Ordinality of solutions of noncooperative games

On the computation of stable sets for bimatrix games

“…Ordinality can be shown by proving that our definition satisfies both invariance and admissible-best-reply invariance. These conditions are sufficient for ordinality as is shown in Mertens (2004) and Vermeulen and Jansen (2000).…”

Making solutions invariant

“…One of the results in that paper states that the type of invariance we use here, combined with two other properties, results in a condition that is marginally stronger than ordinality. For a detailed discussion of the precise di¤erences between these notions we refer to Vermeulen and Jansen (2000). The tool we use to describe equivalence of games in this definition is the notion of reduction map.…”

“…On top of the above requirement he also needed the inverse image of a solution set to be the union of solution sets that project down onto the original solution set. See Vermeulen and Jansen (1997aJansen ( , 2000 for a detailed comparison of these notions. It is however easy to show that invariance implies KM-invariance5.…”

Ordinal Games

“…More generally, it investigates isomorphisms and equivalence classes of games. For the ordinal perspective of games, see the contributions of Thompson (1952), Mertens (1987Mertens ( , 2003, Vermeulen and Jansen (2000), and Morris and Ui (2004). On the other hand, the concept of ordinal games transcends traditional game theory and allows for players' preferences which do not admit utility representations.…”