The fixed price problem asks whether the cost of the orbit equivalence relation of an essentially free probability-measure-preserving action depends only on the countable group, rather than on its action. All actions in the question are on standard probability spaces. Essential freeness means that each nonidentity group element fixes a null set.
Fixed Price Problem
See also
Amalgamated Free Product, Bernoulli Action, Cost of an Equivalence Relation, Free Group, Graphing, Group Action, Probability MeasureExplore with Wolfram|Alpha
References
Gaboriau, D. "What Is ... Cost?" Notices Amer. Math. Soc. 57, 1295-1296, 2010. https://perso.ens-lyon.fr/gaboriau/Travaux-Publi/What-is-cost/What-is-cost.pdf.Cite this as:
Weisstein, Eric W. "Fixed Price Problem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FixedPriceProblem.html