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A Nash equilibrium for a mixed-strategy game is stable if a small change (specifically, an infinitesimal change) in probabilities for one player leads to a situation where two conditions hold: the player who did not change has no better strategy in the new circumstance; the player who did change is now playing with a strictly worse strategy.
In the thermodynamics of equilibrium, a state function, function of state, or point function for a thermodynamic system is a mathematical function relating several state variables or state quantities (that describe equilibrium states of a system) that depend only on the current equilibrium thermodynamic state of the system [1] (e.g. gas, liquid, solid, crystal, or emulsion), not the path which ...
A Nash equilibrium is presumed to be stable even if T scores equally, on the assumption that there is no long-term incentive for players to adopt T instead of S. This fact represents the point of departure of the ESS. Maynard Smith and Price [2] specify two conditions for a strategy S to be an ESS. For all T≠S, either E(S,S) > E(T,S), or
One such ideal condition is that of a stable equilibrium state. Such a state is a primitive object of classical or equilibrium thermodynamics, in which it is called a thermodynamic state. Based on many observations, thermodynamics postulates that all systems that are isolated from the external environment will evolve so as to approach unique ...
In chemistry, Le Chatelier's principle (pronounced UK: / l ə ʃ æ ˈ t ɛ l j eɪ / or US: / ˈ ʃ ɑː t əl j eɪ /) [1] is a principle used to predict the effect of a change in conditions on chemical equilibrium. [2] Other names include Chatelier's principle, Braun–Le Chatelier principle, Le Chatelier–Braun principle or the equilibrium ...
Frank Ackerman points out that it is a corollary of Sonnenschein–Mantel–Debreu that a Walrasian auction will not always find a unique and stable equilibrium, even in ideal conditions: In Walrasian general equilibrium, prices are adjusted through a tâtonnement ('groping') process: the rate of change for any commodity’s price is ...
Common components of a phase diagram are lines of equilibrium or phase boundaries, which refer to lines that mark conditions under which multiple phases can coexist at equilibrium. Phase transitions occur along lines of equilibrium. Metastable phases are not shown in phase diagrams as, despite their common occurrence, they are not equilibrium ...
He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium". [36] P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat ...