  We investigate the possible existence of the bound state in the system of
three bosons interacting with each other via zero-radius potentials in two
dimensions (it can be atoms confined in two dimensions or tri-exciton states in
heterostructures or dihalogenated materials). The bosons are classified in two
species (a,b) such that a-a and b-b pairs repel each other and a-b attract each
other, forming the two-particle bound state with binding energy
$\epsilon_b^{(2)}$ (such as bi-exciton). We developed an efficient routine
based on the proper choice of basis for analytic and numerical calculations.
For zero-angular momentum we found the energies of the three-particle bound
states $\epsilon^{(3)}_b$ for wide ranges of the scattering lengths, and found
a universal curve of $\epsilon^{(3)}_b/\epsilon^{(2)}_b$ which depends only on
the scattering lengths but not the microscopic details of the interactions,
this is in contrast to the three-dimensional Efimov effect, where a
non-universal three-body parameter is needed.
