At last as far as Central Asia goes, there's at least a partial answer in a recent article in Moscow's English-language foreign-policy journal Russia in Global Affairs, by Stanislav Chernyavsky, Deputy Director of the 1st Department of the CIS Countries of the Foreign Ministry of Russia:
Russia’s strategy in Central Asia must take into account not only the increased differentiation of the post-Soviet space, but also potential conflicts of interests between Russia and other actors in the region. The worst-case scenario of developments may include the destabilization and breakup of the existing secular regimes, the coming to power of religious extremists, and the emergence of interstate conflicts.From the above, it seems clear that Russia says that it seeks partnership with the United States in Central Asia, not confrontation.
The transformation of the region into a new field of confrontation is not in Russia’s interests. Gien the specificity of the present level of Russian-U.S. relations, Moscow must pursue a reasonable and clear-cut foreign policy and require that Washington make its military actions transparent and predictable. Considering the two countries’ common struggle against terror, Washington must share its plans with Russia in advance. Russian businesses would benefit from their joint participation with U.S. companies in the development and implementation of large economic projects.
Another major foreign-policy reserve for Russia is the further development of its interaction with China on Central Asian issues. The Shanghai Cooperation Organization, for example, whose organizational and legal formation is approaching the final stage, allows for Russian-Chinese cooperation to play a restraining role with regard to U.S. actions that are against Russian interests.
The Russian strategy must rest on sound pragmatism stemming from the country’s relatively limited foreign-policy resources. These resources must concentrate on key areas, above all, on security, the creation of favorable conditions for economic growth, and the protection of the rights of Russian citizens and ethnic Russians living in the region. Therefore, mutual readiness for cooperation and genuine respect for each other’s interests must become a major criterion of relations between Russia and its Central Asian partners.