Robust Implementation with Costly Information

We construct mechanisms that can robustly implement any desired social choice function when (1) agents may incur a cost to learn the state of the world, (2) with small probability, agents’ preferences can be arbitrarily different from some baseline known to the mechanism designer, and (3) the mechanism designer does not know agents’ beliefs and higher-order beliefs about one another’s preferences. The mechanisms we propose have a natural interpretation and do not require the mechanism designer to be able to verify the state ex post. We also establish impossibility results for stronger notions of robust implementation.