Buck-passing dumping in a garbage-dumping game

We study stable strategy profiles in a pure exchange game of bads, where each player dumps his or her bads such as garbage onto someone else. Hirai et al. (Mathematical Social Sciences 51(2):162–170, 2006) show that cycle dumping, in which each player follows an ordering and dumps his or her bads onto the next player, is a strong Nash equilibrium and that self-disposal is $$\alpha $$ α -stable for some initial distributions of bads. In this paper, we show that a strategy profile of bullying, in which all players dump their bads onto a single player, becomes $$\alpha $$ α -stable for every exchange game of bads. We also provide a necessary and sufficient condition for a strategy profile to be $$\alpha $$ α -stable in an exchange game of bads. In addition, we show that repeating an exchange after the first exchange makes self-disposal stationary.