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Antonio Penta, Ph.D.

University of Wisconsin - Madison, USA

Authors: Antonio Penta and Peio Zuazo-Garin

Abstract: We study the strategic impact of players’ higher order uncertainty over whether their actions are observable to their opponent. We characterize the ‘robust predictions’ of Rationality and Common Belief in Rationality (RCBR), i.e. those which do not depend on the restrictions on players’ infinite order beliefs over the extensive form (that is, the observability of actions). We show that RCBR is generically unique, and that the robust predictions often support a robust refinement of rationalizability. For instance, in unanimity games, the robust predictions of RCBR rule out any inefficient equilibrium action; in zero-sum games, they support the maxmin solution, resolving a classical tension between RCBR and the maxmin logic; in common interest games, RCBR generically ensures efficient coordination of behavior, thereby showing that higher order uncertainty over the extensive form serves as a mechanism for equilibrium coordination on purely eductive grounds.

We also characterize the robust predictions in settings with asynchronous moves, but in which the second mover does not necessarily observe the first mover’s action.  In these settings, higher order uncertainty over the observability of the earlier choice yields particularly sharp results: in ‘Nash-commitment games’, for instance, RCBR generically selects the equilibrium of the static game which is most favorable to the earlier mover. This means that a first-mover advantage arises whenever higher-order beliefs do not rule out that it might exist. Hence, in the presence of extensive form uncertainty, timing alone may determine the attribution of the strategic advantage, independent of the actual observability of choices.

Keywords:  coordination – extensive form – first-mover advantage – higher order beliefs – rationalizability – robustness

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