  We investigate theoretically polyelectrolyte bridging interactions on the
two-body level. The model system is composed of two macroions with two
oppositely charged flexible chains. The electrostatic interactions are treated
on the Debye - H\" uckel level. The formal level of the theory is provided by
the Feynman-Kleinert variational method generalized to include also
self-interactions between polyelectrolyte segments. The variational equations
are shown to exhibit two solution branches corresponding to {\sl strong} and
{\sl weak} coupling, whereas conformations of the chain can be described as
{\sl weakly} or {\sl strongly paired}. We investigate the effective pair
interaction between the macroions in the parameter space and comment on the
relevance of the calculation for bridging interactions in experimental context.
