Coalition-proofness in a class of games with strategic substitutes

Abstract

We examine the coalition-proofness and Pareto properties of Nash equilibria in pure strategy σ -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.

Aggregative games

“…Stamatopoulos (2020) shows that the SC assumption plus other conditions implies the existence of a γ −core. And Quartieri and Ryusuke (2015) prove that, under strategic substitutability, the set of NE, the set of coalition-proof NE under strong Pareto dominance and the set of NE that are not strongly Pareto dominated by other NE are equivalent.…”