Reducing Optimism Bias in Incomplete Cooperative Games

Cooperative game theory has applications in many diverse fields, from economics to explainable AI. However, when applying it in practice, one quickly runs into a problem: to specify a cooperative game means to gather the value of each coalition (subset of players), the number of which is exponential in the number of players. An attempt to remedy this issue is to extend the model to incomplete cooperative games, where we only have the value of a small set of known coalitions, the rest are unknown. This introduces uncertainty, and since is that all the concepts from cooperative game theory require the knowledge of all coalition values, with the incomplete information we can only hope for approximations. The question we attempt to answer is (1) how do we measure how well a certain set of known coalitions captures the underlying full cooperative game, and (2), assuming we are given an upper bound on the number of coalition values we can reveal, how do we choose those coalitions minimizing the uncertainty in the unknown values.