please do it in one hour please urgently... I'll give you up thumb definitely

You have sold the software and now you're supervising the design of the two-sided matching platform, in particular you are in charge of the matching mechanism that A uses to match clients. The system engineers that are designing the platform have an algorithm, called ALE. They want to implement ALE to match your clients. However, you want to verify if the ALE algorithm performs better than the delayed acceptance algorithm by Gale and Shapley as a mechanism to match your clients. You will present your results to your partners and propose either to use the ALE or the GnS algorithm. For this, consider the following information. In the market there are two types of firms, firms of type H, and firms of type K. The algorithm used in the platform will match firms of type H with firms of type K to form pairs (h, k), where h is a firm of type H, and k if a firm of type K. To compare the performance of GnS versus ALE you use the information in Table 3 and Table 4 on firms' preferences. Table 3. Preferences of firms type H Firms type H Order of preference Firm First Second Third Firm 1 Firm 6 Firm 4 Firm 5 Firm 2 Firm 6 Firm 5 Firm 4 Firm 3 Firm 4 Firm 5 Firm 6 Table 4. Preferences of firms type K Firms type K Order of preference Firm First Second Third Firm 4 Firm 2 Firm 1 Firm 3 Firm 5 Firm 3 Firm 1 Firm 2 1:29 Firm 6 Firm 3 Firm 2 Firm 1 Table 3 above presents the preferences for Firm1, Firm 2, and Firm 3, which are the type H firms. Table 4 above presents the preferences for Firm 4, Firm 5, and Firm 6, which are the type K firms. For example, in Table 3 you can see that Firm 1 prefers to be matched with Firm 6 first, Firm 4 second, and Firm 5 last as third most preferred. The results from the matching using ALE (the engineers' algorithm) are the following: ALE matching output: (Firm 1, Firm 6), (Firm 2, Firm 5), (Firm 3, Firm 4) That is, with algorithm ALE, Firm 1 is paired with Firm 6, Firm 2 is paired with Firm 5, and Firm 3 is paired with Firm 4. 6. Verify if the GnS algorithm (Gale and Shapely deferred acceptance algorithm) and the ALE algorithm produce different results or not. If the results are different, show if the ALE matching output is stable or not. Support your answers with adequate economic intuition, theoretical results and concepts, and the corresponding calculations (20 marks) 29 You have sold the software and now you're supervising the design of the two-sided matching platform, in particular you are in charge of the matching mechanism that A uses to match clients. The system engineers that are designing the platform have an algorithm, called ALE. They want to implement ALE to match your clients. However, you want to verify if the ALE algorithm performs better than the delayed acceptance algorithm by Gale and Shapley as a mechanism to match your clients. You will present your results to your partners and propose either to use the ALE or the GnS algorithm. For this, consider the following information. In the market there are two types of firms, firms of type H, and firms of type K. The algorithm used in the platform will match firms of type H with firms of type K to form pairs (h, k), where h is a firm of type H, and k if a firm of type K. To compare the performance of GnS versus ALE you use the information in Table 3 and Table 4 on firms' preferences. Table 3. Preferences of firms type H Firms type H Order of preference Firm First Second Third Firm 1 Firm 6 Firm 4 Firm 5 Firm 2 Firm 6 Firm 5 Firm 4 Firm 3 Firm 4 Firm 5 Firm 6 Table 4. Preferences of firms type K Firms type K Order of preference Firm First Second Third Firm 4 Firm 2 Firm 1 Firm 3 Firm 5 Firm 3 Firm 1 Firm 2 1:29 Firm 6 Firm 3 Firm 2 Firm 1 Table 3 above presents the preferences for Firm1, Firm 2, and Firm 3, which are the type H firms. Table 4 above presents the preferences for Firm 4, Firm 5, and Firm 6, which are the type K firms. For example, in Table 3 you can see that Firm 1 prefers to be matched with Firm 6 first, Firm 4 second, and Firm 5 last as third most preferred. The results from the matching using ALE (the engineers' algorithm) are the following: ALE matching output: (Firm 1, Firm 6), (Firm 2, Firm 5), (Firm 3, Firm 4) That is, with algorithm ALE, Firm 1 is paired with Firm 6, Firm 2 is paired with Firm 5, and Firm 3 is paired with Firm 4. 6. Verify if the GnS algorithm (Gale and Shapely deferred acceptance algorithm) and the ALE algorithm produce different results or not. If the results are different, show if the ALE matching output is stable or not. Support your answers with adequate economic intuition, theoretical results and concepts, and the corresponding calculations (20 marks) 29