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Cycles and Optimistic Stability in Graphs: The Role of Competition, Veto Players and Moderators

Abstract This article provides sufficient conditions for existence of a non-empty optimistic stable standard of behaviour (OSSB) in directed graphs. Graphs which are completely connected by single-player arcs for each player always admit a (non-unique) OSSB. More specifically, a loop is broken by adding a single-player move to some appropriately chosen default position. If there are nodes with a decision cycle over the move to the successor node, introducing veto players ensures that an OSSB exists which assigns a non-empty solution to every vertex along the equilibrium path.