Ordinal Games - Jacques Durieu; Hans Haller; Nicolas Querou; Philippe Solal (ETH Zurich, CER-ETH - Center of Economic Research, 2007)
We study strategic games where players' preferences are weak orders which need not admit utility representations. First of all, we ex- tend Voorneveld's concept of best-response potential from cardinal to ordi- nal games and derive the analogue of his characterization result: An ordi- nal game is a best-response potential game if and only if it does not have a best-response cycle. Further, Milgrom and Shannon's concept of quasi- supermodularity is extended from cardinal games to ordinal games. We find that under certain compactness and semicontinuity assumptions, the ordinal Nash equilibria of a quasi-supermodular game form a nonempty complete lattice. Finally, we extend several set-valued solution concepts from cardinal to ordinal games in our sense.
Keywords: C72; 330; Ordinal Games; Potential Games; Quasi-Supermodularity; Rationalizable Sets; Sets Closed under Behavior Correspondences; Nichtkooperatives Spiel; Nash-Gleichgewicht; Theorie