How to assess the existence of competing strategies in cognitive tasks: a primer on the fixed-point property

PLoS One. 2014 Aug 29;9(8):e106113. doi: 10.1371/journal.pone.0106113. eCollection 2014.


When multiple strategies can be used to solve a type of problem, the observed response time distributions are often mixtures of multiple underlying base distributions each representing one of these strategies. For the case of two possible strategies, the observed response time distributions obey the fixed-point property. That is, there exists one reaction time that has the same probability of being observed irrespective of the actual mixture proportion of each strategy. In this paper we discuss how to compute this fixed-point, and how to statistically assess the probability that indeed the observed response times are generated by two competing strategies. Accompanying this paper is a free R package that can be used to compute and test the presence or absence of the fixed-point property in response time data, allowing for easy to use tests of strategic behavior.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Cognition*
  • Computer Simulation
  • Humans
  • Models, Psychological*
  • Monte Carlo Method
  • Reaction Time

Grant support

This study was funded by the University of Amsterdam and the University of Groningen. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.