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Respond to the question: Generalized Ordinal Potential?

05/17/2002 06:20 AM by Burkhard C. Schipper; Generalized Ordinal Potential
I have some questions regarding games with generalized ordinal potential.

1. Is there a general characterization of games having a generalized ordinal potential?

Potential games were characterized by Monderer/Shapley, GEB 1996. Ordinal potential games by Voornefeld/Norde, GEB 1997. But how about generalized ordinal potential games?

2. Is there a general characterization of supermodular and submodular games having a generalized ordinal potential?

There is a recent paper on supermodular games and potential games by Branzei/Mallozzi/Tijs, mimeo 2001, but it doesn't get very far.

3. Is there a general characterization of n-firm Cournot oligopoly that has a generalized ordinal potential?

I know of examples of Cournot oligopoly games that have and exact (Slade, JIO 94) and ordinal potential (Monderer/Shapley, GEB 96), (see also above paper by Brazei/Mallozzi/Tijs, mimeo, 2001). But how about a general characterization and generalized ordinal potentials?

Many thanks.

Burkhard C. Schipper
www.bgse.uni-bonn.de/~burkhard

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