Game Analysis Of Human Resources Investment

In rencent years,many works have been done on the the human resources investment, most of them are focused on the studies of companies' and enterprises' experiences or investigations. But the articles which use game theory to analyze human resources investment are actually rare, and especially articles investing in the mathematical model for the human resources are still few at present. In this paper,we will utilize the game theory to study the human resources investment. Our main results consisted by three parts:In charpter 2,by set up the payment matrix of human resources investment, analyze the Nash equilibrium in unconstrained and constrained human resources investment, we proved the following results:(1)As peronnal who pay larger expenses to find a new job, enterprises would like to invest in the human resources.(2)The higher the cost of investment of human resources is, the more unwilling to carry out human resources investment enterprises are.(3)In human resources investment ,the more the peronnal's capital increment is, the greater the probability that the peronnal leave enterprises is.In charpter 3,we consider the modle of the human resouces inrestment.First we give some assumption of manpower capital stock.(l)Increment of the personal capital stock of manpower is finite, i.e. no matter how large the amount of investment is, the personal capital stock of manpower has the circle finally. Suppose M(0, x) is the change-function of individual capital stock, x denotes the amount of investment. 6 denotes individual potentiality.(2)Let M(0, x) is derivable and increasing function . Hav-? a n -. n Mta \ ^ n a dM(6,x) ^ n dM(d,x) ^ing 6 > Q,x > O,M(0, x) > 0 and —A ' ' > 0, —AV / > 0, lim M(B,x) = ~M.(3) The number of people in the human resources investment function is the continuous variable.(4) Suppose enterprise total capital stock equal each individual capital total of peronnal.(5)Without the investment, the capital stock increment of the individual is 0, i.e. lim M(0, x) = 0.(6) Suppose among the peronnal investing in it, all the per-onnal's potentiality is the same.Definition 1 Let M(9, x) is the continuous function and|?M(0, x) , 0< z < P;f[M(6,x),P]=l X0 ,z = 0.J, 0) = 0, M{6, x) > 0{x > 0), fix > °' d() > 0> And lim /[M(0,x),P] = 0, lim /[M(0,z),P] < M, */ien we can ca// i/ie model(1.1) a optimal model of the investment of continuous human resources.Analyzing the investment model of human resources, prove: Theorem 1 Assume that P sufficiently large in model (1.1), then exists a xq G (0, P) such that (1.1) gets maximum.Theorem 2 In the model (1.1), if P satisfiedM{0,P) dM(9,x)X=PP dxthen the optimal schema of enterprises investment will be: make an amount investment in single peronnal, the increment of enterprise capital stock is M(9, P).Theorem 3 In the function M(9, x), let 9 be personal potentiality, then enterprises choose the greater one of value 9 to make the investment, the larger enterprise's total capital increment is.Lemma 1 In the model (1.1), if M(9,x) is second order differential for x , then exists x* G (0, +oo) , for any x G (0, +oo)satisfieddM(6,x) dM{9,x)andanadx2dxdxx=x'Corollary 1 If function M(9,x) is second order differential for x , existence and uniqueness x* G (0, -t-oo) satisfiedd2M{9,x)dx1= 0,x=x*then (x*, M(6, x*)) is the flex point of function M(6, x), and M(6, x) is a convex (concave) function in (0,x*) ((#*,+oo)) .Theorem 4 IfM(9, x) satisfied in corollary 1, the flex point is (x*,M(0,x*)), xq gets maximum in (1.1).(l)If x* < xq, invests AP in more than No who has made the investment is better than invest less than No.(2) If x* < xq and ~- < x*, make an investment in some people not making the investment with AP, making an investment in more than n individual is not even more excellent than the optimum one of making an investment in n individual at the most. The largest capital stock that AP produces is( ( AP\ 1max In- M [6,------ n = 1,2 ? ? ? N > ,I V n / Jwhere N = min ln\ ^- I L V xo J J V n J | JTheorem 5 Continuous and dispersed type human resources investment model, r is the error between the optimum investmentresults of two kinds of models, then r < (3 , wherea (AP)2x0 d2M(9,x0)In charpter 4,using the theory of signal transmit game to discuss separating equilibrium and mixing equilibrium of investors in non-envy cases and jealously cases. It offers the correspondingstrategies for enterprises to recruit high potential talented staff.