“…Furthermore, we have treated spite only as a constant, independent of valuation and bid and identical for all members of the population. All these assumptions are taken from the current literature on spite in auctions (Bartling et al, 2017;Morgan et al, 2003;Brandt et al, 2007;Sandholm and Tang, 2012;Sandholm and Sharma, 2010;Mill, 2017) and make the theoretical approach easier and the solutions tractable. Further theoretical work, however, might relax these assumptions.…”