# Coalition-proofness in a class of games with strategic substitutes

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## Abstract

We examine the coalition-proofness and Pareto properties of Nash equilibria in pure strategy \(\sigma \)-interactive games with strategic substitutes and increasing/decreasing externalities. For this class of games: (i) we prove the equivalence among the set of Nash equilibria, the set of coalition-proof Nash equilibria under strong Pareto dominance and the set of Nash equilibria that are not strongly Pareto dominated by other Nash equilibria; (ii) we prove that the fixpoints of some “ extremal” selections from the joint best reply correspondence are both coalition-proof Nash equilibria under weak Pareto dominance and not weakly Pareto dominated by other Nash equilibria. We also provide an order-theoretic characterization of the set of Nash equilibria and show various applications of our results.

## Keywords

Coalition-proof Nash equilibrium Pareto dominance Strategic substitutes Externalities Generalized aggregative games## Notes

### Acknowledgments

The present version of this paper considerably benefited from discerning comments and remarks of two anonymous reviewers. The second author gratefully acknowledges financial support from Grant-in-Aid for Young Scientists (21730156, 24730165) from the Japan Society for Promotion of Science.

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