Endogenous Heterogeneity in Strategic Models: Symmetry-breaking via Strategic Substitutes and Nonconcavities



Figure 5: Square of the length α.

Finally, summarizing, we have:

L(x, x) - L(x - α, x)+bε

U(x + α, x) - U(x, x)

U(x + α, x - α) - U(x,x - α)

U(x, x - α) - U(x - α, x - α)+bε

where, the first inequality comes from (20), the second one from (19) and the
last one from
(22). So we obtain,

U (x, x - α) - U (x - α, x - α)+bε (x, x) - L(x - α, x)+bε.     (23)

Subtracting b from both sides ends the proof. ■

The next lemma extends the property of submodularity of F form the small
square of length
α to any square with two vertices on the diagonal.

Lemma 8.2 If Lemma 8.1 holds, then for any square with points in the diago-
nal, such as depicted in figure 7, we have,

F(z, x) - F(z, z) F(x, x) - F (x, z) .

Proof. (Lemma 8.2) Consider the square formed by the four points defined in
the lemma. Divide this square into rectangles such that their height is equal to

34



More intriguing information

1. Return Predictability and Stock Market Crashes in a Simple Rational Expectations Model
2. The name is absent
3. The demand for urban transport: An application of discrete choice model for Cadiz
4. SOCIOECONOMIC TRENDS CHANGING RURAL AMERICA
5. Incorporating global skills within UK higher education of engineers
6. Learning and Endogenous Business Cycles in a Standard Growth Model
7. Banking Supervision in Integrated Financial Markets: Implications for the EU
8. Peer Reviewed, Open Access, Free
9. Distortions in a multi-level co-financing system: the case of the agri-environmental programme of Saxony-Anhalt
10. Non Linear Contracting and Endogenous Buyer Power between Manufacturers and Retailers: Empirical Evidence on Food Retailing in France
11. The open method of co-ordination: Some remarks regarding old-age security within an enlarged European Union
12. Strategic Effects and Incentives in Multi-issue Bargaining Games
13. Innovation in commercialization of pelagic fish: the example of "Srdela Snack" Franchise
14. RETAIL SALES: DO THEY MEAN REDUCED EXPENDITURES? GERMAN GROCERY EVIDENCE
15. The Folklore of Sorting Algorithms
16. Technological progress, organizational change and the size of the Human Resources Department
17. AN ECONOMIC EVALUATION OF THE COLORADO RIVER BASIN SALINITY CONTROL PROGRAM
18. The name is absent
19. The name is absent
20. Exchange Rate Uncertainty and Trade Growth - A Comparison of Linear and Nonlinear (Forecasting) Models