Incomplete cooperative games

The cooperative game model has been widely studied since 1944, when John von Neumann and Oskar Morgenstern introduced it in Theory of Games and Economic Behavior. However, a key drawback remains its size: for a game with n players, a value must be assigned to each possible subset (coalition), leading to an exponential number of values. This complexity makes the model challenging to work with. To address this issue, we extend the model to an incomplete information setting, where some coalition values are unknown, but additional assumptions about the game are available. We analyze what information can be inferred about the missing values and how this uncertainty impacts standard solution concepts. In doing so, we focus on incomplete information reflecting a view of a single agent but briefly mention other scenarios.