The willingness to pay for partial vs. universal equality

In three-person envy games, an allocator, a responder, and a dummy player interact. Since agreement payoffs of responder and dummy are exogenously given, there is no tradeoff between allocator payoff and the payoffs of responder and dummy. Rather, the allocator chooses the size of the pie and thus—being the residual claimant—defines his own payoff. While in the dictator variant of the envy game, responder and dummy can only refuse their own shares, in the ultimatum variant, the responder can accept or reject the allocator’s choice with rejection leading to zero payoffs for all three players. Comparing symmetric and asymmetric agreement payoffs for responder and dummy shows that equality concerns are significantly context-dependent: allocators are willing to leave more money on the table when universal equality can be achieved than when only partial equality is at stake. Similarly, equality seeking of responders is most prominent when universal equality is possible.