Manipulation through Bribes

We consider allocation rules that choose outcomes and transfers, based on agents' reported valuations of the outcomes. A bribing situation exists when one agent could pay another to misreport his valuations, resulting in a net gain to both. A bribe-proof rule eliminates such opportunities. We show that under a bribe-proof rule, each agent's payoff is a continuous function of other agents' reported valuations. Furthermore, on connected domains, if the set of outcomes is finite or the domain is smoothly connected, each agent's payoff is a constant function of other agents' reports. Finally, under a domain-richness condition, a bribe-proof rule must be constant. The results apply to a broad class of economies. Journal of Economic Literature Classification Numbers: C70, D70.