Towards Multi-Objective Game Theory - With Application to Go

We de...ne a multi-goal as a conjunction and/or disjunction of ordinal-scaled objectives. We give exact formulas to compute the conjunction and disjunction of independent combinatorial games associated with the objectives. Dependence of games is formalized. We also propose a de...nition for the (con/dis)junction of e¤ectively dependent games. In all the above formulas, we can work with uncertain and unresolved (ko) outcomes. With these formulas, the status of a multi-goal can be computed with considerable less e¤ort compared to current search approaches. Algorithms to compute multiple solutions elegantly and to extract the threats to a won game from its search tree are outlined, implemented and applied.