Coalition-proofness in a class of games with strategic substitutes
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- Quartieri, F. & Shinohara, R. Int J Game Theory (2015) 44: 785. doi:10.1007/s00182-014-0452-8
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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.