Consistency, dummy and independence of irrelevant strategies for strategic games

The relationships between the consistency (CONS) principle and two other axioms, dummy (DUM) and independence of irrelevant strategies (IIS) for solution concepts on families of strategic form games are studied. If a solution satisfies DUM and IIS, then it also satisfies CONS (Peleg and Tijs 1996). The converse of this proposition is not true: CONS implies neither DUM nor IIS as shown in two simple examples, using the concept of coalition-proof Nash equilibrium. The axiom of weak dummy (WDUM) is introduced. WDUM, along with IIS, implies CONS. Moreover, CONS implies WDUM. Received: 13 August 1998/Accepted: 19 January 1999