  A greedy personality is usually accompanied by arrogance and confidence. This
work investigates the cooperation success condition in the context of biased
payoff allocation and self-confidence. The first component allows the organizer
in a spatial public goods game to receive a different proportion of goods than
other participants. The second aspect influences the micro-level dynamics of
strategy updates, wherein players can maintain their strategy with a certain
weight. Analytical results are obtained on square lattices under the weak
selection limit. If the organizer attempts to monopolize the public goods,
cooperation becomes more attainable. If the confidence increases, cooperation
is inhibited. Consequently, these elements have conflicting effects on
cooperation, and their simultaneous presence can result in a heterogeneous
change of the critical synergy factor. Our theoretical findings underscore the
subtle implications of a mutual trait that may manifest as greediness or
self-confidence under different circumstances, which are validated through
Monte Carlo simulations.
