Algorithm for pseudo-random function with certain characteristics [closed] - c++

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I am trying to create a game that would need a pseudo-random function of the following characteristics:
Each player would be allotted a variable (of type float) for their money, the products (of type int*) they own and would want to sell and another variable to show what place they are in.
Each player would have the right to sell any of their products they own to any other player; and in addition the game involves a computer player which represents the other citizen population of that place who would want to buy the products or sell certain products.
Each player would have a different place value and each place would have different different cost for each products and the "transport cost" between different places also differs as a function of time.
A brief data structure of a player's profile would is as follows:
typedef struct PLAYER{
char *name;
int place;
int *products;
int noOfProducts;
float money;
PLAYER();
PLAYER(&ply);
.
.
.
}*ptrPLAYER;
Now I need a pseudo-random function that sets the rate of each product, rate of transport from one place to the other, and the function should also determine what products should the "citizens" player buy or sell and at what rate. The values provided by this function should follow a particular trend for some time and change its trend completely, but the variance should not be high. characteristics of the pseudo function:
Should be the function of the previous values generated and time.
Should show a gradual change following some trend up to some point.
The question:
The random function should have the following properties:
The variance should be low.
If we define the function as int *randomFnc( int previousResult[]) the function should follow some trend being very difficult to crack and at the same time, it should not reach a saturation point where beyond that point, the randomFnc(.) provides the same result.
The random function should generate a set of values (for example 100 values) which are directly dependent upon the previously generated values in some unique way.

Answer 1

You can model your process. As a starting point you can choose autoregressive model of type AR(1):
y_t = a_0 + a_1 * y_(t-1) + e_t (1)
where y is your variable of interest, e_t is gaussian white noise with mean 0 and variance sigma_e_t^2 and a0, a1 are constants.
should be the function of the previous values generated and time.
You can generate number of N of white noise assuming you will need N values of y. Then as you can see, value of y in time t is directly dependent on previous value y_(t-1) and you can always switch between two based on your array of e_t and relation (1).
the variance should be low.
The unconditional variance of y_t is
var(y_t) = sigma_e_t^2 / ( 1 - a_1^2) if a_1^2 < 1
so you can make it as small as you would like ( in range [sigma_e_t^2, +inf)) .
This process may looks like
You can add trend to make it y_t = a_0 + a_1 * t + a_2 * y_(t-1) + e_t and it will looks something like
More details are needed to be added in your question in order to advise you how to adjust this process further being subjected to other restrictions.