Optimal mixed strategies in stochastic environments
type: Item
instance of: scholarly article
title: Optimal mixed strategies in stochastic environments
zbMATH Open document ID: 0823.92015
author: Patsy Haccou
author: Yoh Iwasa
published in: Theoretical Population Biology
publication date: 1995-10-31T00:00:00Z
review text: We will discuss the case of non-structured populations where the environment is characterized by a one-dimensional stochastic parameter that varies over the generations according to an ergodic process. It is shown how the optimal strategy in such situations can, in principle, be found. This also leads to a criterion to decide whether pure or mixed strategies are optimal for any given case. Our results make it possible to calculate optimal strategies in stochastic environments explicitly for complicated situations. These include, for instance, a number of cases with continuous strategy sets. As an illustration, we then derive the optimal strategy for the situation in which the payoff function (specifying the relationship between trait values, environment, and expected contributions to the population size in the next generation) has a Gaussian form and the environmental parameter has a normal distribution. After that, more general forms of environmental distributions as well as payoff functions are considered, leading to explicit solutions for specific cases, using results from the statistical literature, and numerical solutions otherwise. Initially we assume that individuals have no information about the current value of the environmental parameter, but they do ``know'' its distribution over the generations. This amounts to assuming that the environment is stable over a large number of generations. Afterwards, we generalize the model for situations where individuals can obtain indications of the environmental conditions using some external cue. As we will show, environmental variability usually leads to mixed rather than pure optimal strategies. Furthermore, there is a minimum environmental variance below which pure strategies are optimal, which depends on the form of the payoff function and, in case there is information about the environment, on the accuracy of such information. We investigate the difference between long-term reproductive success of different strate…
Mathematics Subject Classification ID: 92D15
Mathematics Subject Classification ID: 91A40
Mathematics Subject Classification ID: 91A60
zbMATH DE Number: 756551
zbMATH Keywords: non-structured populations
zbMATH Keywords: ergodic process
zbMATH Keywords: optimal strategy
zbMATH Keywords: mixed strategies
zbMATH Keywords: stochastic environments
zbMATH Keywords: continuous strategy sets
zbMATH Keywords: environmental variability
zbMATH Keywords: pure optimal strategies
zbMATH Keywords: long-term reproductive success
zbMATH Keywords: selection pressure
MaRDI profile type: Publication
full work available at URL: tpbi.1995.1009
OpenAlex ID: W2049435734
Wikidata QID: Q57065589
DOI: 10.1006/TPBI.1995.1009
description: scientific article; zbMATH DE number 756551