We present observations with the Submillimeter Array of the continuum emission at ? =1.3 {mm} from 62 young stars surrounded by a protoplanetary disk in the Serpens star-forming region. The typical angular resolution for the survey in terms of beam size is 3\buildrel{\prime\prime}\over{.} 5× 2\buildrel{\prime\prime}\over{.} 5 with a median rms noise level of 1.6 mJy beam-1. These data are used to infer the dust content in disks around low-mass stars (0.1{--}2.5 {M}? ) at a median stellar age of 1-3 Myr. Thirteen sources were detected in the 1.3 mm dust continuum with inferred dust masses of ? 10{--}260 {M}\oplus and an upper limit to the median dust mass of {5.1}-4.3 6.1 {M}\oplus , derived using survival analysis. Comparing the protoplanetary disk population in Serpens to those of other nearby star-forming regions, we find that the populations of dust disks in Serpens and Taurus, which have a similar age, are statistically indistinguishable. This is potentially surprising as Serpens has a stellar surface density two orders of magnitude in excess of Taurus. Hence, we find no evidence that dust disks in Serpens have been dispersed as a result of more frequent and/or stronger tidal interactions due to its elevated stellar density. We also report that the fraction of Serpens disks with {M}{dust}>=slant 10 {M}\oplus is less than 20%, which supports the notion that the formation of giant planets is likely inherently rare or has substantially progressed by a few Myr.
