The decision to pass the information

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Аннотация

В данной работе я рассмотрел процесс обмена информации о работе между двумя агентами и также изучил факторы, которые влияют на решение обмениваться ли информацией с другим агентом.

Abstract

In this paper I studied the job information exchange process among two agents in the labor market and found factors that influence the decision to exchange information with another agent.

Introduction

The role of information in the modern society is crucial. Many different sources of information are available but getting information from your friends or acquaintances still remains very important.

In the job search process your social contacts are also very important. Different surveys were conducted and they have shown that a large fraction of people find their jobs through their social networks. `The importance of social networks in labor markets is pervasive and well documented. Mark Granovetter (1973, 1995) found in a survey of residents of a Massachusetts town that over 50 percent of jobs were obtained through social contacts. Earlier work by Albert Rees (1966) found numbers of over 60 percent in a similar study. Exploration in a large number of studies documents similar figures for a variety of occupations, skill levels, and socioeconomic backgrounds' (Calvo-Armengol, Jackson, 2004).

In (Calvo-Armengol, Jackson, 2004) the effect of social networks on employment was studied. In their model job information was obtained by the agent' s social network and they have found a positive correlation between employment and agents. But in their model they assumed that an agent who is employed will always pass the information about job opportunities to an agent who is in his network which in reality will not always be true.

In this paper I decided to study the decision to provide information and study the process of passing job information to another agent and I decided to find factors that influence the decision to pass the information. The process of passing information is not free for an agent, since he has to put some effort in order to provide another agent with the information, which is not free, so an agent incurs cost of effort when he passes information to a friend.

I took the model similar to the one from (Calvo-Armengol, Jackson, 2004) but I added the decision to pass the information into it. I solved it for 2 players to find out when an agent will decide to pass information to another agent and which factors will influence his decision.

1. The model

In this paper I considered the following model. There are two agents, all jobs are identical and both agents have similar information about job opportunities. The game starts when one agent is employed and another agent is unemployed. Agent 1 who is employed have 2 options: he can put effort and provide another agent with his job information but it will cost him c - cost of effort, or this agent can decide not to put effort so another agent will be left without agent's 1 job information. Both agents play Grim Trigger strategies so if agent 1 puts effort than when he will be unemployed and another agent will be employed that agent will also put effort so agent's 1 probability of finding a job will increase.

Game is played for infinite number of periods. Effort is a discrete parameter and can be equal to 0 or 1 and agents are able to observe the effort of their rival.

and

Where a is the probability of finding a job and is the probability of finding a job in case of zero effort from another agent.

I assumed stationarity across agent's utilities and I assumed continuous time, so the discount factor is equal to:

where ,

I decided to take utility function similar to the functions in (Pissarides, 2000), but I took a different function of probability of finding a job.

Where U(0,0) is the agent's utility when both agents are unemployed; U(1,1) is agent's utility when both agents are employed; U(1,0) is agent's utility when he is employed and another agent is unemployed; U(0,1) is agent's utility when he is unemployed and another agent is employed.

b is the utility an agent gets when he is not working, w is the utility an agent gets when he is working, is the probability of losing a job.

We can rewrite the utility functions in the following form:

Then I rewrited the equations in the matrix form and computed U(1,0) in cases with e=1 and with e=0 using Kramer rule.

For an agent to choose to cooperate

So, I came up with the following result:

Step-by-step solution is provided in the Appendix.

2. Results

In order to analyze this equation I assumed that , which means that discount factor is close to one. So the equation now becomes:

So,

From the above equation we can conclude that b, the utility that an agent gets when he is not working, has a negative effect on the incentives of an agent to pass the information. This can be explained intuitively: when agent's unemployment benefit rises he becomes less interested in finding the job, that means that he will be less interested in cooperation since it will increase his probability of finding the job.

W, the utility that an agent gets when he is working, has a positive effect on the incentives of an agent to cooperate. This also can be explained intuitively: when utility that an agent gets from working rises he will be more interested in getting the job so he will be more interested in cooperation.

As as

We can conclude that , the probability of job finding, has a positive effect on the incentives to cooperate. This can be explained intuitively: as increases, the marginal increase in the probability of job finding from cooperation will increase so an agent now is more willing to cooperate.

as

So we can conclude that , the probability of losing a job, has a negative effect on the incentives to cooperate. The intuition behind this is that when the probability of losing a job increases, an agent will more likely lose his job, so he is less interested in finding a job and because of that he is less interested in cooperation.

Also, as we can see that an agent will not always decide to cooperate. There will be situations in which it will be better for him not to cooperate.

3. Conclusion

To sum up, in this paper I investigated the process of passing information about job opportunities and found out that the decision to cooperate depends on various factors: utility from working, utility when an agent is not working, probabilities of job finding and losing. Also, I found out that an agent will not always decide to cooperate, since for some values of c, w, b, it will become unprofitable for him. So, the assumption that agents will always pass their information when they are employed will not always hold and the process of passing the information should be taken into account.

This model can be extended in different ways. It is possible to increase the number of agents and study the information exchange process. In that case the network effect will arise and the agents will have to decide whom to provide information. Also, this model can be applied to analyze not only the labor markets, but also other markets where information exchange process is presented.

4. Appendix

Let e=0 than:

; ; A=

, ;

Using Kramer Rule:

For e=1:

; ;

A=

,;

Using Kramer rule:

For an agent to choose to cooperate

information cooperation job utility

References

1. Antoni Calvу-Armengol and Matthew O. Jackson (2004)``The Effects of Social Networks on Employment and Inequality,'' American Economic Review, Vol. 94, No. 3, 426-454.

2. Christopher A. Pissarides, 2000. "Equilibrium Unemployment Theory, 2nd Edition,"MIT Press Books, The MIT Press, edition 1, volume 1, number 0262161877, March.

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