Analysis of Optimum Marketing Strategy with Game Theory (Case Study: Marketplace Indonesian

The increasing number of pandemic cases in early 2021, has made online trading (marketplace) more widespread, making competition for marketplace companies getting tighter. Marketing strategy competition can be tested with a game theory approach. This study aims to determine the optimum marketing strategy in the marketplace so as to increase market share. From the data processing on the payoff matrix, there is no saddle point where the maximum value is not the same as the minimum value so that the pure strategy is not the optimum strategy. Furthermore, the data is processed using the POM-QM program to determine the value of the most optimum marketing strategy for each marketplace. Get games between marketplaces using a mixed strategy. In the Shopee and Tokopedia games, the optimal game value is 9%. In the second game, Shopee and Lazada, the optimal game value is 10%. In Shopee and Bukalapak games, the optimal game value is 8%. In the Shopee and Blibli games, the optimal game value is 16%. In the Tokopedia and Lazada games, the optimal game value is 10%. In the Tokopedia and Bukalapak games, the optimal game value is 9%. In the Tokopedia and Blibli games, the optimal game value is 9%. In the Lazada and Bukalapak games, the optimal game value is 11%. In the Lazada and Blibli games, the optimal game value is 13%. In the last game, Bukalapak and Blibli, the optimal game value was 14%.


Introduction
The increasing number of pandemic cases in early 2021 has made online (marketplace) more widespread [1]. The results of a survey conducted by We Are Social in April 2021 revealed that Indonesia is the first country with the highest percentage of e-commerce in the world, followed by England, Italy, and then other countries. As many as 88.1% of internet users in Indonesia have used e-commerce to buy certain products in the last few months. This percentage is the highest in the world, where the average e-commerce is 78.6% [2].
The high number of E-commerce or marketplace in 2021 will make marketplace compete to attract marketplace by creating more varied features [3] [4]. Based on data in the Top Brand Index Phase 2 2021, it shows that the strength of the brand in the online buying and selling site category was won by Shopee with a percentage of 41.8%. Then followed by Tokopedia at 16.7%, Lazada 15.2%, Bukalapak 9.5% and BliBli 8.1% in order to compete competitively and increase users, an optimal marketing strategy is The description related to problem solving is that field studies and literature studies are precursors to obtaining problem formulation and research objectives. Then the researcher identified the research variables [14]. Collecting data using a questionnaire that begins with making a questionnaire, then distributing the questionnaire and then collecting it to see the results. After the questionnaires are collected, the data will first be tested for adequacy, validity and reliability of the data. If all the test data are met, then the calculation is continued with Game Theory which begins with a comparison based on competitive advantage, then makes a pay off to determine the value of the game so that saddle points occur, saddle points then processing is carried out with mixed methods assisted by software POM-QM [15] [16]. Then the optimal marketing strategy is generated for each marketplace. Then a discussion of the results that have been obtained is carried out so that conclusions and suggestions can be drawn.

Questionnaire Dissemination Questionnaires
Were distributed online with the help of google forms. Questionnaires were distributed through social media with the criteria that the respondents had known the five marketplaces that were used as research objects [17]. The return of the questionnaire that has been filled out by the respondent can be accessed through Microsoft Excel contained in the google form. In this study, 135 questionnaires have been filled out by respondents. A total of 125 questionnaires were declared appropriate, and as many as 10 questionnaires were not appropriate so they could not be continued, because the respondents answered that they had never used the five marketplaces which were the objects of this study. So that the data to be processed are 125 questionnaires.

Data Sufficiency Test
From the results of the questionnaires filled out by 135 respondents, 125 questionnaires were filled out correctly. The researcher uses Bernoulli in the following equation: From the above calculation, it can be seen that the minimum sample is 105 respondents, meaning that the sample is said to be sufficient if there are 105 respondents or more.

Validity and Reliability Test
From the data as many as 125 pieces of questionnaires, it is obtained df = 125-2 = 123. From the error rate of 0.05%, it is obtained from a table of 0.1757. It can be seen in the following From the eleven strategy attributes that have been tested, it can be seen that all the strategy attributes in the marketplace are declared valid. Reliability testing was carried out using software SPSS 20.0test results marketplace are as follows:  The eleven strategic attributes has been tested, it can be seen that all the strategy attributes on the marketplace Tokopedia Reliability testing was carried out using software SPSS 20.0test marketplace Tokopedia.  The eleven strategy attributes that have been tested, it can be seen that all the strategy attributes on the marketplace are declared valid.

Game Theory Calculations
Data in this study were obtained from the questionnaire results which contains the comparison of each attribute that exists between marketplaces being played. Data processing is Game theory presented in the following table based on the output of POM-QM for windows. In the game between the marketplaces Shopee, Tokopedia, Lazada, Bukalapak and Blibli, there were 10 strategy games, namely Shopee against 1.
Shopee game against Tokopedia From table XII it can be seen that the maximum value of 0.03 is not the same as the minimum value of 0.12, meaning that the game cannot be solved using pure strategy. The next step is to finish by using a mixed strategy.
From the results of the mixed strategy, the game value is 0.09. Shopee needs to implement a marketing strategy of X1 of 0.23 or 23%, X2 of 0.2 or 20%, X6 of 0.13 or 13%, X7 of 0.05 or 5%, X8 of 0.19 or 19%, and X10 of 0.2 or 20% in order to have a maximum profit value of 0.09 or 9% While the marketplace (Y) needs to implement a marketing strategy of Y1 of 0.24 or 24%, Y3 with a profit of 0.22 or 22%, Y5 of 0.21 or 21%, Y6 of 3%, Y8 of 2% and Y10 of 0.1 or 1% in order to generate a minimum loss of 0.09 or 9%.

2.
Shopee game against Lazada Table 11. Shopee And Lazada Account Value Matrix From table XIV it can be seen that the maximum value of 0.01 is not the same as the minimum value of 0.12, meaning that the game cannot be solved using pure strategy. The next step is to finish using a mixed strategy assisted by software POM-QM  From the results of the mixed strategy, the game value is 0.1. Shopee needs to implement a marketing strategy of X1 of 0.21 or 21%, X2 of 0.03 or 3%, X4 of 0.01 or 1%, X7 of 0.01 or 1%, X8 of 0.35 or 35%, and X11 of 0.39 or 39% in order to have a maximum profit value of 0.1 or 10% While the marketplace (Y) needs to implement a marketing strategy of Y2 with a profit of 0.15 or 15%, Y4 with a profit of 0.31 or 31% , Y6 of 0.13 or 13%, Y8 of 0.05 or 5%, Y9 of 0.04 or 4% and Y10 of 0.32 or 32% in order to generate a minimum loss of 0.1 or 10%.

3.
Shopee game against Bukalapak  From table XVI it can be seen that the maximum value of 0.02 is not the same as the minimum value of 0.16 meaning the game cannot be solved using pure strategy. The next step is to finish using a mixed strategy assisted by software POM-QM  Source: primary data processed, 2022 From the results of the mixed strategy, the game value is 0.08. Shopee needs to implement a marketing strategy of X3 of 0.1 or 10%, X5 of 0.17 or 17%, X6 of 0.15 or 15%, X7 of 0.1 or 10%, X9 of 0.15 or 15%, and X10 of 0.33 or 33% in order to have a maximum profit value of 0.08 or 8% While marketplace Bukalapak (Y) needs to implement a marketing strategy of Y2 with a profit of 0.02 or 2%, Y3 with a profit of 0.32 or 32% , Y6 of 0.08 or 8%, Y7 of 0.33 or 33%, Y8 of 0.2 or 20% and Y9 of 0.05 or 5% in order to generate a minimum loss of 0.08 or 8%.

4.
Shopee game against Blibli  From table XVI it can be seen that the maximum value of 0.07 is not the same as the minimum value of 0.26 meaning the game cannot be solved using pure strategy. The next step is to finish using a mixed strategy assisted by software POM-QM.  Value of game (to row)

6
Source: primary data processed, 2022 From the results of the mixed strategy, the game value is 0.16. Shopee needs to implement a marketing strategy of X1 of 0.18 or 18%, X4 of 0.16 or 16%, X5 of 0.39 or 39%, X6 of 0.01 or 1%, X9 of 0.04 or 4%, and X10 of 0.21 or 21% in order to have a maximum profit value of 0.08 or 8% While the marketplace (Y) needs to implement a Y2 marketing strategy with a profit of 0.11 or 11%, Y3 with a profit of 0. 16   Source: primary data processed, 2022 From table XXII it can be seen that the maximum value of 0.06 is not the same as the minimum value of 0.13 meaning the game cannot be solved using pure strategy. The next step is to finish using a mixed strategy assisted by software POM-QM Table 17. Game

Source: primary data processed, 2022
From the results of the mixed strategy, the game value is 0.1. Tokopedia needs to implement a marketing strategy of X1 of 0.36 or 36%, X2 of 0.12 or 12%, X5 of 0.01 or 1%, X6 of 0.28 or 28%, and X11 of 0.22 or 22% . in order to have a maximum profit value of 0.1 or 10%. Meanwhile marketplace (Y) needs to implement a marketing strategy of Y3 with a profit of 0.58 or 58%, Y4 with a profit of 0.14 or 14%, Y5 of 0.09 or 9% , Y9 of 14%, and Y10 of 0.05 or 5% in order to generate a minimum loss of 0.1 or 10%. 6.
Tokopedia game against Bukalapak  Source: primary data processed, 2022 From table XIV it can be seen that the maximum value of 0.05 is not the same as the minimum value of 0.18 meaning the game cannot be solved using pure strategy . The next step is to finish using a mixed strategy assisted by software POM-QM.  Source: primary data processed, 2022 From the results of the mixed strategy, the game value is 0.09. Tokopedia needs to implement a marketing strategy of X1 of 0.04 or 4%, X2 of 0.11 or 11%, X6 of 0.12 or 12%, X10 of 0.38 or 38%, and X11 of 0.35 or 35% in order to have a maximum profit value of 0.09 or 9% While the marketplace (Y) needs to implement a marketing strategy of Y2 with a profit of 0.02 or 2%, Y5 with a profit of 0.14 or 14%, Y6 with a profit of 0.2 or 20% ,Y7 of 0.53 or 53%, and Y8 of 0.1 or 10% in order to generate a minimum loss of 0.09 or 9%.  Source: primary data processed, 2022 From table XVI it can be seen that the maximum value of 0.05 is not the same as the minimum value of 0.17 meaning the game cannot be solved using pure strategy. The next step is to finish using a mixed strategy assisted by software POM-QM  Source: primary data processed, 2022 From the results of the mixed strategy, the game value is 0.09. Tokopedia needs to implement a marketing strategy of X2 of 0.14 or 14%, X3 of 0.1 or 10%, X6 of 0.04 or 4%, X7 of 0.29 or 29%, X8 of 0.21 or 21% and X10 of 0.21 or 21% in order to have a maximum profit value of 0.09 or 9% While the marketplace (Y) needs to implement a Y2 marketing strategy with a profit of 0.24 or 24%, Y3 with a profit of 0.1 or 10%, Y4 is 0.18 or 18%, Y5 is 0.32 or 32%, Y6 is 0.09 or 9% and Y9 is 0.07 or 7% in order to generate a minimum loss of 0.09 or 9%.  Source: primary data processed, 2022 From table XXVIII it can be seen that the maximum value of 0.05 is not the same as the minimum value of 0.15, meaning that the game cannot be solved using pure strategy. The next step is to finish using a mixed strategy assisted by software POM-QM  Source: primary data processed, 2022 From table XXX it can be seen that the maximum value of 0.04 is not the same as the minimum value of 0.15, meaning that the game cannot be solved using pure strategy. The next step is to finish using a mixed strategy assisted by software POM-QM  Source: primary data processed, 2022 From the results of the mixed strategy, the game value is 0.13. Lazada needs to implement a marketing strategy of X3 of 0.23 or 23%, X5 of 0.45 or 45%, X7 of 0.25 or 25%, and X11 of 0.08 or 8% in order to have a maximum profit value of 0.13 or 13 % While marketplace (Y) needs to implement a marketing strategy of Y1 with a profit of 0.11 or 11%, Y3 with a profit of 0.12 or 12%, Y5 of 0.75 or 75%, and Y9 of 0.01 in order to resulting in a minimum loss of 0.13 or 13%. 4. Bukalapak Game against Blibli Table 27. Blibli