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Economic Computation and Economic Cybernetics Studies and Research, Issue 4/2015
127
Professor Marinko ŠKARE, PhD (corresponding author)
University Juraj Dobrila of Pula
Faculty of Economics and Tourism “Dr. Mijo Mirković” Pula
E-mail: mskare@unipu.hr
Katarina KOSTELIĆ, PhD student
University Juraj Dobrila of Pula
E-mail: katarina_kostelic@yahoo.com
INTERPERSONAL COMMUNICATION IN THE INTERNAL
MARKETING: BOUNDED RATIONALITY GAME THEORY
APPROACH
Abstract: Interpersonal communication or better known as communication
face-to-face is an integral part of everyday life. It has meaning in the business context
and the organization in which the individual acts of employer and employee is a
complex form of exchange/ trade and an inexhaustible source of research from
different perspectives.
This paper considers the employer - employee relationship from the point of view of
internal marketing communications, pulling an analogy from the sales conversation.
Game theory communication model will explain the phases of the communication
process in a job interview by identifying the factors that influence the conversation,
focusing on limited rationality. Our model will offer a space of possible strategies and
the equilibrium outcome for both sides of the conversation.
Game theory model will offer a causal connection between personality biases,
person’s productivity with the flow and precision of given information, phases, and
outcome. Also, we will consider deviations from equilibrium and their consequences.
This paper offers new concepts that can directly contribute to the progress of the
internal marketing and communications field, and indirectly labor market, and the
human capital area.
Keywords: interpersonal marketing communications, bounded rationality,
game theory, the trade.
JEL Classification: C7, D82, J08, M31, M51
1. Introduction
The role of the job interview or selection interview is critical. It is a moment when
employer and employee choose whether to place trust in their conversationalist by
committing to a business arrangement .Implications of such arrangement can be both
Marinko Škare, Katarina Kostelić
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positive and negative, at the individual level and for a given economy. From the
perspective of the individual employee, positive implications occur if they establish
fruitful cooperation where his trust would be justified, and his expectations met. For
the employer, the fruitful cooperation will result in benefits. The opposite, negative
implications imply cost or loss, both for the employee and employer. Those losses and
costs occur due expense of time, labor, additional education and training costs and
catching the pace in work. Such negative implications arise from lacking an
assessment, pour decision-making model and making judgment errors at the job
interview. Aggregately, wrong decisions at the job interview have effect to the
economy through creating expenses due to employee’s unemployed period or decline
of employer’s business productivity.
For above stated, the theme of job interview draws the attention of numerous
researchers which approach from different perspectives. The most common approach
is from the point of view of management or psychology. Consequently, the
contribution is largest in that area. Studies of the process of the job interview from the
point of view of internal marketing are missing. Namely, internal marketing often
serves as a synonym for training and motivation of employees, which is only one part
of internal marketing. The internal marketing represents sets of efforts in finding,
keeping and developing of the employee. The boundary between finding and keeping
an employee should be a job interview. That part is usually part of the management
process, but in this paper ,we will assess initial job interview as the phase in the
process of internal marketing management. From the marketing perspective, once the
potential employee has been found, he will be observed as a potential “buyer” of the
offered job. In that situation, the employer has two basic assignments.First, to create
candidate’s desire for the job or to “sell” a job. Second, todiscover employee’s
characteristics, to decide whether to hire him. The employer will do that enforcing
semi-structuredinterview
1
while using his negotiation skills forsale. The semi-
structured interview starts with the invitation for the interview. Then follows opening
of the conversation with one self’s introduction and small talk, determining motives,
connecting motives to a particular goals, and finishes with the cooperation offer. Stated
order will be the base for forming a model within game theory framework
2
, namely,
creating a game. Single units of conversation represent a stage in the model. Given
1
There are three sorts of selection/ job interview: structured, semi – structured and not
structured. Structured interview is consisted of previously defined questions, which should be
asked to each interviewee without exceptions. Not structured interview is an open kind of
conversation without previously defined questions. Semi – structured interview is consisted of
previously defined areas or themes, which have to be asked, but the content of each question or
approach adapt for each interviewee.
2
Game theory assumptions apply.
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there are multiple stages, it will be a dynamic game. Dynamic games can be games of
complete or incomplete information. A game of incomplete information will be
considered, given that the employee yet has to discover the employee's characteristics
or, in game theory terminology, the candidate’s type. The behavioral indicator will
specify the type of candidate.It will serve tomatch relative frequencies of personality
traits based on Jung's (1921) typology
3
.Hence, values of Briggs – Mayers test for
determination of personality types, and personal values scale gained from the general
attitudes. The data of individual personality traits are a result of a survey. The survey
has been online in Croatian, and the data consists of the answers of 231 respondents.
Besides that behavioral data determines candidate’s type, they affect the choices in
each stage of the game. Given that the behavioral elements represent a deviation from
rationality in candidate’s decision-making, it implies that the candidate will have
bounded rationality. Employer’s discovery of candidate’s type also describes the
detection of boundaries of candidate’s rationality, which we will model within
auxiliary signaling game. The signaling game and the dynamic game of incomplete
information will derive simultaneously; hence, an equilibrium that is more restrictive
will be necessary, perfect Bayesian equilibrium reinforced with statistical equilibrium.
The contribution of the stated model will enable detailed insight in the job
interview process, and discovering of regularities and patterns in the process of a job
interview. The exact contribution refers to explicit consideration of alternatives during
the negotiations. Since a job interview is a form of negotiations, it deliver sequential
discovering of information on the type of interpersonal communication and a new
insight into the bounded rationality question. Practical implications of findings are
possible within interpersonal communication and employees recruiting.
The contribution regarding alternatives during the negotiation fills in the gap
in related researches, which connect game theory and marketing, which Chaterjee and
Lillien (1984) found.
New studiesthat are connecting marketing and game theory focus on defining
bounded rationality and the assessment of consequences of decision-making, by
creating formal models. To determine the process of making purchasing decisions,
Roozmand et al. (2011) used modeling of people behavior. Author considers that only
“agent – based” modeling enables better understanding of micro processes and their
consequences at macro levels. Within their framework, they have modeled consumer
behavior using MASQ Meta – model. They found that there was a significant
correlation of three of five traits from Five-factor personality model and the position of
power as a sociological element with purchase choices. Nassiri – Mofakham et al.
3
Jung’s paper on psychological types date from 1921, but for purpose of this paper has been
used a translated republish by Princeton, New Jersey: Princeton University Press from 1971.
Marinko Škare, Katarina Kostelić
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(2007) useMASQ Meta – model, which implicates internal agent mechanism, social
variations among individuals, culture characteristics and the personality, whileNassiri
– Mofakham et al. (2009) analyze bargain process given the correlation of personality
traits and bargain process in e-business using OCEAN personality model. Stated
researchers use same experimental data, based on the MASSQ Meta – model, and
found same variables of influence with applications in the area of decision making in
bargaining and buying.
Furthermore, Škare et al (2014)analyze the impact of the differences among
the employees using game theory model in order to determine framework for defining
optimal amount and category of workload given the individual differences among the
employees. The model is oriented in defining the upper boundary of employee’s load,
hence determining the sustainable productivity of a single employee. From the internal
marketing perspective, the productivity of an individual can increase due to lifelong
learning and training. The model also, explains the necessity of individual approach to
determining workload. Same authors (2013) connected general attitudes and derived
value scales with the decision on continuing the education in the form of a micro
process, but also with analysis of aggregated consequences at macro level within game
theory framework. Authors suggested a model with bounded rationality by general
attitudes, such that general attitudes clearly and unambiguously relate to strategic
decision making.
The research of Roozmand (2011) and Nassiri – Mofakham(2007, 2009)
explicitly connect behavioral psycho – social elements to decision making. Tay et al.
(2006) determine the link between personality and behavioral elements of the
candidate to interview success. Therefore, this area enquires further research, which
will confirm the correlation of psychosocial elements with decision making in formal
models. Furthermore, that arises the question of determining concrete alternatives in
bargaining/ negotiation using psychosocial elements.
In this paper, psychosocial elements of personality and scales of values
determinate rationality boundaries and candidate type assessment in the model of a job
interview. Formal game theory model enables identification of specific alternatives in
each stage, which provides an insight in the semi-structured interview.
In the rest of the paper follows literature overview, methodological model
assumptions, results, and conclusions.
2. Literature review
A job interview is an inevitable part of everyday life; hence, it becomes an
object of observation from economic, sociologic and psychological perspective. From
the economic point of view, the goal is to spot quality, highly productive employees
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that will create additional value for the company, as well as avoiding the expenses due
to the employment of non-quality staff. From the sociological perspective, the goal is
to identify interconnections with employees and its consequences. From the
psychological viewpoint, characteristics of the individuals can affect job interview and
later cooperation in various ways. The meeting spot of noted areas is decision making.
Decision-making can follow a default rule, fixed strategies, random choice or adaptive
strategies. For example, if it is sufficiently to provide curriculum vitae and
motivational letter (without a job interview), then making a decision can be guided by
a default rule, such aseducational level or years of work experience. Random choice is
not commonly applied in employment. Non- structured interview can contain any form
of decision-making rules. Structured interviews can follow fixed strategies whether to
ask the same questions to all the interviewees or to continue the interview only while
answers match the expectations. Joshi et al. (2013) offered an example of questions
and answers for a structured interview with appropriate algorithms. Semi – structured
interview enables use of adaptive strategies. Adaptive strategies can be defined using
permanent factors, which will take over different values due to given situational
effects. These strategies are represented by functions. Given that, they can become
formal mathematical expression and model can be set within the game theory
framework. Game theory is a mathematical discipline that creates a methodological
framework for the analysis of players’ interaction. There have to be at least two
players. Players have strategies, which represent “guidelines” for making decisions in
each situation, which could occur in the game. Given the possibility of making an
agreement by changing the rules of the game, games can be cooperative and non-
cooperative games. It is very hard to model cooperative games within a formal model.
Hence, there is a tendency if possible, to model situations within then on-cooperative
game, but with clearly stated possibility of making an agreement if necessary. The
game can be simultaneously or dynamic. Simultaneously game presumes that players
make a move at the same time. The dynamic game implies making moves in turns. By
playing a move, a certain stage finishes, whether with the payoff or it exceeds in the
next stage. The game information can be complete if all players know all the elements
of the game, respectively incomplete if not all players know all information. The
incomplete information entails uncertainty. To diminish uncertainty and to make the
quality decision, it is advisable to gain as many information possible. In general,
players are rational. That means that players will make decisions, which will
maximize benefits or minimize lost. Given that such decision – making form is rare in
reality, to improve theoretical models to describe reality better, the term rationality is
facing numerous re-examination. Various forms of biases or influences, which
influence players such that they do not make perfectly rational decisions, represent
boundaries of rationality.
Marinko Škare, Katarina Kostelić
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Camerer (1998) and Rubinstein (1998) have been modeling bounded
rationality while Kahneman (2002) showed groups of possible influences. Elster and
Rendall (2009) take an analytical approach to human behavior searching for
regularities of reason and rationality. At the interpersonal level, boundaries of
rationality are characteristics of the individual. Davis et al. (2007) define
interconnection of personality traits with the lack in the decision – making.
Individual’s characteristics are composed of psychological, sociological and economic
elements. Psychosocial elements can be defined by determination of personality traits,
cognitive capacity and value scales. The implicit measure of general attitudes reveals
value scales. Hanisch et al. (1998) found the scientific significance of general attitudes
and value scales in repeated individual’s behavior. Chen, Goodard and Casper (2004)
determined the correlation between general attitudes with attitudes toward the work.
Personality traits and value scales are psychometric variables. There are tests, which
facilitate the determination of those values. Psychometric tests often have been using
in hiring selection process. Such data enable employers detail insight in possible
behavior and attitudes of the candidates. Parks and Guay (2012) connected value
scales to a work performance. Kulas (2012) points out on the prevalence of making
personality profiles in the job selection process. Two, the most famous models of
personality, are the ones, which Furnham (1996) compared: Five-factor model
4
and
Briggs – Mayers Type Indication model (MBTI)
5
. The critics of MBTI model points
out Murray (1990) claiming that the model could determine subjects preferences,
rather than personality traits. Exploring the critique of Briggs – Mayers model, in his
research Furham (1996)determined the significant correlation of four personality traits
from Five-factor model to four traits from Briggs – Mayers model. The only non-
correlated trait is neuroticism, which occurs only in Five-factor model. MBTI is the
most commonly used model for the non-psychiatric population. Briggs – Mayers’
model can be used in career counseling according to Kennedy (2004), which confirms
that personality traits are a predisposition for certain jobs.
4
Five-Factor Personality Inventory (FFPI), which was constructed in 1997, by Dutch scientists
Hendriks, Hofstee and De Raad, and it is composed of five personality traits: extraversion,
conscientiousness, openness to experience, agreeableness and neuroticism. Allport and Odbert
(1936) have defined that five personality traits.
5
Katharine Cook Myers and Isabel Briggs Myers are creators of indicators of personality traits
based on Jung’s personality types. Educational Testing Service publishes their questioner for
the purposes of research in 1962. After over a decade of testing the indicators, 1975. Consulting
Psychologists Press, Inc. publishes MBTI as psychological auxiliary tool. Isabel Briggs Myers
later publishes several editions of MBTI Manual. Personality indicator is based on four bipolar
traits: extraversion – introversion, intuition – sensing, thinking – feeling, perception –
judgment.
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Given the stated, we will use Myers – Briggs type indicator, combined with
value scales gained by general attitudes for modeling bounded rationality. The
presumption is that such defined bounded rationality enables detail insight in chosen
moves in stages of the communication process of a job interview. Moreover, we
assume that bounded rationality game theory model can reveal the causal connection
between individual’s characteristics and his productivity with conversation outcome.
3. Methodology
„Because game theory is about people (and groups of people) thinking about
what other people and groups will do, it is unlikely that pure logic alone will tell us
what they will happen “(Camerer, Ho, Chong, 2001: 3).According to that conclusion,
next logical step is to include some indicators of human behavior, i.e. implement
behavioral element in the model. Models of the behavioral game theory are usually
based on statistical equilibrium
6
, which represent a result of experimental research or a
survey on a large number of respondents. In this model, behavioral elements, which
will serve as statistical generalization, will reinforce the classical concept of perfect
Bayesian equilibrium. Behavioral elements will shape bounded rationality, given the
probability of choices, respectively the player’s type. Behavioral elements gained from
personality traits and player’s attitudes condition the probability of a certain choice by
a certain type. Such strategies have „have numerical attractions that determine the
probabilities of choosing different strategies through a logistic response function
“(Camerer, Ho, Chong, 2001: 5).
For convenience, it is simplified assumed that the employer is a rational
player. We assume for the candidate that he will behave rational, within the boundaries
defined by his attitudes, behavior and motivation. There are several tendencies in
modeling bounded rationality (A. Rubinstein, 1998, C. F. Camerer, T. H. Ho, J. K.
Chong, 2001.). Those researchers tend to defineboundaries in making decisions:
biological traits of decision-maker, current motivation, amount of known information
and knowledge, limited memory, effect of limited perception on information
absorption, limited anticipation of future events, cognitive abilities (learning abilities
and thinking processes). Within this paper, we will consider the indicators of
personality traits and attitudes of the decision maker, and implicitly his motivation.
Regarding the influences of limited perception on information absorption, we will
assume that in the considered situation can affect only on the employer. However, we
6
Quantal response equilibrium, statistical generalization of Nash equilibrium
Marinko Škare, Katarina Kostelić
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already assumed that the employer is rational
7
, so there will be no further discussion on
this influence. Limited memory and limited anticipation of events relate to time.
Within the game, we will model the amount of information and knowledge. We will
not analyze cognitive abilities further on. First, because it is assumed that cognitive
abilities of both employer and candidate are high enough to play this game
8
. Second,
the difference in cognitive abilities plays crucial role in strictly non-cooperative game
without possibility of making agreement (where one player wins only if another player
loses), or in cooperative games where rules can be bind and creative thinking can lead
to win. In this case, candidate and employer have to have at least similar interests
9
, so
differences in cognitive reasoning should not affect the outcome.
The players are employer and job candidate. The candidate has a private
information on his type while the information is unknown to the employer. The
communication between employer and candidate is derived trough two simultaneously
played games. The first game is obvious – dynamic game of incomplete information
and the second one is hidden - Cheap talk
10
and it reveals its self, through the
sequenced choices in the first game. Let the structure of the obvious game is set as
follows (see figure 1).
The job interview starts with a contact. While, employer makes the first move
(employer, E) based on received applications, and at his disposal there is strategy E1 =
{contact}, i.e. movesE1a and E1b. Strategy of employer (at each stage) is not a single
line, as it would be stated for the sake of simplicity, but the set or arguments, sales
techniques and persuasiveness in order to gain candidates trust and reveal the
candidate’s type. We will offer the concrete alternatives of the moves and strategies
keeping in mind “average type of personality in observed population”. By discovering
the candidate’s type, employer determinates possible contribution of the candidate to
the company, regarding economic, sociological and psychological elements. This
isalso true for the candidate, whose answers and statements we have summarized and
interpreted as the acceptance or decline. If the employer chooses the move E1a, to
invite the candidate for an interview, the candidate gets to make his move. If the
employer chooses E1b, i.e. not to invite the candidate for an interview, the game ends.
7
One of basic presumptions of game theory models is player’s rationality. In this model, only
one player’s rationality will be modeled as bounded.
8
Cognitive abilities could represent a problem in model generalization without individual
approach.
9
The employer’s interest is to find out candidate’s interests and it is in his interest that
candidate realizes the offer, because he knows the limitation parameter.
10
Crawford and Sobel developed the communication model, and in the sequel, Gibbons’
(2002) variant of the model will be used.
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If the candidate chooses the moveC1b: {decline}, the game goes in a loop
11
to
the beginning of the stage. Then, employer reproaches to the invitation and check if the
candidate move has changed (the employer will reformulate previous statement, and
giving the loop it will be the move Ea1 ).Given the loopback, “a” strategy is strictly
dominant to “b” strategy for the employer.
Figure 1. The loop in the decision tree of the dynamic game of job interview
which occurs when candidate responds negatively for the first time.
Source: Authors
If the candidate chooses the same move again, the game ends. A similar
situation will repeat whenever candidate responds negatively for the first time. The
loopback asks for the confirmation of the candidate’s negative response to a question
in current stage and to not continuing the game.
If the candidate responds positively, game exceeds to stage two. In the second
stage candidate and the employer get to know each other and the employer presents
himself and job and its potential benefits. The employer can do that using the official
approach (E2a) or to use friendly approach (E2b)
12
. The employer chooses the moves,
according to a few available data from the job application and previous part of the
conversation. Regardless to employer’s choice, the candidate can choose between
acceptances or decline of the employers approach and given information. In the case of
a negative response
13
,the game goes in a loop to the beginning of a stage two. Given
the new experience, the employer chooses another “first” approach
14
. Let the employer
chosesE2a, and the candidate responds with
a
C2
, which leads to the third stage of the
game.
11
As shown in the Scheme 2.
12
E2 = {introduction}
13
Decline could mean direct decline of offer, but also misunderstanding of the offer or lack of
establishment of trust and failure of proper assessment of candidate’s type as a result.
14
By loopback,
a
E2
becomes the move of friendly approach.
E1
b
E1
a
C1
a
C
1
b
Marinko Škare, Katarina Kostelić
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In the third stage, the employer’s goal is to identify primarily motives by
determining candidate’s general attitudes
15
and use it to induce the cooperation in
desired direction. He still does that in friendly manner, as the candidate accepted in the
previous stage. The employer tries to motivate candidate and to track his reaction, and
even if the candidate responds negatively, he will be able to try again. The employer
can make a moveE3a, hence motivate through safety needs
16
or the moveE3b, hence
motivation trough the profit
17
. If the candidate responds positively to employer’s
motivation by safety needs, the game forwards to the fourth stage. The employer has
two more information: first, the candidate responds positively to friendly approach and
safety motives.
At the fourth stage, the employer will try to deepen the existing motives and to
check if there is a specific goal tied to a motive
18
. Let the E4abe the move where
employer deepens the motive and connects it to a goal
19
, andE4bthe move where the
employer deepens previously knownmotives. In reality, it is more likely for employer
to try with E4a, so even if the candidate does not respond positively, he gets to change
it by playingE4a. Let the employer chooses E4a, and the candidate response is C4a.
In the fifth stage follows the resume of conversation so far E5 = {resume}.
Employers “a” strategy, E5ais a complete statement, for example: if I understood
correctly, you are anopen-minded young individual, and you want to test your skills in
a new job and you are enjoying working with people.You are a loyal person and have a
need for safety. You value tradition, structure, and organization, and economic benefit
is important to you. Is all I have stated correct?“, and strategyE5bwhere theemployer
asks for the conclusion: „How would you describe yourself given previous
conversation? Do you want to improve your living standard by gaining a permanent
job? “,where the employer deliberately misses out his conclusions to provoke a
reaction from the candidate. The candidate can agree or disagree. If the candidate
responds negatively, loopback takes the game to the beginning of the stage and
employer reformulates the statement.
15
E3 = {discovering candidate’s motives}
16
Group of motives contains safety, risk avoidance, health, comfort, social responsibility;
lower but long-term earnings, long-term offer, etc.
17
The group of motives contains striving for acknowledgement, prestige, image, curiosity, fast
profit, propensity for risk, short-term offers, etc.
18
E4 = {connecting the motives to a goal}
19
for example, does he works in order to be able to afford something specific to himself or to
his family, does he have a higher purpose, is his goal to be employed in such job, where does he
see himself in next 5 years etc..
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In the sixth stage, employer represents eligible possibilities to thecandidate,
keeping in mind previously stated preferences
20
, and stage finishes by achieving the
arrangement. The employer can suggest
a
E6
: taking overall workload (full-time
employment) or
b
E6
: taking over only part of the workload (probationary work or part
– time employment). The candidate can accept or decline. If he declines, the employer
will try to bargain with the counteroffer (but within the utility boundaries). With the
answer game ends.
The given structure intertwines with the game that has been simultaneously
playing off and is based on Crowford and Sobel Cheap talk model (Gibbons, 1992:
210 - 218).Cheap talk model is communication signal model in which the message
itself does not have a direct influence on the payoff, the message itself is just a talk –
without the expenses, a statement, which is not possible to verify at the time. The only
way the messages, the talk, can influence the payment is indirectly if under their
influence the message receiver changes his belief on the sender’s type. To consider the
message informative, several terms have to be met. According to Gibbons (1992), a
necessary condition in “Cheap talk” game is that different senders should have
different preferences on receiver’s actions. Respectively, the second necessary
condition is that a receiver has different preferences on his actions given the type of
the sender. The thirdnecessary condition is that the receivers and senders preferences
on actions are not the complete opposite. For the sake of simplicity, we will divide the
sender’s type in high and low, where high and low, in this case, denote the level of
qualifications
21
.Presumed that the receiver will prefer lower – level – qualification
action if the message comes from lower type sender, respectively high-level
qualification action if it is a high type sender. If the sender also prefers low action for a
low type and high action for a high type, they can establish communication. If it were
any different, it would be deceptive communication; hence, we could not model it
within this framework
22
.
20
For example, if candidate positively responds to profit group of motives, the employer’s
offer should offer additional earnings through the provision system. If candidate positively
responds to safety group of motives, the employer’s offer should contain job with constant
earning.
21
The sender’s type can, but does not have to be treated as behavioral element. In the observed
situation, it represents a behavioral element. If this game would have been played between two
companies, then their type would have been denoted by their productivity, or know-how.
22
Accordingly, it can be presumed that honesty and sincerity is a necessary condition for the
application of the multi stages cheap talk game. For example, the candidate can claim that he
has high-level competences, which is unverifiable statement at that time for the employer. That
message can affect employer’s belief and convince him that candidate in fact has high-level
Marinko Škare, Katarina Kostelić
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Derived from Crowford and Sobel model, it is introduced a parameter that
measures the deviation candidates’ from employer’s goals. The parameter b measures
the allowed deviation of interests, to continue communication:
1 < 2b1)-n(n
.
Respectively, adapted:
])
b
2
+(1+[1
2
1
(b)n*
(1)
4. Results
A certain stage has a positive outcome if the candidate answered positively,
respectively if the candidate answers negatively, game finishes with the payoff 0 (the
payoff that candidate and employer earn if they do not come to an agreement). If it is
positive, the subgame outcome or the outcome of a certain stage represents an
information input for the next stage. The space of possible outcomes for
employers
23
are given as
}E ..., ,{E=E 61
, and each strategy contains feasible moves
biaiiEEE ,
61
. (2)
The space of possible strategies for candidate is defined as
61,...,, CCtC
,
and each strategy has set of feasible moves
biaiiCCC ,
61
. (3)
Cheap talk constraint is true for the entire game and will be denoted with
parameter b. The information set h is continuous during the whole game (in each
following stage higher level of information set occurs. Hence players have access
tolarger set of information for decision-making), and each decision knot h(x) of the
employer follows updated belief on the candidate’s type and implicitly his
rationality
24
.
The first stage is composed of three moves, as the scheme points out. In the
first move, the candidate chooses his type by choosing from the space of the possible
types
competences, but the employer can have the opposite belief. In addition, similar game could be
modeled from the candidate’s perspective and he would have a choice to believe that his
employer wants a cooperation and mutual benefit, or he could believe that employer wants to
take advantage of him.
23
The employer and the candidate can use mixed strategies, which means that they do not have
to stick to one strategy during the whole game.
24
The same indicators that define candidate’s type represent the boundaries of his rationality,
as will be discussed further on.
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h
ttt ,...,
1
(4)
given by the candidate’s nature. For the simplicity, the candidate will choose
between two types tl andth. In the next move, employer chooses between
1a
E
={offer a
job interview to a candidate} and
b
E1
= {not to offer a job interview to a candidate}.
Information sets denote levels of players getting familiar, and at certain levels, it will
be denoted by the belief on candidates attitudes and behavior.
By reaching the higher information set
25
the employer comes closer to
complete reveal the candidate type, therefore, the limitations of his rationality. In the
first information set,
1
h
there are two decision knots. The employer knows that the first
information set has been reached. At that decision knots the employer has belief on
candidate’s type
(t)
which can take values 0 and 1.
At the decision knot
)(x1
the employer’s belief that candidates type
v
t
is 1, and
is equal to the sum of the relative frequencies of behavior and represents the belief that
the candidate is such type
v
t
that is worth the effort and time of the job interview. At
the decision knot
)( '
1
xh
the belief is 0, the employer finds that the candidate does not
fit a profile of a potential candidate (candidate type is
n
t
). Given that, players have to
choose strategies their belief: if employer’s belief is 1, the only move that satisfies the
equilibrium condition is
a
E1
and the game follows to a next stage. If the employer’s
belief is 0, the only move that meets the condition of the equilibrium is
b
E1
, and the
game ends (see figure 2).
25
Figure 2. shows only information sets that can occur in the game, given the limitations, i.e.
feasible sets and moves. The equilibrium moves are denoted with bold line.
Marinko Škare, Katarina Kostelić
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140
Figure 2. Dynamic game of incomplete information decision tree. Source: Authors
The tables present candidate’s type and employer’s belief on the candidate type
and the shown data is the result of the survey. At the beginning of the game, the
employer’s belief of the candidate’s type will be equal to the type of the “average
person”
26
which will define starting strategies, and the beliefs will be adapted as the
26
Frequencies of the value scales of the “average” individual denoted by general attitudes are
individualistic attitude: 0.221009254, theoretical attitude: 0.172787739, economic attitude:
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game takes off. The candidate is randomly chosen from the survey, and it will serve as
a figurative example for the demonstration of the model.
If candidate’s type is
v
t
, and if the employer played
a
E1
, the candidate’s
equilibrium strategy will be
a
E1
= {acceptance} and the game exceeds to a next stage,
respectively if the candidate type is
v
t
, his equilibrium strategy will be
b
C1
= {decline}
and the game ends.
Table 1. The example of the adjustment of beliefs of relative frequencies of
the value scales and personality traits at the beginning of the second stage
of the dynamic game of job interview with incomplete information
Relative
frequencies of
the population
average
Relative
frequencies
Adjusted
ranking
Relative
frequencies of
the candidate
Proposed
deviation in
absolute
value
(x1)
h(x2)
Individualistic attitude
0.1105046
-
0.075
- 0.025
Theoretical attitude
0.0863939
-
0.05
-0.025
Economical attitude
0.0688982
+
0.1
+0.025
Social attitude
0.0756578
+
0.085
+0.025
Traditional attitude
0.071501
+
0.115
+0.025
Esthetic attitude
0.0870445
-
0.075
-0.025
Introversion – Extraversion
0.130341355
+
0.1666667
+0.025
Intuition – Sensing
0.109774067
-
0.0972223
-0.025
Feeling – Thinking
0.108300589
-
0.0694445
-0.025
Perception - Judgment
0.151583989
+
0.1666667
+0.025
Σ
1
1
Σ b = 0.25
In the second stage, employer is first on the move, and he is aware that he is in
the second information set
2
h
. Observes and analyzes candidates move and updates his
0.137796414, social attitude: 0.151315789, traditional attitude: 0.143001735, esthetic attitude:
0.174089069. Frequencies of the behavioral components of the personality type of an “average”
individual: introversion - extraversion: 0.260682711, intuition - sensing: 0.219548134, feeling
– thinking: 0.216601179, perception - judgment: 0.303167976. The indicators denote how
frequently a specific behavior occurs on one’s behavior. For simplicity, the frequencies will be
pondered to sum up to one, which will ease the calculation of the deviation.
Marinko Škare, Katarina Kostelić
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142
beliefs. He will do that by arbitrary ranging value scales and personality traits
27
, as
shown in the table.
The employers belief at the knot
)( 2
xh
is
1)( 1
a
Ct
. The deviation in the
first stage cannot be calculated. The deviation denotes the difference between
employers and candidates interests
28
. It is necessary to calculate that deviation at the
end of each stage, and that serves as an input for the next stage, as shown in Table 1.
So that game exceeds to the second stage, the deviation has to be less or equal to 0.25.
Accordingly, the condition that communication successfully reaches the end of the
stage two is
0.25b
and has been met according to the distribution of suggested
deviations from the table. Simplified, if one observed the job interview and it did not
exceed to a higher stage, that means that the deviation was too big.
Table 2. The example of the adjustment of beliefs of relative frequencies of
the value scales and personality traits at the beginning of the third stage
of the dynamic game of job interview with incomplete information
Relative
frequencies of
the population
average
Relative
frequencies
Adjusted
ranking
Relative
frequencies of
the candidate
Proposed
deviation in
absolute value
h(x2)
h(x3)
Individualistic attitude
0.0855046
-
0.075
-0.00834
Theoretical attitude
0.0613939
-
0.05
-0.00834
Economical attitude
0.0938982
+
0.1
+0.00834
Social attitude
0.1006578
-
0.085
-0.00834
Traditional attitude
0.096501
+
0.115
+0.00834
Esthetic attitude
0.0620445
+
0.075
+0.00834
Introversion – Extraversion
0.155341355
+
0.1666667
+0.00834
Intuition – Sensing
0.084774067
+
0.0972223
+0.00834
Feeling – Thinking
0.083300589
-
0.0694445
-0.00834
Perception - Judgment
0.176583989
-
0.1666667
-0.00834
Σ
1
Σ b = 0.0834
27
Let that is true that employer knows the distribution of relative frequencies of value scales
and personality traits and the process of psychometric data gathering. Accordingly, he will start
the game with the belief of the average individual.
28
The employer learns about the candidate’s type, respectively his interests, and he adapts to
what he has learned. We can see that from the employer’s belief adjustment.
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In the second stage, employer has at his disposal move
a
E2
= {friendly
introduction} and
b
E2
= {official introduction}. If the employer’s belief is a
1)( 1
a
Ct
, his equilibrium strategy can be only
a
E2
. The candidate can choose
between the moves
a
C2
={cooperation/ positive response} and
b
C2
= {decline/
negative response}. Given the candidate has to play his move accordingly to his type,
his only feasible strategy is
a
C2
.
The third stage starts with the employer’s move, and he is at the decision knot
at the third information set,
)( 3
xh
. He observes candidates move and updates beliefs.
Table 3. The example of the adjustment of beliefs of relative frequencies of
the value scales and personality traits at the beginning of the fourth stage
of the dynamic game of job interview with incomplete information
Relative
frequencies of
the population
average
Relative
frequencies
Adjusted
ranking
Relative
frequencies
of the
candidate
Proposed
deviation in
absolute value
h(x3)
h(x4)
Individualistic attitude
0.0771646
-
0.075
-0.004167
Theoretical attitude
0.0530539
-
0.05
-0.004167
Economical attitude
0.1022382
-
0.1
-0.004167
Social attitude
0.0923178
-
0.085
-0.004167
Traditional attitude
0.104841
+
0.115
+0.004167
Esthetic attitude
0.0703845
+
0.075
+0.004167
Introversion – Extraversion
0.163681355
+
0.1666667
+0.004167
Intuition – Sensing
0.093114067
+
0.0972223
+0.004167
Feeling – Thinking
0.074960589
-
0.0694445
-0.004167
Perception - Judgment
0.168243989
+
0.1666667
+0.004167
Σ
1
1
Σ b = 0.04167
Third stage deviation has to be smaller or equal to 0.0834. Table 3 shows the
distribution of the deviations, respectively, the minimum condition for reaching the
end of the third stage has been met. The employer has two feasible moves,
a
E3
=
Marinko Škare, Katarina Kostelić
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{motivation by the group of safety motives} and
b
E3
= {motivation by the group of
profit motives}. The candidates possible moves are
a
C3
= {acceptance and
cooperation} and
b
C3
= {decline}. The employer’s updated belief is
1),( 21
aa CCt
, and congruently the equilibrium move is
a
E3
. The candidate equilibrium move is
a
C3
,
because playing the other move would be contrary to candidate’s type.
The employer observes candidates move and updates his beliefs at the fourth
decision knot, as shown in Table 4. For the fourth stage, the deviation has to be smaller
or equal to 0.04167. In the Table 4, one can read the proposed distribution of
deviations, and see that the condition that communication reaches the end of the fourth
stage is satisfied. The employer’s moves can be
a
E4
= {connect the motives to a
certain goal} and
b
E4
= {deepen the motivation without connection to goals}.
Candidate can respond with
a
C4
= {acceptance/ cooperation} and
b
C4
= {rejection}.
The employer’s belief is
1),,( 321
aaa CCCt
, and his optimal strategy is
a
E4
. With
the given employer’s move and the candidate type, the candidate’s answer is
a
C4
.
Table 4. The example of the adjustment of beliefs of relative frequencies of
the value scales and personality traits at the beginning of the fifth stage of
the dynamic game of job interview with incomplete information
Relative
frequencies of
the population
average
Relative
frequencies
Adjusted
ranking
Relative
frequencies of
the candidate
Proposed
deviation in
absolute value
h(x4)
h(x5)
Individualistic attitude
0.0729976
+
0.075
+0.0025
Theoretical attitude
0.0488869
+
0.05
+0.0025
Economical attitude
0.0980712
+
0.1
+0.0025
Social attitude
0.0881508
-
0.085
-0.0025
Traditional attitude
0.109008
+
0.115
+0.0025
Esthetic attitude
0.0745515
+
0.075
+0.0025
Introversion – Extraversion
0.167848355
-
0.1666667
-0.0025
Intuition – Sensing
0.097281067
-
0.0972223
-0.0025
Feeling – Thinking
0.070793589
-
0.0694445
-0.0025
Perception - Judgment
0.172410989
-
0.1666667
-0.0025
Σ
1
1
Σ b = 0.025
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At the beginning of the stage, employer observes the candidate action and
updates his beliefs, as shown in the table 4. As the table shows, the updated
distribution of the relative frequency has low enough deviation, which has to be lower
or equal to 0.025. Necessary and sufficient condition is satisfied, and the game can
reach the end of stage five.
Possible moves in the fifth stage for the employer are
a
E5
= {partial offer}
and
b
E5
= {complete offer}. The moves can be
a
C5
= {acceptance/ cooperation} and
b
C5
= {decline}. Given the employer’s belief
1),,,( 4321
aaaa CCCCt
, his optimal
move is
a
E5
. Given the employer’s move and the candidate’s type, the only option for
candidate is to play
a
C5
.
Table 5. The example of the adjustment of beliefs of relative frequencies of
the value scales and personality traits at the beginning of the sixth stage of
the dynamic game of job interview with incomplete information
Relative
frequencies of
the population
average
Relative
frequencies
Adjusted
ranking
Relative
frequencies of
the candidate
Proposed
deviation in
absolute value
h(x5)
h(x6)
Individualistic attitude
0.0754976
-
0.075
-0.00167
Theoretical attitude
0.0513869
-
0.05
-0.00167
Economical attitude
0.1005712
-
0.1
-0.00167
Social attitude
0.0856508
-
0.085
-0.00167
Traditional attitude
0.111508
+
0.115
+0.00167
Esthetic attitude
0.0770515
-
0.075
-0.00167
Introversion – Extraversion
0.165348355
+
0.1666667
+0.00167
Intuition – Sensing
0.094781067
+
0.0972223
+0.00167
Feeling – Thinking
0.068293589
+
0.0694445
+0.00167
Perception - Judgment
0.169910989
-
0.1666667
-0.00167
Σ
1
1
Σ b = 0.0167
In the last stage, employer solves the optimization problem. Given the game
limitations, the employer has to place such offer such that the candidate will accept
Marinko Škare, Katarina Kostelić
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146
right away. Otherwise, the game ends with payoffs 0. The employer can take
a
E6
=
{q2, work assignment set according to the group of security motives and goals} or
b
E6
= {q1, work assignments set according to the group of motives}. Candidate moves can
be
a
C6
= {acceptance} and
b
C6
= {decline}. After solving optimization problem and
updated his belief, which now is
1),,,,( 54321
aaaaa CCCCCt
, he chooses move
a
E6
. Given the denoted distribution of deviances, that move is within the limitation.
Allowed deviation for this stage is 0.0167, as shown in the Table 5. Candidate
observes employer’s move and chooses consistent move, which is
a
C6
. The game ends
with positive payoffs for both candidate and employer.
Although at the first sketches looks like there are 190 possible outcomes, at the
equilibrium path there are only two possible outcomes (bolded at the scheme 2). This
model represents a combination of the dynamic game incomplete information model
and behavioral game theory model. By establishing equilibrium strategies rules of both
dynamic games of incomplete information and statistical equilibrium concept. Even
though the game comprises larger parameter number, there is a relatively small
number of outcomes. The reason is reinforced equilibrium concept. If the employer
wants to achieve the positive outcome and confirm the candidate’s type, he must strive
to set up cooperation. Given that the positive outcome for the employer is at the same
time positive outcome for the candidate, there is a motivation for the cooperation. The
employer will achieve that by following the only equilibrium strategy, hence by
implementing his offer into a function of candidate’s motivation, i.e. goals.
5. Conclusion
This paper examines communication relation of the employer and the candidate
at the job interview. We have placed conversation within the game theory framework
to gain detailed insight into the communication process, strategy and move analysis,
and defining equilibrium solution. The model enables definition and explanation of the
causal connection between personality test, value scales and the course of the
information exchange, chosen moves by the stages and equilibrium outcome.
Implementation of behavioral elements affects the conversation outcome, the choices
of strategies and moves, respectively on player’s rationality. By (re)defining
rationality, to achieve more faithfully and precise outcome anticipation at the
interpersonal level emerges bounded rationality. Such defined rationality can explain
individual’s strategic choices in interactions. Respectively, if we redefine rationality,
game theory can offer more faithful individual interaction models. When we
introduced behavioral elements in the game, the rationality does not shape the choices
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of the individuals toward payoff maximization in the classic sense. The term of
payment for the player and his strive to its maximization, as well as the choice of the
strategy depends on attitudes, behavior and player’s type, which can but does not have
to concur with rational choice of the strategies and maximized payment.The enriched
gamehas behavioral elements such that they form a candidate’s type and enable
measuring deviation of employer’s beliefabout candidate’s type and forming a
condition that has to be met in order that game continues.Applying perfect Bayesian
equilibrium in combination with statistical equilibrium, the model provides two
feasible outcomes, regarding the candidate’s type. Therefore, we can conclude that the
model describes proposed case precise enough, and can be used in anticipation of
conversation process and the outcome of the job interview. Therefore, an employer
that spotted potential candidate should carefully discover candidate’s type and achieve
desired outcome by placing his offer in the function of candidate’s goals. Also, by
discovering the candidate’s type, the employer learns trough the game. What he has
learned has to apply immediately by adapting his belief, strategy and choose future
moves, which will lead to the preferred outcome.
It is interesting and not completely expected to notice that the model does not
allow positive outcome for the case of deception. The player that would try to deceive
would eventually be uncovered making the damage to himself as the result. If a
candidate tries to deceive, the employer will recognize that it is a low type instead of
high type, the hence deviation would exceed allowed limit and the game would not
follow to the next stage. Similarly, the candidate would end the communication if he
discovers that the employer’s offer deviates too much form his interests.
The modelmay use as a theoretical framework for better understanding of the
interaction between individuals. Also, it can serve as a preparation for a specific case
of job interview, with the behavioral type input adjustment. The application can be
expanded to similar models (given that substantial amount of data is available, and that
inputs are calculated from epmirical data)of the individual cases of the negotiation of
two persons. With minor adjustments, the model can be applied to theoretical and
practical anticipation of processes and outcome of negotiation or bargaining of two
individuals like recruiting, business partnerships, most forms of sales, mentoring and
coaching of an employee, individual teaching, and even at persuasion at personal
interactions.
Bounded rationality is rationality shaped with attitudes and player’s behavior, so it
is necessary to adjust it to each specific case, which makes this model harder for the
application. Furthermore, the inputs on the “average” individual can vary regarding the
country and the culture. Hence, it would be necessary to conduct research to define
value scales and personality traits. So far, data on“average” individual in this paper is
Marinko Škare, Katarina Kostelić
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148
applicable for Croatia only. Inductively, a framework for the modelling rationality of
population can be set.
Preferably, further researches should provide additional confirmation of
explicatively and predictive abilities of the model. Also, area for further researches
could be the application of this model in various situations of interpersonal
communication, as well as for cross-cultural assessment of the model sustainability.
Furthermore, it would be interesting to check if aggregated individual decisions and
interactions can explain elements of social and economic development.
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