Implementation without Incentive Compatibility: Two Stories with Partially Informed Planners

We consider implementation problems under incomplete information without incentive compatibility. If the social choice functions do not satisfy incentive compatibility, full implementation is unattainable via the existing approaches. By focusing on the actual problems from Typhoon by Joseph Conrad and The Traveler's Dilemma by Kaushik Basu (1994, 2007), we provide a new approach to such implementation problems. For each problem, we first construct a mechanism which takes advantage of a unique feature of these problems, i.e., the planners possess some information regarding the actual state. We then provide a sufficient condition on players' beliefs for each problem under which every player has a unique rationalizable action. The conditions we identify however depend on the informational structures, suggesting that obtaining a general result within this type of frameworks is nontrivial.