# Ordinality in non cooperative games

@article{Mertens2004OrdinalityIN, title={Ordinality in non cooperative games}, author={Jean-François Mertens}, journal={International Journal of Game Theory}, year={2004}, volume={32}, pages={387-430} }

Abstract.We first analyse what a conceptual definition of ordinality for non cooperative games should be. The resulting concept is highly abstract and apparently unmanageable. Nevertheless we obtain in a second part a very simple and fully operational characterization. In the last part, this is used to check the ordinality of a number of concepts that have been proposed in the literature.

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## References

SHOWING 1-10 OF 17 REFERENCES

### On Nash equivalence classes of generic normal form games

- Economics
- 1998

We introduce a procedure that uses basic topological characteristics of equilibrium correspondences of standard equilibrium concepts, to define broad equivalence classes of finite generic games in…

### ON THE STRATEGIC STABILITY OF EQUILIBRIA

- Economics
- 1986

A basic problem in the theory of noncooperative games is the following: which Nash equilibria are strategically stable, i.e. self-enforcing, and does every game have a strategically stable…

### Persistent equilibria in strategic games

- Economics
- 1984

A perfect equilibrium [Selten] can be viewed as a Nash equilibrium with certain properties of local stability. Simple examples show that a stronger notion of local stability is needed to eliminate…

### On some geometry and equivalence classes of normal form games

- EconomicsInt. J. Game Theory
- 2006

It is argued that the procedure leads to broad and game-theoretically meaningful distinctions of games as well as to alternative ways of representing, comparing and testing equilibrium concepts.

### Stable Equilibria - A Reformulation. Part II. Discussion of the Definition, and Further Results

- MathematicsMath. Oper. Res.
- 1991

An equivalent definition that gets rid of the need to use Hausdorff limits is provided, and a "decomposition axiom" eliminates most of the algebraic possibilities, leaving only the "p-stable" sets, for p zero or prime.

### Stable Equilibria - A Reformulation: Part I. Definition and Basic Properties

- EconomicsMath. Oper. Res.
- 1989

A reformulation of stable equilibria is given, yielding a number of additional properties like backwards induction while still giving “typically,” i.e., except in “made up” examples, the same…

### Acceptable and predominant correlated equilibria

- Economics
- 1986

For stategic-form games with communication, acceptable correlated equilibria are defined as correlated equilibria that are stable when every player has an infinitesimal probability of trembling to…