سرمایه گذاری سرمایه انسانی در مسابقات شرکت نامتقارن

We consider a tournament between two workers of different abilities who choose both human capital investment and effort. The employer can influence the workers’ behavior by determining the sequence of human capital investments, i.e. the training design. The workers can either invest simultaneously or sequentially with the favorite being the first mover or sequentially with the underdog as first mover. The results show that the outcome of the tournament crucially depends on the employer’s choice of training design and on the ability difference between the workers. If the two workers clearly differ in their abilities the employer will prefer simultaneous human capital accumulation. However, if the abilities of the two workers are rather similar the employer optimally chooses sequential human capital accumulation with the underdog being the first mover.

In a corporate tournament, workers choose efforts to compete for given prizes. Since only the winner – i.e. the worker with the highest output – receives the highest prize, tournaments play an important role in inducing incentives to workers (e.g. Lazear & Rosen, 1981; Nalebuff & Stiglitz, 1983). Often the employer cannot directly observe the workers’ efforts and sometimes only has an unverifiable performance signal for each worker. Whereas in such situations individual incentive schemes like piece rates or bonuses do not work, tournaments can create efficient incentives for the workers (Malcomson, 1984, 1986). In practice, there are many examples for corporate tournaments. Often salesmen compete for bonuses of different size (e.g. Mantrala, Krafft, & Weitz). In hierarchical firms, workers compete for job promotion; here the winner prize consists of the wage increase following promotion and the increase of power and reputation (e.g. Baker et al., 1994a and Baker et al., 1994b; Treble, van Gameren, Bridges, & Barmby, 2001). There is also relative pay for top managers who compete in the same firm or in the same industry (e.g. Gibbons & Murphy, 1990). Finally, corporate tournaments will always be created if relative performance evaluation is linked to monetary consequences for the employees. Hence, forced-ranking systems, in which supervisors have to rate their subordinates according to a given number of different grades, also belong to the class of tournament incentive schemes. Boyle (2001) reports that about 25% of the so-called Fortune 500 companies use forced-ranking systems to tie pay to performance (e.g. Intel, General Electric). An extreme variant of a forced-ranking system is given when layoffs are tied to the lowest grade. The most prominent advocate of such layoff tournaments is the former General Electric CEO Jack Welch whose incentive philosophy demands dismissal of the bottom 10% of employees each year. In this paper, we combine human capital investment with effort choice in corporate tournaments. In the standard tournament model, players only decide on effort in order to win the competition. However, in practice workers do not only choose efforts but also long-term investments in their human capital. These investments have an impact on the outcome of the tournament since a worker’s productivity typically increases in training or human capital intensity. This productivity effect can be modelled in two different ways—via the production function or via the cost function. First, a worker’s effort and his human capital investments are complements in the sense that a higher investment makes a given effort more productive. Technically, a worker’s effort variable in his production function is multiplied by a positive weight which is an increasing function of human capital investment. Second, effort and human capital investment can be complementary in the sense that a worker with more human capital may find it easier to fulfil a given task so that a worker’s marginal costs of effort are a decreasing function of human capital investment. In this paper, we have chosen the second possibility since we do not discuss individual production functions of the workers but individual performance signals which are not identical with output. We model the interaction of human capital investment and effort choice in a multiple-stage game where heterogeneous workers first choose human capital investments and then their efforts. Heterogeneity between workers refers to different abilities ex ante, i.e. we have a more able worker (the “favorite”) who competes against a less able one (the “underdog”). We differentiate between simultaneous and sequential investment decisions in order to allow the employer to choose the timing of worker training. Hence, we focus on the question how human capital accumulation should be organized from the employer’s viewpoint. The underlying presumption is that the employer regulates training and further education of his workers as part of his personnel policies. For example, he can decide on whether an individual worker has to register for the present training course or another course in the future. Alternatively, the employer may leave the workers the freedom to choose their own training courses. In that situation, he only has to fix in the labor contract that each worker has to register for exact one training course within a certain time. Our results show that the outcome of the tournament crucially depends on the employer’s choice of training scenario – simultaneous versus sequential – as well as on the decision whether, in case of sequential human capital investment, the underdog should follow the favorite or vice versa. In particular, we can show that if the ability difference between the favorite and the underdog is not very small the employer will prefer simultaneous human capital accumulation. However, if the abilities of the two workers are very similar the employer will optimally choose sequential human capital accumulation with the underdog being the first mover. We also consider the situation in which the employer leaves the workers the freedom to endogenously choose the timing of their human capital investments. In this situation, each worker prefers to gain a first-mover advantage but, as a consequence, the workers end up in a simultaneous training scenario. The dual choice of effort and human capital within the context of a tournament as an incentive device has hardly been discussed so far in the literature, although both aspects are central for real firms. The only directly related paper we are aware of is Münster (in press). Münster also assumes that investment reduces marginal costs of spending resources in the contest at the next stage of the game. However, he uses a completely different contest-success function for modeling competition. He assumes that players participate in a perfectly discriminating contest or all-pay auction. In such contests, a player wins with certainty even when he has chosen resources that are only marginally larger than the resources of the other player. This assumption seems to be very extreme for the case of a corporate contest in which the employer or the supervisor typically does not have a perfect signal of a worker’s effort choice. As a technical consequence, such all-pay auctions only have mixed-strategy equilibria. However, in the context of corporate tournaments this would mean that each worker chooses effort as a random draw from an optimally created probability distribution. Hence, not surprisingly Münster does not speak of human capital investments, effort choices and corporate contests throughout his paper, but analyzes bidding and rent dissipation in rent-seeking contests. Our paper is somewhat related to those tournament or contest papers which also consider a sequential-move structure. Particularly, Leininger (1991), Leininger and Yang (1994), Baik (1998), and Weimann, Yang, and Vogt (2000) also analyze a logit-form contest with a sequential-move structure and an exogenous winner prize. Similar to our findings, in these papers the first mover may preempt the second mover who drops out of the competition by choosing zero effort. However, our paper differs in several aspects from these papers. First, in our paper human capital investments and not effort choices are sequential. Second, in the other papers players only have one choice variable. Third, in this paper the employer can design the structure of choices (here: the structure of human capital accumulation). Our paper is also related to the one by Jost and Kräkel (2005) who consider preemption in a sequential-move rank-order tournament or probit-form contest. In that paper, the players again have only one choice variable. Finally, there are parallels to the paper by Baik and Shogren (1992) since we apply their endogenous-ordering game to our model with human capital investments. The paper is organized as follows. In the next section, the model is introduced. Section 3 deals with the case of simultaneous choices of human capital investments. Sections 4 and 5 consider the two sequential-move scenarios. Whereas the favorite is the first mover in Section 4, the underdog acts as Stackelberg leader in Section 5. Section 6 contains a discussion of three further aspects—the outcome of a game in which the workers determine the sequence of moves endogenously, modifications of the employer’s objective function and the consequences of risk aversion. Section 7 concludes.

This paper focuses on the dual choice of human capital investments and efforts by two heterogeneous workers within a corporate tournament. The employer can choose between different scenarios of human capital accumulation. Depending on the ability difference of the workers the employer will either prefer simultaneous human capital accumulation (if heterogeneity is large), or sequential investment with the less able worker being the first mover (if heterogeneity is small). If the sequence of human capital investments is not determined by the employer but endogenously chosen by the workers, each worker wants to be the first mover so that they end up in a simultaneous-move setting. As the title of the paper indicates, the results above refer to the organization of competition between workers in internal labor markets. However, our findings can also be applied to other fields like sports. There human capital investments may be interpreted as training of the athletes, and the effort choices as their chosen performance during the sport contest. Then the organizer of the contest has to decide which ordering of training is the most attractive one. Note that, in this context, “most attractive” does not necessarily mean maximization of total effort or investments during the training. Perhaps the organizer of a sport contest may have a completely different objective function (see, e.g. Szymanski, 2003). The organizer may prefer a rather even competition between the athletes in order to maximize the attention of the audience. Alternatively, the organizer may be most interested in the event that one of the athletes breaks the actual record. In this case, he would choose the design of the contest which leads to maximum effort by at least one of the players.