We report on a series of behavioral experiments in social networks in which human subjects continuously choose to play either a dominant role (called a King) or a submissive one (called a Pawn). Kings receive a higher payoff rate, but only if all their network neighbors are Pawns, and thus the maximum social welfare states correspond to maximum independent sets. We document that fairness is of vital importance in driving interactions between players. First, we find that payoff disparities between network neighbors gives rise to conflict, and the specifics depend on the network topology. However, allowing Kings to offer "tips" or side payments to their neighbors substantially reduces conflict, and consistently increases social welfare. Finally, we observe that tip reductions lead to increased conflict. We describe these and a broad set of related findings.