In real life situations, one often encounters situations where the offers are constrained as there is a suggestion for a minimum offer. For example, in donation situations there can be a limit on minimum donation, similarly in a negotiation situation there can be a limit on minimum offers. We study the effect of such constraints in the context of economic games, using two experimental studies. We show that constraints that increase the minimum amount that can be offered tend to reduce the average offer size instead of increasing it. We apply the theory of anchoring and adjustment and argue that this is a result of constraints acting as anchors. We also show that constraints on minimum offers have stronger effect on Dictator games than on Ultimatum games. Ultimatum games are more strategic in nature and hence seem to be less vulnerable to anchoring effects. Overall, the results show that constraints on minimum offers can have a significant effect on offers in distribution games and instead of increasing average offers are more likely to reduce them. © Serials Publications.