We study the problem of assigning a set of objects to a set of agents, when each agent receives one object and has strict preferences over the objects. In the absence of monetary transfers, we focus on the probabilistic rules, which take the ordinal preferences as input. We characterize the...

A social choice function is group strategy-proof on a domain if no group of agents can manipulate its final outcome to their own benefit by declaring false preferences on that domain. There are a number of economically significant domains where interesting rules satisfying individual...