On Choosing Which Game to Play When Ignorant of the Rules

This paper suggests a theory of choice among strategic situations when the rules of play are not properly specified. We take the view that a "strategic situation" is adequately described by a TU game since it specifies what is feasible for each coalition but is silent on the procedures that are used to allocate the surplus. We model the choice problem facing a decision maker (DM) as having to choose from finitely many "actions". The known "consequence" of the ith action is a coalition from game f_i over a fixed set of players (N_i union d) (where d stands for the DM). Axioms are imposed on her choice as the list of consequences (f_1,..., f_m) from the m actions varies. We characterize choice rules that are based on marginal contributions of the DM in general and on the Shapley Value in particular