Coalition-Proof Nash Equilibria and Weakly Dominated Strategies in Aggregative Games With Strategic Substitutes : A Note

We examine the relation between coalition-proof Nash equilibrium (Bernheim et al., 1987) and weakly dominated strategies in games with strategic substitutes (SS) and monotone externalities (ME). We show that in sigma-interactive games with SS and ME, every coalition-proof Nash equilibrium is a Nash equilibrium with undominated strategies. We also find as a by-product that the set of Nash equilibria coincides with the set of undominated Nash equilibria in those games. The relation between the coalition-proof Nash equilibrium and weakly dominated strategies in games with SS is completely different from that in games with strategic complements