Existence of valuation equilibria when equilibrium strategies cannot differentiate between equal ties

This paper reconsiders the valuation equilibrium concept (Jehiel and Samet, 2007) and proposes an additional regularity condition concerning the playersʼ equilibrium strategies. The condition, which requires equilibrium strategies to induce the same local behaviour at all nodes with “similar” optimal actions, increases both the predictive power and the internal consistency of the concept — especially when used as a tool to study boundedly rational behaviour in games with imperfect information and/or imperfect recall. It is shown not to conflict with existence.