Monotone comparative statics: Changes in preferences vs changes in the feasible set

Kukushkin, Nikolai S. (2011): Monotone comparative statics: Changes in preferences vs changes in the feasible set.

Abstract

Let a preference ordering on a lattice be perturbed. As is well known, single crossing conditions are necessary and sufficient for a monotone reaction of the set of optimal choices from every chain. Actually, there are several interpretations of monotonicity and several corresponding single crossing conditions. We describe restrictions on the preferences that ensure a monotone reaction of the set of optimal choices from every sublattice whenever a perturbation of preferences satisfies the corresponding single crossing condition. Quasisupermodularity is necessary if we want monotonicity in every conceivable sense; otherwise, weaker conditions will do.

• Item Type: MPRA Paper
• Language: English
• Keywords: strategic complementarity; monotone comparative statics; best response correspondence; single crossing; quasisupermodularity
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

Agliardi, E., 2000. A generalization of supermodularity. Economics Letters 68, 251-254.

Athey, S., 2001. Single crossing properties and the existence of pure strategy equilibria in games of incomplete information. Econometrica 69, 861-889.

Dushnik, B., and E.W. Miller, 1941. Partially ordered sets. American Journal of Mathematics 63, 600-610.

Edlin, A.S., and C. Shannon, 1998. Strict monotonicity in comparative statics. Journal of Economic Theory 81, 201-219.

Kukushkin, N.S., 2009. On the existence of monotone selections. Munich Personal RePEc Archive Paper. Available at http://mpra.ub.uni-muenchen.de/15845/

Kukushkin, N.S., S. Takahashi, and T. Yamamori, 2005. Improvement dynamics in games with strategic complementarities. International Journal of Game Theory 33, 229-238.

LiCalzi, M., and A.F. Veinott, Jr., 1992. Subextremal functions and lattice programming. Unpublished manuscript. Available at http://ideas.repec.org/p/wpa/wuwpge/0509001.html

Milgrom, P., and J. Roberts, 1990. Rationalizability, learning, and equilibrium in games with strategic complementarities. Econometrica 58, 1255-1277.

Milgrom, P., and C. Shannon, 1994. Monotone comparative statics. Econometrica 62, 157-180.

Quah, J., 2007. The comparative statics of constrained optimization problems. Econometrica 75, 401-431.

Quah, J., and B. Strulovici, 2009. Comparative statics, informativeness, and the interval dominance order. Econometrica 77, 1949-1992.

Reny, P.J., 2011. On the existence of monotone pure strategy equilibria in Bayesian games. Econometrica 79, 499-553.

Shannon, C., 1995. Weak and strong monotone comparative statics. Economic Theory 5, 209-227.

Strulovici, B., and T.A. Weber, 2010. Generalized monotonicity analysis. Economic Theory 43, 377-406.

Topkis, D.M., 1978. Minimizing a submodular function on a lattice. Operations Research 26, 305-321.

Topkis, D.M., 1979. Equilibrium points in nonzero-sum n-person submodular games. SIAM Journal on Control and Optimization 17, 773-787.

Veinott, A.F., Jr., 1989. Lattice Programming. Unpublished lectures.

Vives, X., 1990. Nash equilibrium with strategic complementarities. Journal of Mathematical Economics 19, 305-321.