  This paper attempts to develop a graph-theoretic multi-agent perspective of
population games to study the \quotes{truncation} behavior. The proposed method
considers fitness of the population as a dynamical system to address the issue
of restrictive description of this behavior which pertains to the underlying
population dynamic. The fitness dynamic resembles an agreement protocol that
enables comments on the steady-state characteristics of the graph that
represents the population structure. The structural attributes of the
underlying graph and the truncation behavior are emphasized by exploiting the
spectral properties of the associated Laplacian matrix. The asymptotic
stability of the fitness agreement protocol has been shown to be sufficient in
concluding the stability of population dynamics. Simulation results validating
the proposed hypothesis have been discussed.
