  Federated learning (FL) is rapidly gaining popularity and enables multiple
data owners ({\em a.k.a.} FL participants) to collaboratively train machine
learning models in a privacy-preserving way. A key unaddressed scenario is that
these FL participants are in a competitive market, where market shares
represent their competitiveness. Although they are interested to enhance the
performance of their respective models through FL, market leaders (who are
often data owners who can contribute significantly to building high performance
FL models) want to avoid losing their market shares by enhancing their
competitors' models. Currently, there is no modeling tool to analyze such
scenarios and support informed decision-making. In this paper, we bridge this
gap by proposing the \underline{mar}ket \underline{s}hare-based decision
support framework for participation in \underline{FL} (MarS-FL). We introduce
{\em two notions of $\delta$-stable market} and {\em friendliness} to measure
the viability of FL and the market acceptability of FL. The FL participants'
behaviours can then be predicted using game theoretic tools (i.e., their
optimal strategies concerning participation in FL). If the market
$\delta$-stability is achievable, the final model performance improvement of
each FL-PT shall be bounded, which relates to the market conditions of FL
applications. We provide tight bounds and quantify the friendliness, $\kappa$,
of given market conditions to FL. Experimental results show the viability of FL
in a wide range of market conditions. Our results are useful for identifying
the market conditions under which collaborative FL model training is viable
among competitors, and the requirements that have to be imposed while applying
FL under these conditions.
