Coalition-Proofness in Aggregative Games with Strategic Substitutes and Externalities

Coalition-proofness in a class of games with strategic substitutes

“…That counterexample is a game with weakly positive externalities in the sense of Yi (1999). Proposition 2 in Quartieri and Shinohara (2012) proves that a statement similar to Yi's Theorem is true in case of weakly negative externalities and convex strategy sets; anticipating unjustified conjectures based on Proposition 2 in Quartieri and Shinohara (2012) and on the third remark at p. 358 in Yi (1999), we claim (and prove in the Appendix) the following.…”

“…The difficulty of such a comparison resides in the simple fact that Yi's Theorem does not generally hold true (we refer to Quartieri and Shinohara (2012) for a detailed examination of this issue). That Theorem states that s F N ⊆ E sC P N for a class of games with strategic substitutes and monotone externalities (and with only strict Nash equilibria) which is seemingly similar to that considered here (as it is clear from the proofs in Yi (1999), wF N and E wC P N are not examined).…”

“…Similarly, the games associated to the model of voluntary contribution of a public good described in Kerschbamer and Puppe (1998) (or of its extension to n players illustrated in Quartieri and Shinohara (2012)) are real -interactive games with strategic substitutes and increasing externalities with E ST N = E N ( = ∅ by the above Existence result II). In this case, our Corollary 2 ensures even that E wC P N = E sC P N = E N = wF N = s F N and our Corollary 5 implies that no renegotiation of a (w-or s-)coalition-proof Nash equilibrium for can increase the contributions of all agents.…”