SUCCESSION AND SURVIVAL OF FAMILY BUSINESSES

Khai Sheang LEE* Wei Shi LIM Guan Hua LIM Faculty of Business Administration National University of Singapore 10 Kent Ridge Crescent Singapore 119260 Singapore

January 2000

* Please address correspondences to Dr. Khai Sheang LEE, Department of Marketing, Faculty of Business Administration, National University of Singapore, 10 Kent Ridge Crescent, Email: [email protected], Tel: (65) 874-3163, Fax: (65) 779-5941.

SUCCESSION AND SURVIVAL OF FAMILY BUSINESSES

SUMMARY In this paper, we present a dynamic game of uncertainty to investigate the succession and survival issues faced by family businesses. Our objective is to determine how succession in family businesses impacts their survival over future generations, and to provide an economic explanation for the low survival rate of family businesses being observed. We show that, because of potential opportunistic behaviours by outsiders, a family prefers to hand over its business to a family member. However, given the uncertain ability of the family member chosen to succeed, a family business will eventually fail if the family persists in passing the business only to family members over future generations. To overcome this problem of eventual demise, the family needs to turn to outsiders to manage its business. However, in doing so, it is important that mechanisms are devised to preempt potential opportunistic behaviors of outsiders. Towards this aim, various mechanisms are discussed.

INTRODUCTION It is well documented that many family businesses prefer to pass the reins to the business on to a family member [1], sometimes even regardless of the ability of the chosen family member to contribute to the success [2] of the family business. Family ties can be so strong that incompetent and untrained relatives are preferred over outside professionals [3]. Equally well documented is that fact that many family businesses in the USA go out of existence after ten years, and that only three out of every ten survive into the second generation (e.g. [4], [5], [6]). Furthermore, only some 15%-16% of all family businesses survive into the third generation (e.g. [6], [7]). The average life expectancy for a family business is estimated by some at 24 years, which ironically, is equal to the average tenure for the founders of the family business [8]. The comparable numbers in the UK is 24% and 14% respectively [9]. Another study documented that only 30% of family businesses in the UK reach the 2nd generation, less than 2/3 survive through the 2nd generation, and only 13% survive through the 3rd generation [10]. The fact that very few family businesses survive beyond the first generation (e.g. [11], [12]) is thus rather universal and independent of cultural context or economic/business environment [13]. There is even an old popular saying among Chinese businessmen that the third generation would dissipates the family's fortune and lose the family business that the first generation creates with great difficulties and the second generation helps to build upon. The interesting research question is why most family businesses do not last beyond the third generation.

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There are many possible reasons for these low survival rates amongst family businesses. Some argue that the fault lies with the inability of the founder to plan the succession properly and groom the chosen successor adequately. Poorly timed succession or otherwise mishandled succession could threaten the very survival of the entire family business [14]. Others argue that the third generation, being born with the silver spoon in its mouth, is unable and unwilling to put in the long hours needed to run the family business successfully [3]. They took the accomplishments of their parents and grandparents for granted, concentrated on enjoying the fruits of labour of their ancestors, and lack the drive to sustain, let alone expand the family business. Yet others point the finger at power struggles and internal disagreements amongst siblings and members of the extended family, which inevitably arise as the family business is passed down the generation, for causing the break-up of the business and the loss of management control in many family businesses. Examples of such cases abound.

The Jumabodhy family lost control over Singapore-listed property and hotel group Scotts

Holdings, while the Yeo family lost control of Yeo Hiap Seng. In this paper we present an economic explanation for the mortality of family businesses. We develop a 2-period dynamic game with uncertainty to examine the succession problem. The game is then repeated to examine the impact of succession strategy on the survival of a family business over multiple generations. We consider the case where, in each period, the intrinsic ability of the family member may be one of two types, namely high, or low. We show that it is economically rational for a family to prefer handing over its business to a family member. This is because of the agency paradox that a family faces in appointing an outsider to takeover the running of its business. A highly competent outsider would up his salary demands after acquiring sufficient knowledge of the business and hence, extract substantial gains from the family business. On the other hand, an incompetent outsider may jeopardise the business. However, if the family follows a succession strategy of persistently handing-over its business to a family member from one generation to another, the eventual demise of the family business results. This is because the probability of a family producing a capable heir to in each successive generation is small by the law of large numbers. Our results suggest that family businesses look seriously at their succession strategies and expand their source of successors beyond the family.

LITERATURE REVIEW The issue of survival of family businesses is closely related to that of succession. Much has already been written on the fact that many family businesses fail to plan for succession [2]. Very often, the founder is the crux of the problem. The founders, for example, may fear losing their identity by turning over the family

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business or they simply hate losing their power base and position in the family. Many researchers have offered practical advice on how to ensure a successful transition (e.g. [15], [16], [17], [18]).

Specifically, family

businesses are advised to identify a successor and groom the chosen successor. It is important for the successor to learn about the peculiarities of the family business. This exposure to others in the family business early also facilitates acceptance of the successor and the achievement of credibility by the successor amongst the key stake holders [19]. It is also very important that there is a plan for when responsibilities for, and power over, the business is actually handed over. A progressive delegation of authority to the successor is essential if the successor is to assume full control of the family business [20]. The actual transfer of power is a critical issue in the successful implementation of any succession plan (e.g. [21]. [22]. Finally, family businesses are advised to seriously consider the possibility of appointing an outsider to head the family business. Promoting from within the family can be a mistake especially if there is no one within the family with the requisite skills to take over ([15]. [23]). As such many writers in family businesses have advocated that founders/owners seriously consider passing the reins of the business to outsider professional managers, at least temporarily. However, the fact remains that most family businesses are still succeeded by family businesses [1]. This is despite the fact that sometimes the chosen successor is obviously inferior to the outside manager [2]. In this paper, we provide an economic rationale for such a succession strategy followed by many family businesses. The model we proposed here is a game theoretic one. Such game theoretic models are best suited for situations that involve interactions among multiple parties [24]. Game theoretic methods are increasingly being used in small business research. For example, Lee et al. [25] and Lim et al. [26] applied it to study strategic choices for SMEs, while Bjuggren and Sund [27] applied it to also examine the issue of succession in family businesses. Oughton and Geoff [28], on the other hand, used game theory to explain competition and cooperation in the small firm sector. Aiginger [29] tested the implications of the standard Cournot oligopoly model, which is a form of non co-operative game theory, on the performance of large and small firms. Corriveau [30] looked at a model of a one-good economy where long-run growth and output fluctuations are endogenous consequences of the decisions taken by entrepreneurs on the allocation of their resources between production and innovation in a Markovian sequence of one-period games. Choe [31], on the other hand, used game theoretic methods to study how the entrepreneur can design a contract that would credibly signal his commitment to the project to prospective investors. Finally, Cable and Shane [32] used the prisoner-dilemma paradigm to develop a conceptual model of entrepreneurs' and venture capitalists' decisions to co-operate.

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THE GAME THEORETIC MODEL Model Set-up To examine the succession and survival problem faced by a family business, we propose a model, representing any one generation j: j = 1, 2, … N, which is repeated over N generations. Each generation consists of a 4 stage sequential game played over 2 periods (Figure 1), with each period consisting of 2 sequential stages. In stage one of period 1, an outsider, who is a candidate for succession as the head of the family business, decides on the optimal compensation or price level (P1) that is commensurate with the position. We assume that the market is competitive in that the required expertise to manage the business is available from multiple competing candidates. Hence, there exists a competitive market rate in compensation level, defined by P*. After assessing the candidate and his demand for compensation level, the family decides whether to engage the outsider or to appoint a family member to succeed in heading the family business in stage two. In deciding on the candidate, the family faces the uncertainty that the chosen candidate may fail to perform as expected. This depends on the ability of the chosen candidate (α), which may be high (H) or low (L) and is unobservable prior to the family’s decision [33]. In period 2, given the family’s decision in period 1 to appoint an outsider, the incumbent outsider decides on whether or not to continue with his appointment with the family business. If he chooses to continue, he also decides on the compensation level to demand from the family in period 2. Having observed the compensation demand from the incumbent outsider, the family then decides whether to accept his demand or to terminate his appointment. In the event of a termination of service, the family has to employ another outsider to head the business. Figure 1 illustrates the game tree in the extensive form. Let f and o represent the family and the outsider, respectively. In addition, let

π f (F) and π o (F) refer to the family’s payoffs and the outsider’s payoffs,

respectively, when the family decides to appoint a family member to head the business. Whereas,

π f (O, T)

[ π o (O, T)] refers to the family’s [outsider’s] payoff, when the family decides to engage an outsider at a price P1 in the first period and the incumbent outsider decides to terminate his services with the family business in the second period.

π f (C, R) [ π o (C, R)] refers to

the family’s [outsider’s] payoff, when the incumbent outsider

decides to continue in his current appointment and demands a compensation package P2 in the second period, but

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the family rejects his demand. Finally,

π f (C, A) [ π o (C, A)] refers to the family’s [outsider’s] payoff, when the

incumbent outsider demands a compensation package P2 in the second period and the family accepts his demand. Let Pik be the compensation package paid to the head of the family business, k ∈ {f, o}, in period i. The family maximises family wealth as defined by

πf,

which we assume is dependent on the competency of the

head of the business, which is denoted by ηk. Hence, the family’s payoff in period i may be written as

πf=

(gi(ηk) – Pik), where, i = 1, 2, and ηk ∈ {ηf, ηo}. The notations ηf and ηo represent the competencies of the family member and that of the outsider, respectively, who is chosen to succeed the incumbent head of the family business. While, Pif and Pio refer to the compensation package paid to the family member and to the outsider, respectively, in period i. The family chooses the candidate k to maximise its payoff. The family’s objective function may be defined as follows.

Max.

π f = Max.{k} åi (gi(ηk) – Pik),

where, k ∈ {f, o},

ηk =

i = 1, 2 , refers to periods 1 and 2, and

ηf(k = f) ηo(k = o) Pif(k = f)

Pik =

Pio(k = o)

An outsider chooses compensation levels to maximise his individual payoff. Hence, his objective function is as follows. Max.

π o = Max.{P} åi (Pio),

where, {P} = {P1o, P2o}

Incorporating the Effects of Idiosyncratic Knowledge and Uncertainty in Abilities We model an individual’s competency as comprised of two components – his intrinsic ability as defined by α, and the extent of idiosyncratic knowledge that he possesses about the business as represented by z. An individual becomes more competent as he acquires idiosyncratic knowledge, or learns, of the business over time, and that such knowledge is business and position specific. This means that idiosyncratic knowledge is a form of

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specific assets as defined in transaction cost economics [34]. Including ability and idiosyncratic knowledge in our model, we thus rewrite gi(ηk) = l(αk, zik), where αk is exogenous and zik is endogenous on the number of periods a candidate has been in the position as head of the business. We assume that the function l, with respect

∂l ∂ 2l > 0 , and 2 < 0 . to z, takes a general and regular form in that it is concave and strictly increasing, that is ∂z ∂z This implies that the profitability of the business increases with increasing idiosyncratic knowledge at a diminishing rate. Given that abilities are uncertain, αk ∈ {αkH, αkL}, let θk be the probability that a chosen candidate k is of high ability, k ∈ {o, f}. Hence, the probability that a candidate is low ability is (1-θk). We assume that the function l increases with ability, such that l(αoL, z0) = l(αfL, z0) < l(αoH, z0) = l(αfH, z0), for a given level of idiosyncratic knowledge z0.

ANALYSIS We apply the subgame perfection criteria to derive the Nash equilibrium for the game (e.g. Rasmusen, 1989), in terms of the family’s and the outsider’s optimal strategies. We first derive the equilibrium for a generation j, before extending the game to n generations.

If the family engages an outsider in period 1 In line with the perfection criteria, for each generation, we will first examine the incumbent outsider’s responses in period 2, given that the family engages an outsider in period 1.

(a)

If outsider turns out to be of high ability (αoH) Given that this is the case, in period 2, the incumbent outsider’s competency is defined by (αoH, z2o),

such that z2o > z1o, as a result his acquisition of idiosyncratic knowledge over periods 1 and 2. In contrast, outside candidates who had no experience with the family business would not possess idiosyncratic knowledge of the business. Thus, in period 2, an incumbent outsider has an advantage in idiosyncratic knowledge over other outsider candidates, making him difficult to be replaced. Given that the market for candidates is competitive and the competitive price level for a new recruit is P*, P1 = P*. If the incumbent outsider chooses to continue his appointment with the family business and the

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family accepts his demand in compensation, then

π f (C, A) = [l(αoH, z1o) – P* + l(αoH, z2o) - P2].

On the other

hand, if the family rejects his demand in compensation and replaces the incumbent outsider by engaging another outsider, then

π f (C, R) = [l(αoH, z1o) – P* + l(αo, z1o) – P*].

However, since the ability of the new replacement

is uncertain, αo ∈ {αoH, αoL}, the expected profitability of the business is therefore l(αo, z1o) = [θol(αoH, z1o) + (1θo)l(αoL, z1o)]. Hence,

π f (C, R) = [(1+θo)l(αoH, z1o) + (1-θo)l(αoL, z1o) – 2P*], if the family decides to replace

the incumbent outsider. As long as the incumbent outsider demands a compensation level P2 such that

π f (C, A) > π f (C, R),

the family will rationally accept his demand. This condition reduces to [l(αoH, z1o) – P* + l(αoH, z2o) - P2] > [(1+θo)l(αoH, z1o) + (1-θo)l(αoL, z1o) – 2P*], which implies that P2 = P2H = [l(αoH, z2o) - {θol(αoH, z1o) + (1θo)l(αoL, z1o)} + P* - ε], such that ε > 0. However, being opportunistic, he maximises his payoffs by choosing ε → 0, to extract the increase in the business profitability that results from his acquisition of idiosyncratic knowledge. Since ε → 0, and l(αoH, z2o) > {θol(αoH, z1o) + (1-θo)l(αoL, z1o)}, for all θo between 0 and 1, it immediately follows that P2H > P*. Hence, we have the following result.

Lemma 1: Given that the family engages an outsider in period 1 who turns out to be high in ability: (a) The incumbent outsider demands a compensation of P2H = [P* + l(αoH, z2o) - {θol(αoH, z1o) + (1θo)l(αoL, z1o)} - ε] > P* (ε is any small positive number), which is accepted by the family. (b) At the equilibrium, π f (C, A) =[(1+θo)l(αoH, z1o) + (1-θo)l(αoL, z1o) - 2P* + ε].

Lemma 1 implies that, in period 2, although the incumbent outsider could increase profits for the family business as a result of his acquisition of idiosyncratic knowledge of the business, he would also demand an increased compensation level above market rates. Indeed, being opportunistic, the incumbent outsider could exploit the risk faced by the family in engaging another outsider of uncertain ability and appropriate the incremental gains that result from the idiosyncratic knowledge that he acquired (z2o > z1o), amounting to [P2H P*] = {l(αoH, z2o) - {θol(αoH, z1o) + (1-θo)l(αoL, z1o)} - ε}. This price premium paid to the incumbent outsider compared to the competitive market rate can be defined as the cost of opportunism in engaging an outsider, which results from the specific assets acquired by the outsider and the uncertain ability of a new replacement.

Proposition 1: An incumbent outsider of high ability can exploit the risk faced by the family in replacing him with another outsider of uncertain ability and appropriate the incremental gains that

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result from his acquisition of idiosyncratic knowledge of the family business, by demanding a premium in compensation: P2H = [P* + l(αoH, z2o) - {θol(αoH, z1o) + (1-θo)l(αoL, z1o)} - ε] > P* .

In period 2, if the incumbent outsider decides to terminate his services, then the family will have no choice but to replace him with another outsider. In this case, the family’s payoffs will be the same as when the family rejects the demand by the incumbent outsider for higher compensation and replaces him instead. Hence,

π f (O, T) = π f (C, R) = [(1+θo)l(αoH, z1o) + (1-θo)l(αoL, z1o) – 2P*]. terminate his appointment with the family business if

The incumbent outsider will choose to

π o (O, T) = P* > P2H = [l(αoH, z2o) - {θol(αoH, z1o) + (1-

θo)l(αoL, z1o)} + P* - ε] (Lemma 1), which never holds (Proposition 1) and according to the definition of l(αoH, z2o). The subgame perfect equilibrium, given that the family engages an outsider in period 1, therefore follows.

Lemma 2: The subgame perfect equilibrium, given that the family engages an outsider in period 1, who turns out to be high in ability, is such that the incumbent outsider chooses (C, P2H), where P2H is given in Lemma 1, and the family chooses (A).

(b)

If outsider turns out to be of low ability (αoL) When the outsider recruited in period 1 is known to be low in ability, the family may decide to replace

him with another outsider. Doing so, the family’s payoffs will be

π f (C, R) = [θo{l(αoH, z1o)} + (2-θo){l(αoL,

z1o)} – 2P*]. The family will choose to replace the incumbent outsider if given that the incumbent outsider is known to be low in ability, P2}]. Hence,

π f (C, R) > π f (C, A).

In period 2,

π f (C, A) = [{l(αoL, z1o) – P*} + {l(αoL, z2o) –

π f (C, R) > π f (C, A) requires that [θo{l(αoH, z1o)} + (2-θo){l(αoL, z1o)} – 2P*] > [{l(αoL, z1o) –

P*} + {l(αoL, z2o) – P2}], which implies that the family will replace the incumbent outsider if his demand of P2 is greater than [P* + l(αoL, z2o) – {θol(αoH, z1o) + (1-θo)l(αoL, z1o)}]. Anticipating this, and to preempt being replaced, the incumbent outsider therefore optimally chooses P2L = [P* + l(αoL, z2o) – {θol(αoH, z1o) + (1-θo)l(αoL, z1o)} - ε] > P*, if z2o is sufficiently large, such that l(αoL, z2o) > {θol(αoH, z1o) + (1-θo)l(αoL, z1o)}. Otherwise, P2L = P*, the competitive market rate, which is the amount the incumbent outsider can get if he chooses to terminate his appointment and to seek for a new appointment elsewhere instead. Therefore, an incumbent with known (low) ability will not choose to terminate his service at the equilibrium.

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Lemma 3: Given that the family engages an outsider in period 1 who turns out to be of low ability: (a) The incumbent outsider demands P2L = [P* + l(αoL, z2o) - {θol(αoH, z1o) + (1-θo)l(αoL, z1o)} - ε] > P*, if l(αoL, z2o) > {θol(αoH, z1o) + (1-θo)l(αoL, z1o)}. Otherwise, P2L = P*. (b) π f (C, A) = {θol(αoH, z1o) + (2-θo)l(αoL, z1o)} – 2P* + ε, if l(αoL, z2o) > {θol(αoH, z1o) + (1-θo)l(αoL, z1o)}. Otherwise,

π f (C, A) = [l(αoL, z1o) + l(αoL, z2o) – 2P*].

The next question that we need to address is whether there is any benefit for the family to reject the offer of the incumbent outsider, who has low ability. If the offer as given in Lemma 3 is rejected, the family’s payoff will be

π f (C, R) = θol(αoH, z1o) + (2-θo)l(αoL, z1o) – 2P*, which is less {θol(αoH, z1o) + (2-θo)l(αoL, z1o)} –

2P* + ε, but more than [l(αoL, z1o) + l(αoL, z2o) – 2P*] if l(αoL, z2o) < {θol(αoH, z1o) + (1-θo)l(αoL, z1o)}.

The

subgame perfect equilibrium, given that the family engages an outsider in period 1, who turns out to be low in ability, follows.

Lemma 4: The subgame equilibrium, given that the family engages an outsider in period 1, who turns out to be low in ability, is such that the incumbent outsider chooses (C, P2L), if l(αoL, z2o) > {θol(αoH, z1o) + (1-θo)l(αoL, z1o)}, and the family chooses (A). Otherwise, the incumbent outsider chooses (C, P*), but the family chooses (R), in which case π f (C, R) = θol(αoH, z1o) + (2-θo)l(αoL, z1o) – 2P*.

Lemma 4 implies that as long as the incumbent outsider possess sufficient idiosyncratic knowledge, such that l(αoL, z2o) > {θol(αoH, z1o) + (1-θo)l(αoL, z1o)}, he is secure in his position. What is more, he can even command a premium in compensation over the competitive market rate, P2L > P* (Lemma 3), although he is known to be low in ability. Given the idiosyncratic knowledge that he has acquired, plus the uncertainty faced by the family in recruiting a new replacement of high ability, the family therefore becomes reluctant to terminate his appointment even though he is known to be of low ability to the family.

Proposition 2: Even though an incumbent outsider is known to be of low ability, as long as l(αoL, z2o) > {θol(αoH, z1o) + (1-θo)l(αoL, z1o)}: (a) he is secure in his appointment. (b) he can command a premium in compensation, P2L > P* .

The Agency Paradox: If the family engages an outsider in period 1 whose ability is uncertain When the family engages an outsider who is high in ability, then the profitability of family’s business will be increased, as l(αoH, zio) > l(αoL, zio). However, it is known from Lemma 1, such able outsiders will

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demand a compensation in period 2 that amounts to P2H = [l(αoH, z2o) - {θol(αoH, z1o) + (1-θo)l(αoL, z1o)} + P* ε].

On the other hand, from Lemma 3, if the outsider recruited turns out to be of low ability, then the

compensation demanded by the incumbent outsider is Max [P2L = P* + l(αoL, z2o) – {θol(αoH, z1o) + (1-θo)l(αoL, z1o)} - ε, P*]. l(αoH, z2o) > l(αoL, z2o) implies that P2H > P2L, i.e., the cost of opportunism faced by the family is higher when it employs an outsider of high ability than when it employs one of low ability. An outsider who is high in ability is more able to increase the profitability of the family business. However, this comes at a higher price to the family, in terms of the future cost of opportunism faced. The family thus faces a paradox in engaging an outsider as head of the business.

Proposition 3: The family faces an agency paradox in engaging an outsider to head the family business: (a) If αo = αoL, then profitability is reduced as l(αoL, zio) < l(αoH, zio). However, the cost of opportunism is also reduced, since [P2L - P*] < [P2H - P*]. (b) If αo = αoH then profitability is increased as l(αoH, zio) > l(αoL, zio). However, the cost of opportunism is also increased, since [P2H - P*] > [P2L - P*].

From Lemma 1, when the outsider is high in ability, the family’s payoffs

π f (C,

A)αoH

=

[(1+θo)l(αoH, z1o) + (1-θo)l(αoL, z1o) - 2P* + ε]. On the other hand, from Lemma 3, if the outsider turns out to be of low ability, then the family’s payoffs is

π f (C, A)αoL = [{θol(αoH, z1o) + (2-θo)l(αoL, z1o)} – 2P* + ε], if l(αoL,

z2o) > {θol(αoH, z1o) + (1-θo)l(αoL, z1o)}. Otherwise, the family is better-off replacing the incumbent outsider with another outsider (Lemma 4), in which case

π f (C, R)αoL = [θo{l(αoH, z1o)} + (2-θo){l(αoL, z1o)} – 2P*].

Hence,

given that the ability of the outsider is uncertain prior to recruitment, the family’s expected payoffs is E( π f (O)) = [θo{ π f (C, A)αoH} + (1-θo){ π f (C, A)αoL}] = 2[θol(αoH, z1o) + (1-θo)l(αoL, z1o) – P*] + ε, if l(αoL, z2o) > {θol(αoH, z1o) + (1-θo)l(αoL, z1o)}. Otherwise, E( π f (O)) = [θo{ π f (C, A)αoH} + (1-θo){ π f (C, R)αoL}] = 2[θol(αoH, z1o) + (1-θo)l(αoL, z1o) – P*] + θoε. Proposition 4 therefore follows.

Proposition 4: Given that ability is uncertain prior to recruitment, the family’s expected payoffs in recruiting an outsider is E( π f (O)) = 2[θol(αoH, z1o) + (1-θo)l(αoL, z1o) – P*], as ε tends to 0.

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Proposition 4 implies that, not only will the family not benefit from the idiosyncratic knowledge acquired by an opportunistic outsider engaged, it also faces the risk of losses in the event that the outsider recruited turns out to be of low ability. This is because an opportunistic outsider, regardless of his ability, will appropriate any incremental gains that result from his acquisition of idiosyncratic knowledge of the family business by demanding increasing compensation. What is more, if the business prospers as a result his ability, then an opportunistic outsider will also demand increasingly higher compensation from the family. The fear of the cost of opportunism faced by the family in engaging an outsider, and the risk to the business performance due to the non-verifiability of an outsider’s ability prior to recruitment, are therefore legitimate reasons why family businesses are reluctant to appoint outsiders to key executive positions. This is especially so when idiosyncratic knowledge is crucial for the success of the business [35].

Corollary 1: If a family appoints an outsider to run its business: - an opportunistic outsider, regardless of his ability, appropriates the gains from the idiosyncratic knowledge he acquired. - the family business faces the risk of losses in the event that the outsider recruited turns out to be of low ability.

If the family engages a family member As given in Proposition 4, the family’s payoff is E( π f (O)) = 2[θol(αoH, z1o) + (1-θo)l(αoL, z1o) – P*], if the family engages an outsider to succeed as the head of the family business.

Hence, if

πf

(F) ≥ E( π f (O)),

then obviously the family’s dominant strategy is to appoint a family member to head the business. Otherwise, the family’s optimal strategy is to engage an outsider as head of the business.

Lemma 5: The Nash equilibrium is such that the family chooses to appoint a family member to head the family business if π f (F) ≥ E( π f (O)), and to engage an outsider otherwise.

Having determined the optimal responses in each stage of the game, we can now examine how differential abilities and idiosyncratic knowledge between the family member and the outsider, who are candidates for heading the family business, impact the family’s equilibrium strategy. We shall consider the scenarios: (1) when the family member is high in ability, αf = αfH, (2) when the family member is low in ability, αf = αfL, and (3) when the family member’s ability is uncertain prior to appointment: αf ∈ [αfL, αfH].

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(a)

When the family member is high in ability, αf = αfH When αf = αfH, then the family’s payoff over the two period is

Given that E( π f (O)) = 2[θol(αoH, z1o) + (1-θo)l(αoL, z1o) – P*] <

π o (F) = [l(αfH, z1f) + l(αfH, z2f) – 2P*].

π o (F) = [l(αfH, z1f) + l(αfH, z2f) – 2P*], as l(αfH,

zif) = l(αoH, zio) > l(αoL, zio), Lemma 5 implies that the obvious and dominant strategy is for the family to appoint the family member who is suitably qualified to succeed as the head of the family business.

Proposition 5: When αf = αfH, appointing a family member as head of the family business is a Nash equilibrium, in which case π f (F) = [l(αfH, z1f) + l(αfH, z2f) – 2P*] > E( π f (O)), as given in Proposition 4 .

(b)

When the family member is low in ability, αf = αfL When αf = αfL, then the family’s payoff over the two periods is

π o (F) = [l(αfL, z1f) + l(αfL, z2f) – 2P*].

Given that E( π f (O)) = 2[θol(αoH, z1o) + (1-θo)l(αoL, z1o) – P*], the family should appoint the family member provided the condition [l(αfL, z1f) + l(αfL, z2f)] > 2[θol(αoH, z1o) + (1-θo)l(αoL, z1o)] is satisfied. Since l(αoH, zio) > l(αfL, zif) = l(αoL, zio), and l(αfL, z1f) < [θol(αoH, z1o) + (1-θo)l(αoL, z1o)], the family should therefore appoint a family member to succeed as head of its business only if l(αfL, z2f)] is very much greater than [θol(αoH, z1o) + (1θo)l(αoL, z1o)], such that [l(αfL, z1f) + l(αfL, z2f)] > 2[θol(αoH, z1o) + (1-θo)l(αoL, z1o)]. Otherwise, it should engage an outsider.

Proposition 6: When αf = αfL, appointing a family member as head of the family business is a Nash equilibrium, only if [l(αfL, z1f) + l(αfL, z2f)] > 2[θol(αoH, z1o) + (1-θo)l(αoL, z1o)]. Otherwise, the family should appoint an outsider.

It would appear that the family should engage an outsider to succeed as head of the family business when αf = αfL. However, given the agency paradox faced by the family (Proposition 3) and its consequences (Corollary 1), the family can be better off appointing a family member, even though he is low in ability. This is provided that, in the long run, the possession of idiosyncratic knowledge is crucial for the business performance, more so than just ability alone. By appointing a family member who is low in ability, the profitability of the family’s business will suffer initially, as l(αfL, z1f) < [θol(αoH, z1o) + (1-θo)l(αoL, z1o)]. However, in the long run,

12

if the family business is highly dependent on the possession of idiosyncratic knowledge by the head of the business, such that l(αfL, z2f)] is very much greater than [θol(αoH, z1o) + (1-θo)l(αoL, z1o)], then the initial reduction in profitability of the family business can be recovered.

Corollary 2: When the profitability of the family business is highly dependent on the acquisition of idiosyncratic knowledge, it is economically rational for a family to hand over the business leadership to a family member, even though he is less able compared to outsiders.

Compared to an outsider, the family is more confident that a family member is more likely to stay on in his position over the long run. Hence, the family is more willing to appoint a family member to succeed as head of the business, if it feels that he is able to acquire sufficient idiosyncratic knowledge to manage the family business profitably. In addition, by appointing a family member to succeed as the head of the business, the family also preempts the future opportunism that it might face in the long run in engaging an outsider. Corollary 2 is therefore consistent with the long held argument in transaction cost economics that a firm should internalize when specific assets are acquired by the exchange party in the process of transactions ([36], [37], [38]). Proposition 6 and Corollary 2 thus provide an economic rationale, as opposed to any altruistic reasons, as to why a family hands over leadership of its business to a family member, even though the latter is less able compared to potential outsider candidates.

(c)

When the ability of the family member is uncertain, αf ∈ [αfL, αfH] When αf = αfH, then the family’s payoffs over the two periods is

π o (F) = [l(αfH, z1f) + l(αfH, z2f) – 2P*],

as given in Proposition 5. On the other hand, when αf = αfL, then the family’s payoffs over periods is

π o (F) =

[l(αfL, z1f) + l(αfL, z2f) – 2P*]. Hence, when the ability of the family member is uncertain, the expected payoffs to the family E( π o (F)) = [θf{l(αfH, z1f) + l(αfH, z2f) – 2P*} + (1-θf){l(αfL, z1f) + l(αfL, z2f) – 2P*}], or [θf{l(αfH, z1f) + l(αfH, z2f)} + (1-θf){l(αfL, z1f) + l(αfL, z2f)} - 2P*], on simplification. This gives the following lemma.

Lemma 6: When αf ∈ [αfL, αfH],

π o (F) = [θf{l(αfH, z1f) + l(αfH, z2f)} + (1-θf){l(αfL, z1f) + l(αfL, z2f)} -

2P*].

13

Hence, the family should appoint the family member to succeed as head of the family business if

π o (F) = [θf{l(αfH, z1f) + l(αfH, z2f)} + (1-θf){l(αfL, z1f) + l(αfL, z2f)} - 2P*] > E( π f (O)) = 2[θol(αoH, z1o) + (1θo)l(αoL, z1o) – P*], or [θf{l(αfH, z1f) + l(αfH, z2f)} + (1-θf){l(αfL, z1f) + l(αfL, z2f)}] > 2[θol(αoH, z1o) + (1-θo)l(αoL, z1o)].

Lemma 7: When αf ∈ [αfL, αfH], appointing a family member as head of the family business is a Nash equilibrium, only if [θf{l(αfH, z1f) + l(αfH, z2f)} + (1-θf){l(αfL, z1f) + l(αfL, z2f)}] > 2[θol(αoH, z1o) + (1θo)l(αoL, z1o)].

Note that the probability of recruiting an outsider of high ability, and that the family member is of high ability, need not be the same, θf ≠ θo. If θf ≥ θo, then the dominant strategy is for the family to appoint the family member, as [{θfl(αfH, z1f) + (1-θf)l(αfL, z1f)} – {θol(αoH, z1o) + (1-θo)l(αoL, z1o)} + {θfl(αfH, z2f) + (1-θf)l(αfL, z2f)} – {θol(αoH, z1o) + (1-θo)l(αoL, z1o)}] > 0. However, even if θf < θo, it can still be optimal for the family to appoint the family member provided that z2f, the extent of idiosyncratic knowledge that the family member acquires, is sufficiently high and important for the profitability of the family business. Proposition 7 thus follows.

Proposition 7: When the ability of the family member is uncertain, αf ∈ [αfL, αfH], appointing a family member as head of the family business is a Nash equilibrium if and only if θf ≥ θo or if θf < θo but z2f, is sufficiently high such that [θf{l(αfH, z1f) + l(αfH, z2f)} + (1-θf){l(αfL, z1f) + l(αfL, z2f)}] > 2[θol(αoH, z1o) + (1-θo)l(αoL, z1o)].

To summarise, in each generation j, the family always appoints a family member to manage the business if θf ≥ θo or if θf < θo, but [θf{l(αfH, z1f) + l(αfH, z2f)} + (1-θf){l(αfL, z1f) + l(αfL, z2f)}] > 2[θol(αoH, z1o) + (1-θo)l(αoL, z1o)]. In other words, the family will always appoint a family member to be the head of the family business as long as θf is not very much smaller than θo and the idiosyncratic knowledge acquired by the family member is significant. Otherwise, the family appoints an outsider as head of the family business. In the event that the outsider turns out to be of high ability, the outsider will remain to head the family business for another period. However, in the event that the outsider turns out to be of low ability and his idiosyncratic knowledge is insufficient to make up for his lack in ability, his service will be terminated after one period and the family will engage another outsider.

14

Extension to Multiple Generations In this section we extend the analysis to multiple generations to examine how a family’s business succession strategy impacts its long-term survival. We shall first examine the case when the family follows the optimal succession strategy, followed by when the family follows the traditional strategy. In extending our results to multiple generations, we note that the individuals in any generation j do not survive into the subsequent generation (j + 1).

(a)

The Optimal Strategy The optimal strategy is one in which the family follows the succession strategy as described by

Proposition 7 in each and every generation. In this case, the family prefers to appoint a family member, provided the family is suitably qualified (as defined by the conditions in Proposition 7). Otherwise, the family will engage an outsider until a suitably qualified family member arrives. This means that if an outsider is engaged in generation j, the family can still revert to a family member in future generations. Since the family can revert to the appointment of a family member in any generation, the family’s decision to appoint an outsider or a family member to head the family business in any generation is independent of the family’s decision in other generations. Hence, the subgame perfect equilibrium of a multi-generation game is comprised of the Nash equilibrium in each generation, which has been provided for in the previous sections, which show that the family prefers to appoint a family member. The result is stated in the following Proposition.

Proposition 8: In any generation j, the family appoints a family member if and only if θf ≥ θo, or θf < θo but [θf{l(αfH, z1f) + l(αfH, z2f)} + (1-θf){l(αfL, z1f) + l(αfL, z2f)}] > 2[θol(αoH, z1o) + (1-θo)l(αoL, z1o)]. The parameters θf and θo are specific to this particular generation j. Otherwise, the family appoints an outsider, whose contract with the family is renewed if and only if the individual is of high ability or if the individual is of low ability but l(αoL, z2o) > {θol(αoH, z1o) + (1-θo)l(αoL, z1o)}. In either case, the individual seeks re-appointment with the family business.

(b)

The Traditional Strategy Suppose the family follows “tradition” in that it chooses to hand over its business to a family member in

each and every generation, regardless of the ability of the family member chosen. Clearly, the family business cannot be better off by implementing the traditional strategy since the strategy space is smaller than if the option of engaging an outsider is available. Although this result is obvious, we include it as a proposition for comparison purposes.

15

Proposition 9: The traditional strategy of always appointing a family member to manage the business is dominated by the equilibrium strategy as specified in Proposition 8. Let Γ denote the collection of generations such that the conditions specified in Proposition 7 are not satisfied. That is, for all generations t in the set Γ, it is optimal for the family business to engage an outsider. Formally,

Γ = {t ∈ {1, N } : θ ft [l (α fH , z1 ft ) + l (α fH , z 2 ft )] + (1 − θ ft )[l (α fL , z1 ft ) + l (α fL , z 2 ft )] < 2θ ot [l (α oH , z1ot ) + l (α oH , z 2ot )]}.

Let πft(F) and πft be the family’s payoffs in following the traditional strategy and the optimal strategy respectively. We can write the difference in payoffs between the traditional strategy and the optimal strategy derived earlier as follows.

å δ t [π ft ( F ) − π ft ]

t∈Γ

The above term is negative, as every term in the summation is negative. Furthermore, each term in the summation is increasing in θft, the intrinsic ability of the family member, and z2ft, the level of idiosyncratic knowledge that is acquired by the family member in the second period of his service. In other words, the intrinsic ability of the family member and the amount of acquired idiosyncratic knowledge are pivotal to the growth of the family business. We summarize this result as follows:

Proposition 10: The disparity between the traditional strategy and the equilibrium strategy derived in Section 4.3 is decreasing in (a) the intrinsic ability of the family member and (b) the level of idiosyncratic knowledge acquired during the first period of service.

Proposition 10 implies that the family business will decline if the family sticks to the “traditional” strategy of appointing a family member, regardless of his/her ability, to head the business. It is also consistent with observations that family businesses seldom survive beyond the third generation ([6], [7]). To explain this phenomenon, we make the following observations based on the literature:

16

1.

z2f2 is such that [l(αfL2, z1f2) + l(αfL2, z2f2)] > 2[θo2l(αoH2, z1o2) + (1-θo2)l(αoL2, z1o2)], i.e., the intrinsic knowledge acquired by a second generation successor is significant enough so that the conditions established in Proposition 7 are satisfied;

2.

z2f3 is such that [l(αfH3, z1f3) + l(αfH3, z2f3)] > 2[θo3l(αoH3, z1o3) + (1-θo3)l(αoL3, z1o3)], i.e., the intrinsic knowledge acquired by a third generation successor is low and that the conditions established in Proposition 7 are thus violated. With these conditions, it is clear from our analysis and Proposition 7 that it is optimal for the family

business to engage an outsider to manage the business in the third generation. Otherwise, the family business will decline since it is sub optimal to have a family member in the third generation to manage the business.

CONCLUSIONS The implications of our game theoretic model are obvious. The family’s optimal strategy is to appoint a family member to take-over its business in successive generations, unless the targeted family member successor in any generation is severely lacking in competency to the extent that the business may be jeopardised. In the latter case, an outsider should be appointed in the interim. However, if the family follows the traditional strategy of always appointing a family member in every generation, regardless of the competency of the member chosen, then the eventual demise of the family business can be expected. On extension, it is also to be expected that fewer businesses would be successfully passed on to the third generation compared to those passed on to the second generations. The question now is can the family business do something to avoid its eventual demise. If the family is not willing to look beyond the family, then eventual demise of the family business is inevitable. The family could however, avoid this by enlarging the family, and hence the pool of candidates for succession, through marriages. Many Chinese and Korean families who are unable to produce capable sons and not willing to hand over the businesses to daughters [39], have expanded the family by roping their sons-in-laws into the family. Some families have even forced the son-in-laws to take the family name and be absorbed into the family. For example, Y.K. Pao, the Hong Kong shipping and property magnate who have no sons, arranged for his son-inlaws (a Chinese doctor, a Japanese architect, a Shanghai banker, and an Austrian lawyer) to take over his businesses prior to his death in 1992. Alternatively, two family businesses may merge or form a strategic alliance by marrying their offsprings to one another. In this way, the two family businesses are combined into one and the chances that either

17

family is able to produce a capable heir to inherit the business is increased. A third alternative is to hand the family business to a close associate or to the children of a loyal employee who have been in the business for a long time and who have contributed to its success. Family members typically fill most of the top management positions in the typical Chinese family business. Other strategic posts in the business are usually reserved for close relatives and for those who have worked for the family for long periods of time. The fortunate few in the latter category become "honorary" family members [3]. Passing the business to successors from such "honorary" family members are deemed to be in line with keeping the business in the family and preferred to employing professional outside managers. The other way to ensure that the family business continue to survive is to separate ownership from dayto-day management of the business. The family can create a trust or a privately held company to hold the shares of the family and leave the day-to-day management of the business to outside professional managers. The Ford family, for example, maintains some control over the Ford Motor Company through special ordinary shares held through a private family trust. In this way, the family maintains ownership control of the business but share part of the executive management of the business with outside managers. As long as the family retains a significant (not necessarily majority) share of the equity, it would be able to get its family members in its board of directors and/or on its payroll. This helps to keep the family in the family business even though the company could be led by a chief executive officer/president that is not a family member. A family business frequently maintains crossownership with other firms controlled by the family. The result is a web of holdings, which is reinforced by placing family members in key management positions. This allows the family to maintain ultimate, albeit circuitous, control over a large array of business activities.

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Figure 1. Game Theoretic Model for a Generation j Outsider Price, P1 Family

Engage Outsider (O) Appoint Family Member (F)

Nature

Nature

αf ∈ {αfH, αfL}

πf (F), πo (F)

αo ∈ {αoH, αoL}

Incumbent Outsider

Continue Service (C) Price, P2

Terminate Service (T) Family πf (O, T), πo (O, T)

Reject (R)

πf (C, R), πo (C, R)

Accepts (A)

πf (C, A), πo (C, A)

20