disadvantages, Flexibility method - Related topics

Read more here: » Flexibility method: Encyclopedia II - Flexibility method - Nodal equilibrium equations

The reaction of nitrogen and hydrogen (1) is reversible, meaning the reaction can proceed in either the forward or the reverse direction depending on conditions. The forward reaction is exothermic, meaning it produces heat and is favored at low temperatures. Increasing the temperature tends to drive the reaction in the reverse direction, which is undesirable if the goal is to produce ammonia. However, reducing the temperature reduces the rate of the reaction, which is also undesirable. Therefore, an intermediate temperature high enough to allow the reaction to proceed at a reasonable rate, yet not so h ...

See also:

Haber process, Haber process - Equilibrium and the Haber Process, Haber process - Links

Read more here: » Haber process: Encyclopedia II - Haber process - Equilibrium and the Haber Process

At first, the temperature of the bottom plane is the same as the top plane. The liquid will go towards an equilibrium, where its temperature is the same as the one outside. Once there, the liquid is perfectly uniform : an observer in it would see the same environment in any spot, and in any direction. This equilibrium is also asymptotically stable: after a local, temporary perturbation of the outside temperature, it will go back ...

See also:

Bénard cells, Bénard cells - Equilibrium and thermal conduction, Bénard cells - Far from equilibrium: convection and turbulence, Bénard cells - Rayleigh-Bénard and Bénard-Marangoni convection

Read more here: » Bénard cells: Encyclopedia II - Bénard cells - Equilibrium and thermal conduction

The distribution of kinetic energy among molecules is not uniform, and it changes randomly. This means that at, say, the surface of a liquid, there may be an individual molecule with enough kinetic energy to jump into the gas phase. Likewise, individual gas molecules may have low enough kinetic energy to join other molecules in the liquid phase. This phenomena means that at any given temperature and pressure, multiple phases may co-exist. For example, under standard conditions for temperature and pressure, conditions, a bowl of liquid ...

See also:

Phase matter, Phase matter - Definition, Phase matter - Example 1: Solid liquid and gas phases, Phase matter - Example 2: Magnetic phases, Phase matter - General definition of phases, Phase matter - Other examples of phases, Phase matter - Phase diagrams, Phase matter - Metastable phases, Phase matter - Phase equilibrium, Phase matter - Emergence and universality

Read more here: » Phase matter: Encyclopedia II - Phase matter - Phase equilibrium

Let g represent the joy of eating the expensive meal, b the joy of eating the cheap meal, h is the cost of the expensive meal, l the cost of the cheap meal, and n the number of players. From the desciption above we have the following ordering h > g > b > l. Also, in order to make the game sufficiently similar to the Prisoner's dilemma we presume that one wou ...

See also:

Diner's dilemma, Diner's dilemma - Formal definition and equilibrium analysis

Read more here: » Diner's dilemma: Encyclopedia II - Diner's dilemma - Formal definition and equilibrium analysis

Suppose that entropy S is given as a function of a collection of extensive variables Ei. Each extensive variable has a conjugate intensive variable called a thermodynamic force: so that dS = Σi Ii dEi. Each of the extensive variables Ei is assumed to be conserved. This means that the following continuity equations hold: where J_{See also:}

Non-equilibrium thermodynamics, Non-equilibrium thermodynamics - Basic concepts, Non-equilibrium thermodynamics - Flows and forces, Non-equilibrium thermodynamics - Entropy production the second law and the Onsager relations, Non-equilibrium thermodynamics - Stationary states and the principle of minimal entropy production

Read more here: » Non-equilibrium thermodynamics: Encyclopedia II - Non-equilibrium thermodynamics - Flows and forces

A sender of type ,tj sends a message m * (tj) in the set of probability distributions over M (a mixed message!). (m(tj) represents the probabilities that type tj will take any of the messages in M.) The receiver observing the message m takes an action a * (m) in the spac ...

See also:

Signaling games, Signaling games - Perfect Bayesian equilibrium, Signaling games - Definition of perfect Bayesian equilibrium of the signaling game, Signaling games - Requirement 1, Signaling games - Requirement 2, Signaling games - Requirement 3, Signaling games - Requirement 4, Signaling games - Applications of signaling games

Read more here: » Signaling games: Encyclopedia II - Signaling games - Definition of perfect Bayesian equilibrium of the signaling game

If we progressively increase the temperature of the bottom plane, there will be a temperature at which something dramatic happens in the liquid : convection cells will appear. The microscopic random movement spontaneously became ordered on a macroscopic level, with a characteristic correlation length. The rotation of the cells is stable and will alternate from clock-wise to counter-clockwise as we move along horizontally: there is a spontaneous symmetry breaking. A small perturbation will not be able to change the rotation of the cells, but a larger one could very we ...

See also:

Bénard cells, Bénard cells - Equilibrium and thermal conduction, Bénard cells - Far from equilibrium: convection and turbulence, Bénard cells - Rayleigh-Bénard and Bénard-Marangoni convection

Read more here: » Bénard cells: Encyclopedia II - Bénard cells - Far from equilibrium: convection and turbulence

Wolpoff suggests that after an African origin of Homo sapiens (evolving from Homo ergaster/Homo erectus), local evolutionary events took place in several places (Africa, Europe, Asia, etc.). According to Wolpoff, populations of Homo erectus and Homo ergaster evolved separately into populations of Homo sapiens through a range of intermediate species (all the time the geographically distinct populations maintained small amounts of gene flow). This idea directly challenges the 'Out of Africa' model, which suggests Homo sapiens evolved in Africa ...

See also:

Milford H. Wolpoff, Milford H. Wolpoff - Education, Milford H. Wolpoff - Multiregional evolution and the punctuated equilibrium theory, Milford H. Wolpoff - Books and monographs

Read more here: » Milford H. Wolpoff: Encyclopedia II - Milford H. Wolpoff - Multiregional evolution and the punctuated equilibrium theory

In many fields, equilibrium or stability are fundamental concepts that can be described in terms of fixed points. For example, in economics, a Nash equilibrium of a game is a fixed point of the game's best response correspondence. In compilers, fixed point computations are used for whole program analysis, which is often required to do code optimization. The vector of PageRank values of all web pages is the fixed point of a linear transfor ...

See also:

Fixed point mathematics, Fixed point mathematics - Attractive fixed points, Fixed point mathematics - Theorems guaranteeing fixed points, Fixed point mathematics - Applications

Read more here: » Fixed point mathematics: Encyclopedia II - Fixed point mathematics - Applications

Coined after the evolutionary biologist, George C. Williams, the Williams revolution is a paradigm shift which occurred in evolutionary biology in the mid-1960s in which verbal arguments, couched in terms of "survival of the species" (essentially group selection arguments) were largely replaced by a gene-centered view of evolution, epitomised by kin selection. Models of the period showed that group selection was severely limited in its strength, although these models have since b ...

See also:

History of evolutionary thought, History of evolutionary thought - From ancient times to 1850s, History of evolutionary thought - Acquired characteristics Lamarckism and natural selection, History of evolutionary thought - Later discrediting of Lamarckism and Orthogenesis, History of evolutionary thought - 1850s - early 20th century: Darwin's theory, History of evolutionary thought - 1920s-1940s: the modern evolutionary synthesis, History of evolutionary thought - 1940s-1960s: developments following molecular biology, History of evolutionary thought - 1960s-1980s: Williams revolution punctuated equilibrium, History of evolutionary thought - 1970s-2000s: evolutionary biology as a discipline, History of evolutionary thought - Recent developments in evolutionary theory, History of evolutionary thought - Symbiogenesis, History of evolutionary thought - Neo-structuralist themes in evolutionary theory, History of evolutionary thought - Altruism, History of evolutionary thought - Horizontal gene transfer, History of evolutionary thought - Unconventional extensions to evolutionary ideas, History of evolutionary thought - De Chardin's and Huxley's theories

Read more here: » History of evolutionary thought: Encyclopedia II - History of evolutionary thought - 1960s-1980s: Williams revolution punctuated equilibrium

The preceding reaction has a chemical equilibrium constant. For reactions in water (or any aqueous solutions), the molarity (a unit of concentration) of water, [H2O], is practically constant and is omitted from the equilibrium constant expression by convention. The resulting equilibrium constant is called the ionization constant, dissociation constant, or self-ionization constant, or ion product of water and is symbolized by Kw. After omitting [H2O], the equilibrium expression is:< ...

See also:

Self-ionization of water, Self-ionization of water - Concentration and Frequency, Self-ionization of water - Acidity, Self-ionization of water - Mechanism

Read more here: » Self-ionization of water: Encyclopedia II - Self-ionization of water - Concentration and Frequency

Main article: Backward induction There are games that have multiple Nash equilibria, some of which are unrealistic. In the case of dynamic games, unrealistic Nash equilibria might be eliminated by applying backward induction, which assumes that future play will be rational. It therefore elimates noncredible (or incredible) threats because such threats would be irrational ...

See also:

Solution concept, Solution concept - Rationalizability & Iterated Dominance, Solution concept - Nash equilibrium, Solution concept - Backward induction, Solution concept - Subgame perfect Nash equilibrium, Solution concept - Perfect Bayesian equilibrium, Solution concept - Forward induction

Read more here: » Solution concept: Encyclopedia II - Solution concept - Backward induction

Main article: Rationalisability In this solution concept, players are assumed to be rational and so strictly dominated strategies are eliminated from the set of strategies that might feasibly be played. A strictly dominated strategy is one for which there is a strategy that a player is always better off playing and so a rational player would never play such a strategy. (Strictly dominated strategies are also important in minimax game-tree search). For example, in the (single period) prisoners' ...

See also:

Solution concept, Solution concept - Rationalizability & Iterated Dominance, Solution concept - Nash equilibrium, Solution concept - Backward induction, Solution concept - Subgame perfect Nash equilibrium, Solution concept - Perfect Bayesian equilibrium, Solution concept - Forward induction

Read more here: » Solution concept: Encyclopedia II - Solution concept - Rationalizability & Iterated Dominance

Signalling games constitute an example of Bayesian games. In such a game, the informed party (the agent) knows their type, whereas the uninformed party (the principal) does not know the (agent's) type. In some such games, it is possible for the principal to deduce the agent's type based on the actions the agent takes (in the form of a signal sent to the principal) in what is known as a separating equilibrium. A more specific example of a signalling game is a model of the job market. The players are the applicant (agent) ...

See also:

Bayesian game, Bayesian game - Specification of games, Bayesian game - A signalling example, Bayesian game - Bayesian Nash equilibrium, Bayesian game - Perfect Bayesian equilibrium, Bayesian game - Belief systems, Bayesian game - Sequential rationality, Bayesian game - Definition, Bayesian game - An example

Read more here: » Bayesian game: Encyclopedia II - Bayesian game - A signalling example

The 3-D strain-displacement equations are as follows: Where εi is the normal strain in the i direction, γij is the shear strain in the ij plane, and u, v, and w are the respective displacements in the x, y, and z directions. These equations have 9 more unknown quantities, and only 6 more equations. With equilibrium there are a ...

See also:

3-D Elasticity, 3-D Elasticity - Equilibrium, 3-D Elasticity - Strain-Displacement Equations, 3-D Elasticity - Constitutive, 3-D Elasticity - Compatibility

Read more here: » 3-D Elasticity: Encyclopedia II - 3-D Elasticity - Strain-Displacement Equations

The first application of signaling games to economic problems was Spence's model of job market signaling (1973). Spence describes a game where workers have a certain ability (high or low) that the employer does not know. The workers send a signal by their choice of education. The cost of the education is higher for a low ability worker than for a high ability worker. The employers observe the workers education but not their ability, and chooses to offer the worker a high or low wage. In this model it is assumed tha ...

See also:

Signaling games, Signaling games - Perfect Bayesian equilibrium, Signaling games - Definition of perfect Bayesian equilibrium of the signaling game, Signaling games - Requirement 1, Signaling games - Requirement 2, Signaling games - Requirement 3, Signaling games - Requirement 4, Signaling games - Applications of signaling games

Read more here: » Signaling games: Encyclopedia II - Signaling games - Applications of signaling games

The normal form representation of a non-Bayesian game with perfect information is a specification of the strategy spaces and payoff functions of players. A strategy for a player is complete plan of action that covers every contingency of the game, even if that contingency can never arise. The strategy space of a player is thus the set of all strategies available to a player. A payoff function is a function from the set of strategy profiles to the set of payoffs (normally the set of real numbers), where a strategy pro ...

See also:

Bayesian game, Bayesian game - Specification of games, Bayesian game - A signalling example, Bayesian game - Bayesian Nash equilibrium, Bayesian game - Perfect Bayesian equilibrium, Bayesian game - Belief systems, Bayesian game - Sequential rationality, Bayesian game - Definition, Bayesian game - An example

Read more here: » Bayesian game: Encyclopedia II - Bayesian game - Specification of games

See main article: Thermochemistry. Thermochemistry deciphers whether a specific chemical reaction can or cannot occur. Thermodynamics (or what is now known as equilibrium thermodynamics) understands the reaction in terms of the initial and final states of the reaction mixture. Reactions very seldom occur directly. Usually, reactants must collide to form an activated complex. This complex has a higher internal energy than the original reactants combined, having gained some from the kinetic energy of the reactant substance ...

See also:

Chemical reaction, Chemical reaction - Reaction types, Chemical reaction - Thermochemistry, Chemical reaction - Chemical equilibrium, Chemical reaction - Exothermic reactions, Chemical reaction - Endothermic reactions, Chemical reaction - Chemical kinetics

Read more here: » Chemical reaction: Encyclopedia II - Chemical reaction - Thermochemistry

See main article: Chemical kinetics. The rate of a chemical reaction is a measure of how the concentration of the involved substances changes with time. Analysis of reaction rates is important for several applications, such as in chemical engineering or in chemical equilibrium study. Rates of reaction depends basically on: Reactant concentrations, which usually make the reaction happen at a faster rate if raised, Surface Area, the amount of the substance being used, Pressure, By increasing the pre ...

See also:

Chemical reaction, Chemical reaction - Reaction types, Chemical reaction - Thermochemistry, Chemical reaction - Chemical equilibrium, Chemical reaction - Exothermic reactions, Chemical reaction - Endothermic reactions, Chemical reaction - Chemical kinetics

Read more here: » Chemical reaction: Encyclopedia II - Chemical reaction - Chemical kinetics