Platform cross-market operation has become more and more popular in recent years， and how platforms provide cross-market service in multimarket competition has aroused widespread social concern. Based on the Hotelling model， a multimarket competition system between two platforms serving sellers and consumers is built with different cross-market service preferences in two different markets， and the decision-making issue of platforms is examined from two available options： implementing the customizing strategy or the default strategy when providing cross-market services to consumers. The following findings are derived by the analysis. （1） Platforms price competition does not always tend to be fiercer when the same strategy is chosen by platforms than when the different strategies are chosen. Under some circumstance， it tends to be more relaxed. （2） Three situations， which are both platforms implementing the default strategy， one platform implementing the customizing strategy while the other implementing the default strategy， and both platforms implementing the customizing strategy， may be the final Nash equilibrium for platforms providing cross-market services， depending on the cross-side network externalities of platforms and the proportion of consumers who like and dislike the cross-market service. （3） Two situations， which are only one or both platforms implementing the default strategy， have the chance to bring the highest social welfare， while the situation in which both platforms implementing customizing strategy results in the lowest social welfare.