  Resources are often limited, therefore it is essential how convincingly
competitors present their claims for them. Beside a player's natural capacity,
here overconfidence and bluffing may also play a decisive role and influence
how to share a restricted reward. While bluff provides clear, but risky
advantage, overconfidence, as a form of self-deception, could be harmful to its
user. Still, it is a long-standing puzzle why these potentially damaging biases
are maintained and evolving to a high level in the human society. Within the
framework of evolutionary game theory, we present a simple version of resource
competition game in which the coevolution of overconfidence and bluffing is
fundamental, which is capable to explain their prevalence in structured
populations. Interestingly, bluffing seems apt to evolve to higher level than
corresponding overconfidence and in general the former is less resistant to
punishment than the latter. Moreover, topological feature of the social network
plays an intricate role in the spreading of overconfidence and bluffing. While
the heterogeneity of interactions facilitates bluffing, it also increases
efficiency of adequate punishment against overconfident behavior. Furthermore,
increasing the degree of homogeneous networks can trigger similar effect. We
also observed that having high real capability may accommodate both bluffing
ability and overconfidence simultaneously.
