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Recently, we introduced the class of matrix games under time constraints and characterized the concept of (monomorphic) evolutionarily stable strategy (ESS) in them. We are now interested in how the ESS is related to the existence and stability of equilibria for polymorphic populations. We point out that, although the ESS may no longer be a polymorphic equilibrium, there is a connection between them. Specifically, the polymorphic state at which the average strategy of the active individuals in the population is equal to the ESS is an equilibrium of the polymorphic model. Moreover, in the case when there are only two pure strategies, a polymorphic equilibrium is locally asymptotically stable under the replicator equation for the pure-strategy polymorphic model if and only if it corresponds to an ESS. Finally, we prove that a strict Nash equilibrium is a pure-strategy ESS that is a locally asymptotically stable equilibrium of the replicator equation in n-strategy time-constrained matrix games.
This article was published in the following journal.
Name: Journal of mathematical biology
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Games designed to provide information on hypotheses, policies, procedure or strategies.
A form of interactive entertainment in which the player controls electronically generated images that appear on a video display screen. This includes video games played in the home on special machines or home computers, and those played in arcades. (McGraw Hill Encyclopedia of Science & Technology, 7th ed, v19, p223)
The study of systems which respond disproportionately (nonlinearly) to initial conditions or perturbing stimuli. Nonlinear systems may exhibit "chaos" which is classically characterized as sensitive dependence on initial conditions. Chaotic systems, while distinguished from more ordered periodic systems, are not random. When their behavior over time is appropriately displayed (in "phase space"), constraints are evident which are described by "strange attractors". Phase space representations of chaotic systems, or strange attractors, usually reveal fractal (FRACTALS) self-similarity across time scales. Natural, including biological, systems often display nonlinear dynamics and chaos.
A secreted matrix metalloproteinase that is the predominant proteolytic activity in the enamel matrix. The enzyme has a high specificity for dental enamel matrix protein AMELOGENIN.
A transmembrane domain-containing matrix metalloproteinase. It is synthesized as an inactive zymogen that is activated by the proteolytic action of PROPROTEIN CONVERTASES. Matrix metalloproteinase 16 plays a direct role in the cleavage of proteins in the pericellular environment. In addition it can function indirectly by enzymatically activating the proprotein form of other MATRIX METALLOPROTEINASES such as the zymogen of MATRIX METALLOPROTEINASE 2.