Another characterization of quasisupermodularity

Kukushkin, Nikolai S. (2009): Another characterization of quasisupermodularity.

Abstract

An ordering on a lattice is quasisupermodular if and only if inserting it into any parametric optimization problem with the single crossing property cannot destroy the monotonicity of the set of optima. More detailed conditions for the monotonicity of the set of optima in a parameter influencing the preference ordering are also obtained.

• Item Type: MPRA Paper
• Language: English
• Keywords: best response correspondence; increasing correspondence; single crossing; quasisupermodular ordering
• Subjects: 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.

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.

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, 2007. Comparative statics, informativeness, and the interval dominance order. Oxford University, Nuffield College. Working Paper 2007-W04. Available at http://econpapers.repec.org/paper/nufeconwp/0704.htm

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 Unpublished lectures.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.