Intergenerational Conflicts of Interest and Seniority
Systems in Organizations∗
Munetomo Andoa, †, Hajime Kobayashiba Advanced Research Institute for the Sciences and Humanities, Nihon University,
12-5, Goban-cho, Chiyoda-ku, Tokyo 102-8251, Japanb College of Economics, Osaka Prefecture University,
1-1 Gakuen-cho, Sakai, Osaka 599-8531, Japan

December 12, 2005

Abstract
This paper studies the role of a proposed seniority system in an
organization. The organization consists of at least three overlapping
generations of short-lived members and chooses either a shortsighted
or a farsighted action in each period. This results in intergenerational
conflicts of interest. The old generation desires to obtain an immediate
profit, while the middle and young generations have incentives to invest
for future profits. We use a model of infinitely repeated games anddemonstrate that the seniority system solves these conflicts in the sensethat the farsighted action profile is sustainable in equilibrium.
JEL classification numbers: C72, C73, D82, J31, M14.
Keywords: Seniority system, endogenous choice of decision-maker,
profit allocation rule, overlapping generations game, communication.

∗

This research was initiated when we attended the meeting, Summer in Tsukuba 2001.
We are grateful to the organizers of the meeting. In addition, we wish to thank seminar/conference participants at Kobe University, Kyoto University (the Contract Theory
Workshop), Tohoku University, the University of Tokyo, the 2002 Annual Meeting of theJapanese Economic Association in Hiroshima, as well as Hideshi Itoh, Shinsuke Kambe,
Akihiko Matsui, Noriyuki Yanagawa, two anonymous referees and the editor for helpful comments and suggestions. The first author acknowledges financial supports by the
Inamori Foundation, the MEXT Grant-in-Aid for Scientific Research (No. 16330034),
and the 21st Century COE program “Dynamics of Knowledge, Corporate System andInnovation” at Graduate School of Commerce and Management, Hitotsubashi University.
†
Corresponding author. Tel.: +81 3 5275 9609; fax: +81 3 5275 9204. E-mail address:
munetomo.ando@arish.nihon-u.ac.jp (M. Ando).

1

1

Introduction

In the 1980s, it was generally believed that managers in Japanese firms
were more concerned with long-term results, compared with managers in
US firms. Kagono et al. (1985) conjectured that the reasons for this difference may be differences in financial markets, labor markets, and so on. In
this paper, we investigate what supports the Japanese management style.
Specifically, we show that the seniority system in organizations, which includes both the seniority-based task allocation system and the senioritybased profit allocation system, supports the Japanese management style.
We study an organization that consists of three overlapping generations(young, middle, and old). The organization plays a repeated prisoners’
dilemma game. In each period, the organization chooses a farsighted action
C or a shortsighted action D. The action C stands for Cooperation andD stands for Defection. The current profit of the organization depends on
both current and previous actions, and is allocated among the current members.1 In this situation, the old generation desires to obtain an immediate
profit by choosing the shortsighted action D, whereas the middle and young
generations have incentives to invest for future profits (i.e., they are willingto choose the farsighted action C). We demonstrate in this paper that theseniority system solves these conflicts of interest in the sense that the organization can sustain the farsighted action profile in equilibrium. Here theseniority system means that the middle generation person is the decisionmaker of the organization under a low-powered reward scheme, whereas theold generation person is the residual claimant.
There have been some theoretical explanations of the positive relationship between seniority and wages. Two famous explanations of this relationship are the specific human capital theory and the incentive theory. The
former was introduced by Becker (1962), who emphasized that on-the-job
training increases workers’ firm-specific productivity. Wages also increase
with increases in productivity. Lazear (1979, 1981) described a model of adeferred compensation scheme as an incentive device. He concluded thatthe principal should keep part of the compensation for a worker as a deposit
to prevent the worker from shirking. Moreover, this compensation scheme
reduces the frequency and the costs of monitoring activities.2
These two theories are tested by empirical data in some works. The
specific human capital theory is not well supported by empirical data (see,for example, Kotlikoff and Gokhale (1992) and Levine (1993)). On theother hand, the incentive theory is supported by data (see Barth (1997) and1
So examples of organizations studied in this paper include labor-managed firms andtraditional Japanese firms.
2
Other explanations are studied in Salop and Salop (1976) and Harris and Holmstrom(1982). The former introduced a model of self-selection and the latter introduced a modelof insurance for risk averse workers who are uncertain about their own productivity.

2

Bayo-Moriones, Galdon-Sanchez, and Güell (2004)).
However, none of these studies examines the relationship between seniority systems and management styles in organizations. In this respect,
our analysis differs from previous work.
Instead, our analysis can be regarded as a study of an endogenous choiceof the decision-maker, as we will try to answer the question, “who (or which
generation) is more appropriate as the decision-maker of an organization?”In the situation where conflicts of interest among generations exist, ouranswer is that the middle generation is the most suitable decision-makerunder seniority-based wage schemes when the long-term stability of profits
is necessary.3
From another point of view, the present paper is a study of corporate
reputation management. In our model, the firm can choose a farsighted action or a shortsighted action. The former corresponds to building or keeping
a good reputation and the latter corresponds to cheating consumers. Obviously, to maintain the good reputation of an organization, the management
style is a matter of great importance. We show that an efficient seniority
system helps to maintain a good reputation.4
We investigate the conflict situation in an organization within a framework of infinitely repeated games. Fudenberg and Maskin (1986) establisheda Folk Theorem in infinitely repeated games played by infinitely lived individuals with perfect memory of previous histories. Extensions to the worldof mortal players are studied in Cremer (1986), Kandori (1992), and Smith(1992). In these studies, the stage game is played among different generations in each period. On the other hand, in our paper, it is assumed thatthe action of the organization is chosen by the current decision-maker, thecurrent profit is dependent on the current action and the previous action,and the current profit is allocated among all the current members by profit
allocation rules that represent the seniority-based wage system. So the stage
game is not a variation of the game of public goods provision and is different
from the existing literature.
The work most closely related to the present study is Dickson and Shepsle (2001). They studied a repeated public goods game in an overlapping
generations (OLG) environment, and showed that there are three types of
equilibria, including the seniority equilibrium. In the seniority equilibrium,young generations contribute to public goods provision, while old generations do not. This can be interpreted as a seniority-based task allocation
system, because in this equilibrium the young generations exert effort, butthey do not exert effort when they get older. Moreover, it is similar toour paper in that profit is distributed from the young generations to the3

Recently, some papers have dealt with endogenous choice of decision-makers. See, forexample, Aghion and Tirole (1997).
4
In management literature, corporate reputation management has received much attention recently. See, for example, Fombrun and Riel (2003).

3

old generations. This may be interpreted as a seniority-based profit allocation system. However, there are considerable differences between us in the
motivation and results.
First, in the Dickson and Shepsle paper, the task allocation and theresulting profit allocation are endogenously determined as the consequencesof members’ equilibrium behavior. On the other hand, our paper assumes
that the task and profit allocation rules are exogenously given from theviewpoint of members. This modeling enables us to analyze the relationshipbetween the seniority-based profit allocation rule and the seniority-basedtask allocation rule explicitly.
Moreover, in the present paper, we focus the situation where the current
action choice by a firm has an intertemporal effect (i.e., the current action
affects the firm’s current profit and the set of possible profits in the next
period). In addition, in our framework, deviation increases the current total
profit of the firm. As a result, our framework has many applications (e.g.,
the study of corporation reputation management), which cannot be analyzed
in the game of public goods provision.
Muthoo and Shepsle (2004) studied the allocation of agenda-setting (orbargaining) power in organizations under an OLG setting. They studied
the properties of the optimal organizational structure and the conditions forsustaining the dynamically optimal outcome in equilibrium. Although the
motivation of this paper is similar to ours, the models are quite different
from each other. In Muthoo and Shepsle (2004), there are two overlapping
generations of players, young and old, and it is assumed that the numberof periods any particular player participates in is endogenously determinedby his or her past performance. Therefore, the United States Senate, inwhich legislators have staggered terms of office, is a good example of theorganization studied in their paper.
In this paper, we also study the role of intraorganizational communication. As mentioned above, we first study the situation where the decisionmaker of the organization is the middle generation person. Then we showthat intraorganizational communication is necessary to sustain the cooperative action profile if the decision-maker of the organization is the young
generation person. The reason is that the young generation person is unable to observe directly the events that occurred before his or her entry into
the organization. Moreover, we show that the seniority system also works insuch situations as a device for solving intergenerational conflicts of interest.
Extensions to repeated games played by sequences of short-lived playerswith informational constraints are considered by Bhaskar (1998), Anderlini
and Lagunoff (2005), Lagunoff and Matsui (2004), and Kobayashi (2004).
Bhaskar (1998) established an Anti-Folk Theorem result in a line of Kandori(1992) and Smith (1992). Lagunoff and Matsui (2004) studied the role ofpublic communication as a surrogate for memory in the same line as Bhaskar(1998). Anderlini and Lagunoff (2005) introduced intergenerational altru4

istic links in dynastic repeated games and demonstrated the emergence ofcooperation. Kobayashi (2004) introduced another type of intergenerational
altruistic links, known as passive altruism, and demonstrated a Folk Theorem in games played by organizations with short-lived members under asetting of imperfect memory of past histories.
The rest of the paper is organized as follows: Section 2 describes themodel. Section 3 describes the main results. Section 4 studies the role ofcommunication. Section 5 concludes.

2

The Model

We consider the following situation. Time is discrete, and periods are indexed by t (t = 0, 1, . . .). There is an organization that consists of threeoverlapping generations. We call them Young, Middle, and Old. An individual enters the organization at some date t, and after three periods heor she retires from the organization and is replaced by a new entrant. We
call the entrant at period t “agent t.” The organization therefore consistsof agents {t − 2, t − 1, t} at period t. We introduce the agents −2 and −1,
who enter the organization at the beginning of period zero.
at−1 \at
C
D

C
1
−`

D
1+g
0

Table 1: The payoffs
In each period, the organization chooses the current action at ∈ {C, D}.
The action C stands for Cooperation and D stands for Defection. The
payoffs πt (at−1 , at ) are given in Table 1, where the row indicates the organization’s previous actions, and the column indicates the current actions. The
numbers g and ` in the table are strictly positive. We assume that ` > g,that is, sustaining C is efficient for the organization. Thus, the organization
plays a kind of infinitely repeated prisoners’ dilemma game.
In this situation, there is a conflict among generations. The old generation desires to get an immediate profit, whereas the middle and young
generations take account of future profits. Therefore, our question is whether
cooperative action is sustainable in equilibrium.
We assume that each agent acts as the decision-maker of the organization only once in his or her life. We abbreviate the decision-maker as the DM
hereafter. Moreover, we assume the symmetry of task allocation among generations (for example, the DM is always a member of the young generation).
We call the generation assigned the task of DM the DM generation.
5

The profit obtained in period t is assumed to be allocated among thecurrent members by an exogenously given and time-invariant allocation rule
Λ = {λY , λM , λO }. Here, λj : R → R is the allocation function for generation j of the organization. We assume that the allocation rule satisfies thefollowing properties:(P1) for all πt , λY (πt ) + λM (πt ) + λO (πt ) = πt ,(P2) if πt ≥ 0, λj (πt ) ≥ 0 for all j, and(P3) for any π̂t > π̄t , λj (π̂t ) ≥ λj (π̄t ) for all j.
The first property means that the present profit (or loss) cannot be carried over to the following periods. The second implies that the minimum
wage is zero if the profit is nonnegative. The third means that the wage isnondecreasing in πt .
To summarize, the DM generation and the profit allocation rule characterize the organizational structure. We assume that the structure is exogenously determined and is common knowledge among the agents.
When each agent chooses his or her action, he or she is subject to an
informational constraint. The agent is unable to observe what happened
before his or her entry into the firm. He or she can observe the outcomes
during his or her lifetime only. Then, each agent can choose his or her
action depending only on his or her observed history if there is no additional
information on the history of the organization’s actions (e.g., messages fromolder generations). We will study the communication technology in Section
4.
Given the organizational structure and an agent’s information on the histories, the agent t chooses his or her action to maximize his or her discounted
sum of lifetime payoffs:
ut = λY (πt (at−1 , at )) + δλM (πt+1 (at , at+1 )) + δ 2 λO (πt+2 (at+1 , at+2 )),where δ ∈ [0, 1] is a common discount factor. In the above situation, we use
the sequential equilibrium as a solution concept.

3

Analysis

In this section, we consider whether cooperative action is sustainable in equilibrium. More precisely, we will answer the question, “under which type oforganizational structure is the cooperative action profile sustainable?” We
will show that, under the seniority system, the agents can sustain the cooperative action by using a one-period memory trigger strategy, the Markovian
trigger strategy. Here, the Markovian trigger strategy is the following strategy: the DM chooses C when t = 0 or if at−1 = C, and he or she chooses D
if at−1 = D.
First, we define the notion of sustainability of the cooperative action.
6

Definition 1. The organization can sustain the cooperative action profile
if there exist an organizational structure (i.e., a pair of a task allocation
rule and a profit allocation rule) and members’ strategies that satisfy thefollowing:
1. In every period, the realized action is C.
2. The members’ strategies and beliefs constitute a sequential equilibrium.
3. The DM has strict incentives to choose C if the previous action is C
in equilibrium.
Now, let us explain the reason we impose the third condition in the above
definition. In our overlapping generations environment, if we do not require
the third condition, we can easily achieve the cooperative outcome in equilibrium. For example, consider the following organizational structure. The
task allocation is that the Old agent is the DM. The profit allocation is that
the Young agent obtains all of the profit or loss, and the Middle and the
Old agents obtain zero for any πt . Under this structure, the cooperative outcome is achieved by the Markovian trigger strategy. Obviously, if all othermembers choose this strategy, no one can gain from deviation. However, theabove equilibrium is not stable in the sense that each DM only has weak
incentives to choose C. Therefore, we require strict incentives for choice ofthe cooperative action in equilibrium.

3.1

Proportional Allocation Mechanism

In this subsection, we restrict our attention to the proportional allocation
rule as a profit allocation rule, and consider whether cooperative action issustainable in equilibrium. We denote the proportion for Young (Middle,
Old, respectively) by λy (λm , λo , respectively), where λy + λm + λo = 1.
Proposition 1. The organization can sustain the cooperative action profileby the Markovian trigger strategy for any δ > 0, if the DM generation is
Middle and if the proportional allocation rule satisfies `/δ > λo /λm > g/δ.
Proof. When the Middle agent is the DM, the necessary and sufficient conditions to ensure that each DM chooses the Markovian trigger strategy are
as follows:λm π(C, C) + δλo π(C, C) > λm π(C, D) + δλo π(D, D)⇔ λo /λm > g/δ.

(1)

λm π(D, D) + δλo π(D, D) > λm π(D, C) + δλo π(C, C)⇔ `/δ > λo /λm .

(2)Under the assumption of ` > g, we can choose the profit allocation rule thatsatisfies (1) and (2). Thus, we obtain Proposition 1.
7

We obtain the following implication from Proposition 1. When an organization consists of more than two generations, the organization can employ
a type of “seniority system” as an organizational structure.5 The seniority
system satisfies the following properties: a middle management person is
the DM of his or her organization and he or she faces a low-powered incentive scheme, whereas an old generation agent is the residual claimant.
The young generation agent, who will become the DM in the next period,
observes the current action of the current DM. Under this system, the agent
who has the real authority (i.e., the middle management person) has no incentive to deviate from the equilibrium path, because it decreases his or her
profit in the next period through the punishment behavior of the following
generation. Moreover, once the deviation occurs, the next DM has a strict
incentive to choose D. Consequently, this kind of seniority system can solve
the intergenerational conflict in the organization.6
Obviously, to sustain the cooperative outcome, the DM has to satisfy
the following two conditions: (i) he or she will remain in the game in thenext period, and (ii) he or she knows the realized action in the preceding
period. The latter condition is necessary to choose the Markovian trigger
strategy.
The old generation agent will not remain in the game in the next period,so that he or she is not appropriate for the DM. When the DM is in neither
the old nor the young generation, he or she satisfies these two properties.
This is the key for Proposition 1. Although the young generation agent
does not satisfy the latter property, he or she satisfies the former property.
Therefore, if information on the previous history of the action is substituted
in any way, the young generation agent may become a cooperative DM. We
will consider this in Section 4.

3.2

A More General Allocation Rule

Under the proportional allocation rule, the organization cannot sustain acooperative action if ` < g. On average, if ` < g, choosing C and D
alternately is more profitable than sustaining C. However, under this action
profile, the discounted sum of lifetime payoffs ut is not equal to ut+1 . So
in this subsection we study a more general allocation rule that represents
the seniority system and show that the cooperative action profile can beachieved regardless of the values of ` and g when δ > 0.
Note that, to sustain the cooperative action profile, the following condi-

5

The wage profile becomes in practice the seniority-based wage on the equilibrium
path, when λy and δ are sufficiently small. That is, λy π(C, C) < λm π(C, C) < λo π(C, C).
6
Spagnolo (2005) considers a repeated delegation game and shows that a low-powered
incentive scheme helps firms’ collusion.

8

tions are necessary if the DM generation is Middle.
λM (π(C, C)) + δλO (π(C, C)) > λM (π(C, D)) + δλO (π(D, D)), (3)λM (π(D, D)) + δλO (π(D, D)) > λM (π(D, C)) + δλO (π(C, C)). (4)Note first that from the properties (P1) and (P2), λM (π(D, D)) and λO (π(D, D))should be zero. Note also that a smaller λM (π(C, D)) is easier to satisfy
inequality (3). Then we set λM (π(C, D)) = λM (π(C, C)). As a smaller
λM (π(D, C)) is easier to satisfy inequality (4), we set λM (π(D, C)) = −`.
λO (π(C, C)) should be not so large (to ensure the DM chooses D, if at−1 =D) and strictly positive (to ensure the DM chooses C, if at−1 = C). Consequently, conditions (3) and (4) become the following.
δλO (π(C, C)) > 0,
0 > −` + δλO (π(C, C)).

(5)
(6)

From (5) and (6), if `/δ > λO (π(C, C)) > 0, the cooperative outcome canbe sustainable.
To sum up, we obtain the following.
Proposition 2. If the DM is Middle and the profit allocation rules are
λY (π(C, C)) = λY (π(C, D)) = λY (π(D, D)) = λY (π(D, C)) = 0,λM (π(C, C)) = λM (π(C, D)) = 1 − min{1, `/δ} + ε,λM (π(D, D)) = 0, λM (π(D, C)) = −`,λO (π(C, C)) = min{1, `/δ} − ε, λO (π(C, D)) = min{1, `/δ} + g − ε,λO (π(D, D)) = λO (π(D, C)) = 0,
the organization can sustain the cooperative action profile by using the Markovian trigger strategy regardless of the values of ` and g if δ > 0.
Figure 1 depicts an example of the profit allocation rule for Middle andOld described in Proposition 2. The current profits of the organization areon the horizontal axis and the allocations are on the vertical axis.
The profit allocation rule described in Proposition 2 satisfies the following properties. The temporary gain from deviation g does not go to the DM’s
hand, but goes to Old’s hand. This removes the DM’s deviation incentive.
On the other hand, the temporary loss −` goes to the DM. This guarantees
that the DM will punish the deviant. We may regard this profit allocation
rule as the seniority wage system. In practice the wage profile described in
Proposition 2 seems to be the seniority-based wage on the equilibrium path,when `/δ > 1/2. That is, λY π(C, C) < λM π(C, C) < λO π(C, C).

9

−`

1

1+g

−`

Middle

1

1+g

Old

Figure 1: An example of the profit allocation rule for Middle and Old

4

The Role of Communication

In this section, we show that if information on the history of the action issubstituted in any way, the agent of the young generation is able to be acooperative DM. We introduce intraorganizational communication into ourmodel and study how it works.
If the Old generation is the message sender, he or she tells the Young theprevious action is D irrespective of the previous action, as it is a (weakly)
dominant strategy irrespective of the profit allocation rule that satisfies theproperties (P1)-(P3). Therefore, the sender should be the Middle generation.
The stage game is played with the following timing of events. First, theMiddle agent sends a message mt ∈ {C, D} to the Young agent. Then, theYoung agent chooses his or her action at ∈ {C, D}.
Proposition 3. Even if the DM is Young, the cooperative action profile issustainable if δ > 0.
Proof. We consider the following profit allocation rule.
λY (π(C, C)) = λY (π(C, D)) = 1 − ε, λY (π(D, D)) = 0, λY (π(D, C)) = −`/2,λM (π(C, C)) = λM (π(C, D)) = λM (π(D, D)) = 0, λM (π(D, C)) = −`/2,λO (π(C, C)) = ε, λO (π(C, D)) = g + ε, λO (π(D, D)) = λO (π(D, C)) = 0.
Let us consider the following strategies for each active generation.
Strategy for the sender of message: the sender sends C if at−1 = C and heor she sends D if at−1 = D.

10Strategy for the DM: the DM chooses C when t = 0 or if the message is C,
and he or she chooses D if the message is D.
Under the above profit allocation rule and members’ strategies, the following inequalities are satisfied.
λM (π(C, C)) + δλO (π(C, C)) > λM (π(C, D)) + δλO (π(D, D)), (7)λM (π(D, D)) + δλO (π(D, D)) > λM (π(D, C)) + δλO (π(C, C)), (8)λY (π(C, C)) + δλM (π(C, C)) + δ 2 λO (π(C, C))> λY (π(C, D)) + δλM (π(D, D)) + δ 2 (π(D, D)),

(9)2

λY (π(D, D)) + δλM (π(D, D)) + δ λO (π(D, D))> λY (π(D, C)) + δλM (π(C, C)) + δ 2 λO (π(C, C)).

(10)

Inequalities (7) and (8) are the conditions of truth telling for the sender(Middle) and inequalities (9) and (10) are the conditions of choosing theMarkovian trigger strategy for the DM (Young). Then we obtain the result.
Figure 2 depicts the profit allocation rule described in the proof of Proposition 3.7 The current profits of the organization are on the horizontal axis
and the allocations are on the vertical axis.
In the situation described in the proof of Proposition 3, Middle behavesas the in-company trainer and Young is on-the-job trainee. In this setting,the profit allocation rule should satisfy the incentive constraints for both
Middle (the sender) and Young (the DM). When the conditions for truthtelling hold, the current DM knows the previous action on the equilibrium
path and it is necessary to support the cooperative action profile.
We have assumed that the number of generations is three. As we haveseen, the Old agent has no strict incentive to truth telling (i.e., to send D
is a weakly dominant strategy irrespective of the previous action under theproperty (P3)) and an informational supplement is necessary for Young if
Young is the DM. Therefore, we obtain the following.
7
Note that, under the profit allocation rule described in the proof of Proposition 3, thewage profile is not the seniority-based wage on the equilibrium path. This is because theallocation rule is an extreme case, under which the cooperative action profile is sustainable
regardless of the values of ` and g when δ > 0. For example, when ` > 2, we can constructa profit allocation rule that satisfies conditions (7)–(10) and that seems to be the senioritybased wage on the equilibrium path. The profit allocation rule is as follows:

λY (π(C, C)) = λY (π(C, D)) = λY (π(D, D)) = 0, λY (π(D, C)) = −`/2,λM (π(C, C)) = λM (π(C, D)) = ε, λM (π(D, D)) = 0, λM (π(D, C)) = −`/2,λO (π(C, C)) = 1 − ε, λO (π(C, D)) = 1 + g − ε, λO (π(D, D)) = 0, λO (π(D, C)) = 0.

11

1

−`

1+g

1

−`

Young

1+g

Middle

1

−`

1+g

Old
Figure 2: The profit allocation rule described in the proof of Proposition 3

12Proposition 4. If the organization consists of only two generations, thecooperative action profile is not sustainable for any δ.

5Conclusion

In this paper, we studied the situation where an organization is infinitely
lived, while its composition changes, and there are intergenerational conflictsof interest. Under this situation, we showed that the seniority system solves
these conflicts in the sense that the farsighted action profile is sustainablein equilibrium if the organization consists of more than two overlapping
generations. Here the seniority system means that the middle generation
person is the decision-maker of the organization and faces a low-powered
reward scheme, whereas the old generation person is the residual claimant.
This means that a separation of decision-making and profit allocation may
be optimal in some situations. We also studied the role of intraorganizational
communication.
To conclude the paper, we make three comments. First, in the present
paper, we assumed for simplicity that each individual lives three periods andacts as the decision-maker of the organization only once in his or her life.
In the real world, however, managers typically work for many years. The
insights of our model are that the manager must not be of the old generationand the rewards for the managers are sufficiently low-powered.
Second, we assumed that there is a generation assigned the task ofdecision-making. We assumed this to simplify the analysis and we can extend the present model to the situation of decision by a majority. In sucha situation, it is necessary for the young generation person to mimic the
middle generation person’s action to sustain the farsighted action profile inequilibrium.
Finally, we also assumed that the organization chooses an action in eachperiod and the current profit depends on both current actions and previous
actions. We can extend the present model to the situation of repeatedinteraction among firms consisting of overlapping generations of members.
We plan to study this topic in another paper.

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