Learn Russian: Согласно вашей просьбе, мы вчера подписали договор. - According to your request, we signed the contract yesterday.

The preposition согласно (according to) strictly requires the Dative case in modern Russian. Therefore, the feminine noun просьба and its modifier ваша change to their Dative forms: вашей просьбе.

I sometimes hear native speakers use the Genitive case with согласно. Is that correct?

You might hear phrases like согласно закона (Genitive) instead of согласно закону (Dative) in highly bureaucratic speech or older texts. However, standard modern Russian grammar firmly requires the Dative case. Always stick to the Dative to sound educated.

Could I say по вашей просьбе instead of согласно вашей просьбе?

Yes! По вашей просьбе (at your request) also takes the Dative and means essentially the same thing. Согласно sounds a bit more formal and professional, which fits the context of signing a business contract perfectly.

Why is there a comma after просьбе?

In Russian, extended introductory phrases starting with prepositions like согласно, вопреки (contrary to), or благодаря (thanks to) are usually set off by a comma when they appear at the very beginning of a sentence.

Since the action happened in the past (вчера), why do we use the perfective verb instead of the imperfective?