A Remark on the Consistency Principle for Games in Strategic Form.

If a solution (on a closed family of games) satisfies dummy axiom (DUM) and independance of irrelevant strategies (IIS) then it also satisfies consistency (CONS) (proposition 2.21, 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 coalition-proof Nash equilibrium. However, CONS implies weak dummy axiom (WDUM) which can replaceDUM in the above proposition.