The problem of the development of the state information stimulation system of Russian citizens' socio-optimal actions is considered according to the optimum of collective utility function as criterion. The algorithm of the information system is formed taking into account the conditions of individual rationality, Pareto efficiency and non-manipulability. The algorithm for analyzing the effect of various functions of the probability distribution density of the altruism degree of Russian citizens on the effectiveness of the system for stimulating socially-optimal actions is developed. The simulation of social groups behavior, covering more than ten percent of Russia's economically active population, is confirmed the stability of the stimulation system for citizens' opportunistic behavior.
In a transitional economy [
The concept of socio-optimal actions’ stimulation provides for the establishment of information system of personified registration of the actions of citizens (hereinafter, agents). The system also includes the distribution of state stimulation fund in the form of incentives between agents according to certain mechanisms. The dynamics of the system is a two-period. In the first period (registration period) performed socio-optimal actions are recorded, and in the end of this period the stimulation fund is distributed. In the next period (period of stimulation) the earlier distributed incentives are used.
In addition to the utilitarian stimulating function information system also solves the problem of the formation of the agent’s status in the hierarchy of the citizens, used for non-material motivation. On a longer time horizon, the state’s social priorities could changed by varying the attributes of sociooptimal actions and their monetary valuation can be varied as a result of inflation. Therefore, to comparability of agents’ statuses the system accumulates not only incentives as the current cash equivalent of social activity, but also agents’ rating in comparable dimension.
The object of stimulation is socio-optimal actions of citizens, that is, actions that correspond to certain attributes. The actions should maximize collective utility function without increasing the individual utility function. Therefore, the attributes correspond to the terms of gratuitousness, public utility and unconnectedness with professional activities of citizens. Consequently, socio-optimal actions do not require special qualification, whereby the stimulation object’s dimension is duration of action excluding the content of the action. The subject of stimulation is citizen, performing a sociooptimal action in certain period. The apparatus of stimulation is the state represented by certain ministries (departments).
The investigations of stimulation systems and distribution mechanisms produce the following
mechanisms corresponding the individual rationality. Competitive mechanism is developed with
noncooperative [
On the base of this ideas an algorithm of the information system (Fig. 1) was developed [
In [
K (t ) = {1,..., n(t )} is a set of agents, including citizens who perform actions that correspond to the attributes of Z; index n(t) denotes the number of agents in a certain period t;
A(Z , t ) = {ak (Z , t ), k ∈ K} is a vector of socially-optimal actions; the vector includes quantitative estimations of the actions of the k-th agent corresponding to the attributes Z in the t-th period; estimation a is expressed in the time spent by the agent for performing these actions; the vector belongs to the allowable set A = {ak ∈ [0, a max ] , a max > 0, k ∈ K }, where the symbol a max denotes the upper limit of the agents’ available time;
F (t ) ∈ (0, F max ] , F max > 0 is a stimulation fund in the t-th period t ∈ (0,T ] ; further, the index t is omitted, all parameters of the model correspond to a certain period of time; uk =ψ (ak ), k ∈ K , ψ (ak ) = αakβ ,α ∈ (0,α max ] ,β ∈ (0,β max ],β max ∈ (0,1], k ∈ K is dimensionless function of registration of socially-optimal actions; where u is a score, α ,β are constant coefficients; E = ∑ ak is a system effectiveness indicator;
k∈K xk = ϕ (uk ) = ϕ min + b1 − b2 ∑ uk ak , k ∈ K is monetary incentive function; where ϕ min is k∈K guaranteed incentive of non-zero agent’s action, b1 , b2 > 0 are coefficients of the incentive function, calculated from formulas ∑ uk 2u ∑ uk k∈K k∈K The algorithm of a one-period cycle of the information system is shown in Fig. 1.
b1 =
F − nϕ min 2u + ∑ uk k∈K 2u , b2 =
F − nϕ min , u = 1
∑ uk . n k∈K
The action registration block identifies agents’ actions in the scoring. The stimulation block is intended for distribution of the stimulation fund depending on the vector of scoring actions. The effectiveness analysis block controls the dynamics of the change in the social efficiency criterion of the system in the selected time interval until the maximum number of work periods is reached.
Let us consider the problem of the information system algorithm modeling for various probability density functions of the existence of social groups with a greater or lesser inclination for altruism.
Let the following continuous functions are defined for the k-th agent
ak (Dk ) = Dkδ ak , d k (Dk ) = Dkδ dk ,δ ak ,δ dk ∈ [
k
The functions (1) express the connection between the time interval of charitable actions, the time
interval of working time and the available time fund. The derivatives of the functions (1) decrease
with increase of D , expressing the propensity of individuals [
k
Definition: altruism (propensity to charity) of the k-th agent is a type of function (1), under which δ ak > δ dk .
The introducing of the socially-optimal actions stimulation system by the algorithm (Fig. 1) leads to the fact that altruistic actions bring a non-zero income.
Therefore, to select the value of the action, the k-th agent, taking into account the individual rationality, solves the following problem: to maximize the total income from the working and «charitable» time with a restriction1 on the available time fund: x mak∈aAx I k = max( pak ak + pdk d k ), pak , pdk > 0, pak = k , ak∈A ak
1 1 akδ ak + d kδ dk = Dk , k ∈ K , where pak is the price of the «charitable» time; pdk is the price (tariff rate) of working time.
Note that the restriction (3) does not coincide with the identity ak + dk = D , because of the k «charitable» time is not an absolute substitute in relation to working time, as shown in Fig. 2.
2 The solution of the problem (2), (3) has the form : δδ adkk Dk − ak*δ1ak δ dk −1 ak*δ1ak −1 = ppadkk , (4)
* 1 δ dk dk* = Dk − akδ ak , k ∈ K ,
(2) (3) (5) 1 δ dk 1 δ dk −1 1 −1 2The equation dk = Dk − akδ ak follows from (2) ; therefore dk/ak = −δ dk Dk − akδ ak akδ ak ; as at the δ ak tangency point B the angular coefficients of the functions (2) and (3) are equal, the optimum condition has the form (4). where the symbol «*» denotes the optimal values.
The elasticity coefficients δ ak ,δ dk are known, and price vectors are given
Pa = {pak , k ∈ K},Pd = {pdk , k ∈ K}, (6) (7) the first vector is calculated on the basis of the results of algorithm (Fig. 1) by formula (2), and the second vector is given based on the statistics of the national labor market. Thus, the solution of the equation (4) gives an individually rational vector of socially-optimal actions А.
Let the coefficient δ ak in the general population of agents (population) is a random variable [
In this case, the expected values of the agents’ number having these values of the elasticity coefficients δ ak ,δ dk = 1 −δ ak , are calculated by the formulas
nˆ(δ a ) = f (δ a )n, nˆ(δ d ) = n − nˆ(δ a ), where nˆ(δ a ), nˆ(δ d ) are the expected values of the agents’ number at given values of the elasticity coefficients.
The algorithm of the effectiveness analyzing block of the information system for various parameters of the probability density function of the social groups presence with a greater or lesser inclination for altruism is shown in Fig. 3.
The simulation of the stimulation effect on the population’s behavior is carried out by changing the asymmetry and kurtosis of the probability density function (7) of a normal distribution. The characteristics of the population’s distribution variants by social groups with greater or lesser inclination for altruism are given in Table. 1. The variant θ = 1 corresponds to the normal distribution law; variant θ = 2 simulates the case of exceeding the mathematical expectation of the population's inclination to altruism over the median value due to right asymmetry; variant θ = 3 simulates the case of a more uniform distribution of the population's propensity for altruism in comparison with the normal distribution law due to the decrease in kurtosis.
Model parameter Characteristics l w
The following initial data are considered: the value of the stimulation fund is set F = 1000000 thousand rubles, the values of the registration function coefficients (α = 67, β = 0,8 ) are selected from the condition u = 100 at the initial value of the time price and θ = 1, the minimum stimulus is assumed equal to zero, the number of the population n = 9727 thousand corresponds to the group of Russian Federation population with income below the subsistence minimum, the price of working time is Pd = 0.21 thousand rubles per hour based on the average wage of 35.369 thousand rubles per month, the range of the elasticity coefficient of the «charitable» time is chosen taking into account the possibility of equation (4) solution equal to δ a ∈ [0,1;0,7]. Since ϕ min = 0 , the price of «charitable» time is the same for all agents and it is equal to Pa = x akk = b1 − b2 k∑∈K uk .
In Fig. 4 the distribution functions of the population depict depending on the elasticity coefficient of the «charitable» time for various simulation variants.
In Fig. 5 the functions of average per capita effectiveness indicator Eav. = E / n for different simulation variants are given. The sharp increase in the effectiveness indicator at t = 1 is due to the increase in the price of the «charitable» time (Fig. 8) in the first period in comparison with the initial date adopted by Pа=Pd to adjust the stimulation system in the zero period. From Fig. 6 it follows that the reason for this growth is a significant increase in socially-optimal actions in groups with relatively low of «charitable» time elasticity coefficient in the range (0.2, 0.5). 0,1 θ=1 0,2 0,3 0,4 0,5
0,6 δа0,7 θ=2
θ=3 0
1 θ=1 2 3
4 θ=2 θ=3 5 t 5000
Population groups with very low values (0,1 ... 0,2) and very high (0,5, 0,7) values of the «charitable» time elasticity coefficient are less susceptible to the stimulating effect of the high price Pа: the first because of the prevalence of work in their disposable time fund, the latter due to high altruism. Since at t = 2, as the price Pа decreases (Fig. 8), the effectiveness indicator also decreases taking into account (Fig. 6) sharp reduction of such actions in the range (0.2, 0.5). Consequently it can be concluded that population groups with relatively low «charitable» time elasticity coefficient are prone to opportunistic behavior, that is, the motivation for socially-optimal actions for them is individual rationality. As a result, in all variants θ = 1,2,3 the value of the average effectiveness indicator stabilizes even at t = 3. simulation variants are given. In all variants, the value uav. stabilizes at t = 3. The highest values of uav. 180 170 160 150 140 130 120 110 100 90 80
Pa 1,2 1,0 0,8 0,6 0,4 0,2 0,0 0 average score are recorded at θ = 2, the lowest values are recorded at θ = 3, which is due to the dependence of the average score through the registration function on the social effect Eav. .
In Fig. 8 the «charitable» time price dependences on the period for different simulation variants are given, which also stabilize at t = 3. The lowest price Ра corresponds to θ = 2, the highest price is reached in the case θ = 2. Since the price Ра is a state incentive for a single socially-optimal action, the stimulation system is most economically effective at θ = 2, the least effective at θ = 3. 0 2 3 4
5 t 1 θ=1 θ=2 θ=3
1 θ=1 2
3 θ=2 4
5 t θ=3
The stabilization of the effectiveness indicator of the simulation system (Fig. 5) and the price of time (Fig. 8) at t> 2 leads to the conclusion about the stability of the simulation system for opportunistic behavior of citizens: persons with relatively low values of «charitable» time elasticity, performing socially-optimal actions based on individual rationality, demonstrate the greatest negative sensitivity to the change in the price of time as a stimulus. Due to this, the positive deviation of the stimulus in one period from a certain equilibrium value is damped by the opportunistic behavior of citizens, leading in the next period to a decrease in the number of socially-optimal actions.
The problem of informational support of the state strengthening morality strategy by stimulating citizens’ actions performed on the basis of maximizing the collective utility function is considered. The following main results are obtained in the article.
The algorithm for analyzing the effectiveness of the information simulation system for various parameters of the probability distribution function of social groups with greater or lesser inclination to altruism in society is developed.
The influence of stimulation on the population’s behavior is studied by changing the asymmetry and kurtosis of the probability density function of the normal distribution. The case of exceeding the mathematical expectation of the population's inclination to altruism over the median value is simulated by introducing asymmetry. The case of a more uniform distribution of the population's inclination to altruism in comparison with the normal distribution law is simulated by the introduction of kurtosis.
The analysis shows that the stimulation system is resistant to opportunistic citizens’ behavior due to the fact that persons performing socially-optimal actions based on the individual rationality demonstrate the greatest negative sensitivity to the change in the stimulus.