The process of simulation

acted, the market would be closed, and every trader got the closing price to calculate their profits. The profit functions for the two type traders are

*( ) induction, this game will be a total different one.

If a trader’s action is 1, there will be two situations after the market closing; the first situation is that when the closing price pT is higher than the current price pt, the trader will gain, and the difference between this two prices is his positive profit; the second situation is that when the closing price pT is lower than the current price pt, the trader will lose, and the difference between this two prices is his negative profit.

As to the part of selling, which means at is -1, and there is no need to go into details, you could deduce by yourself. In the appendix table A2, we used a series of simple diagrams to show the relationship between actions and profits.

4.2. The process of simulation

After the preliminary realization of our model, we would like to interpret the main contribution in this paper.

The sequential trading line model is randomly drawing traders into the game to trade. If the game had run for only one time, the profits we wanted to calculate must

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be un-precisely. There are a lot of traders on the market waiting to be selected, if we re-run this game again, the traders, the sequential order of traders, the signals, the conjectures, the actions, and the prices, even the profits will be a totally different one.

Every run for this game will get a diametrically opposed result, the probability for having the same result will almost be zero, and hence we have to run this game over and over until we have found its properties.

Simulation provides a good way for simplifying the complicated works.

Throughout the simulations, it does help us confirm the ideas we assumed in this paper, thus we put concentration not on the mathematical proofs but on the simulating results.

A run of this game we called it as one round, we ran this game for n rounds.² The procedure of this game is a random process, and the results of every round are independent and hence could not ignore any one of them. We then have to make the average of every round to display our results.

In order to simulate the model with a convenient way, we substituted the discrete uniform distribution for the hyper geometric distribution. To prevent the traders selecting repeatedly, we set the population is ten times total periods, which means N = 10*T. In the following simulations, we basically assumed that the T would be 100, and the N would be 1,000.

The initial price p0 would be 100, and we assumed that the general signals would not deviate too far from the opening price, sg ~ N (100, 10). It implied that there would not have any material changes. This assumption helps us focus on the signal the manager gave.

After calculating the conjectures of the history trend lines, we will give them the

2 We use the program MATLAB.

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When the game ended, the profit for each trader will be counted. We set the club fee be zero in the following model. At the same time, the profit of the manager will be omitted. The analysis of the market maker’s profit would also be omitted.

We have the actions, the price schedule, and the profits now. Then we would like to recommend the concepts of performances.

It is meaningless to calculate the profit for each trader. Since the trading order is a random process, it will be different during each round. It forces us to calculate the profit of each type. If we do know how many traders of each type are in the sequential line, then we could calculate the average individual profit for each type.

Using the vertical aggregation and dividing by total rounds, we could get the average market price and the average profits.

Then we move to the tremendous works, the average performance of each type. If we use the average individual profit of type II to subtract the average individual profit of type I, we could get the absolute performance. The other measure way, relative performance, is much complicated. We could get it by using the absolute performance to divide by the average individual profit of type I. However, if the average individual profit of type I is negative, we need to add a minus sign to the relative performance as our final relative performance, while if the average individual profit of type I is zero, and the relative performance would be equal to the average individual profit of type II.

After the completely known of this game, we know that we could control the n, T, p0, Pg, σg, Pc, σc, N, beta, w1, w21, w22, the upper bound, and the lower bound to master this game.

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We use two simple examples to show the process of simulations.

4.3.1. The one round game

For simplicity and clarity, we assumed there were only four periods, the opening price was 100, both the general signals and the club signal were drawing from N (100, 10), the N was 10, the beta was 0.5, the w1 was 0.5, the w21 and the w22 were 1/3, and the range of the bounds were 50 %.

In the beginning of this game, the manager sent the club signal, 111.9092. At the first period, the market selected a type II trader to trade. His general signal was 111.9004, his history was 100, and thus his base was 107.9336. When facing the previous price p₀, the base was larger than the previous price, and then his action was 1. The price went to 101. The second trader was coming from type I with his general signal 99.6237 and the history 102. The base for him was 100.8118 which were smaller than the previous price 101. Thus he chose to sell the asset, and the price backed to 100. The third trader also came from type I, his general signal was 103.2729, the history was 100.6667, and hence the base was 101.9698 which were larger than the previous price 100. He bought one unit and the price went to 101.

The last trader was a type II trader, his club signal was also 111.9092, and the general signal was 106.8278. With the 100.6667 history, his base was 104.7741 which were larger than the previous price 101, thus his action was 1 and the closing price was 102.

The game ended.

According to the final price 102, using the profit functions, we could find out what