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Games with Complementarities

By CALCIANO Filippo L.


We introduce a class of games with complementarities that has the quasisupermodular games, hence the supermodular games, as a special case. Our games retain the main property of quasisupermodular games : the Nash set is a nonemply complete lattice. We use monotonicity properties on the best reply that are weaker than those in the literature, as well as pretty simple and linked with an intuitive idea of complementarity. The sufficient conditions on the payoffs are weaker than those in quasisupermodular games. We also separate the conditions implying existence of a greatest and a least Nash equilibrium from those, stronger, implying that the Nash set is a complete latticeComplementarity, Quasisupermodularity, Supermodular games, Monotone comparative statics, Nash equilibria

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  2. (1955). A lattice-theoretical fixpoint theorem and its applications.
  3. (1974). Complementarity - an essay on the 40th anniversary of the Hicks-Allen revolution in demand theory.
  4. (1979). Equilibrium points in nonzero-sum n-person submodular games.
  5. (1996). Fixed point theorems for correspondences with values in a partially ordered set and extended supermodular games.
  6. (1967). Lattice Theory. Third edition,
  7. (1978). Minimizing a submodular function on a lattice.
  8. (1994). Monotone comparative statics.
  9. (1990). Nash equilibrium with strategic complementarities.
  10. (1998). Supermodularity and complementarity.
  11. (1994). The set of Nash equilibria of a supermodular game is a complete lattice.
  12. (1995). Weak and strong comparative statics.

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