Abstract
We study the interactions between supervisors and workers via evolutionary game-theory. We develop a simple model where workers select their effort level and decide whether to cooperate or defect. Supervisors, in turn, have two different functions: first, they act as coordinators and convert team-effort into output; and second, they act as monitors and induce workers to cooperate. In doing both, they may either behave as “motivators” through charisma and persuasion (authoritative style), or as “punishers” through authority and control (authoritarian style). In our framework, motivators encourage independence-seeking and reward cooperators through inspiration and engagement, while punishers take all relevant decisions and reprehend defectors when these are caught shirking. The message is that authoritative leadership improves both productivity and worker well-being. For this to happen, supervisors must improve their charisma, while workers must develop their decisional skills. When either of these conditions is unmet, a variety of welfare-depressing situations may emerge.
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Notes
Of course, this is a simple abstraction to capture the collective nature of production and analyze some of the team-problems that it entails. In an evolutionary game-theoretic framework like ours, the main implication of considering larger teams relates to the frequency with which players experience a given payoff, and thus, to the numerosity and topological properties of the stationary points of the dynamics. The main messages of the of the model, however, carry over for any of these quantitative variations. For a model displaying a similar structure of interactions, see Antoci et al. (2017).
In reality, the organizational spectrum consists of a continuum of arrangements combining delegation and control in many different ways. The primary scope of this paper, however, is to compare the effects of conflictual and cooperative relations between supervisors and workers. Hence, we decided to ignore the possible complementarities between workplace autonomy and control. Indeed, we see the forms combining delegation and tight monitoring as a variation of our P-mode, as they are fundamentally based on a bitter relation between the different agents in the organizations
Allowing for situations where workers “take better decisions” than their likely more experienced supervisors may sound counterintuitive. On second thoughts however, the reasons for this to happen are multiple. First, the workload of business leaders is often overwhelming, up to the point where they get to concede but cursory attention to each of their multiple tasks. Workers, on the other hand, are normally in charge of fewer duties and should be able to pay greater attention to their daily decisions and routines. In his study on managerial work, Mintzberg (1971) highlights how frenetic the typical day of a manager can be, thus providing support to the idea that delegating decision-making may improve organizational performance. Second, business leaders may have “the vision” and the skills to coordinate it throughout, but may lack the idiosyncratic knowledge to decide on task-specific matters. Third, as workers are closer to production, autonomous decision-making reduces costly communication.
More realistically, the supervisory compensation may consist in a uniform fixed wage plus a premium which varies with team performance. From a game-theoretic viewpoint, however, we are interested in analyzing the payoff difference of a strategy with respect to its alternative strategy. Hence, we can focus on the variable premium only.
In this specification, it is implicitly assumed that punishers cannot mistake genuine productive workers for shirkers. Our results are robust to alternative specifications of the monitoring process. Alternative versions of the model are available from the authors upon request.
Support to this hypothesis comes from the field of industrial psychology. In particular, Alge (2001) analyzes the impact of computer surveillance on employees’ morale and find that increasing control in organizations improves the sense of procedural justice among co-workers.
The supervisors’ charisma may also affect worker wellbeing though another channel, that is closely related to the mode of coordination described in section 2.2. As a matter of fact, the motivators’ choice of delegating decisions to their low-level workers may either raise the cost of effort – e.g., by generating anxiety and fear of failure – or decrease it – e.g., by improving intrinsic motivation and self-fulfilment – see Dughera (2020) and the references therein. Which of these two effects outweighs the other, in turn, may depend on the supervisors’ skills, as better supervisors may help workers to manage their anxiety in decision-making. We are grateful to an anonymous referee for point out this point.
Beware that there two roots of equation (4). Yet, one of them is always >1, as the opposite would require p > 1.
Meaning that all trajectories starting from an initial pair \( \left({x}_0,{y}_0\right)=\left(1,\hat{y}\right) \), \( \left({x}_0,{y}_0\right)=\left(0,\hat{y}\right) \), \( \left({x}_0,{y}_0\right)=\left(\hat{x},0\right) \) and \( \left({x}_0,{y}_0\right)=\left(\hat{x},1\right) \) will lie on the side with x = 1, x = 0, y = 0 and y = 1 respectively, where \( 0\le \hat{x}\le 1 \) and \( 0\le \hat{y}\le 1 \).
All proofs are given in the Appendix, which is available from the author upon request.
In a game where players are perfectly rational, \( \left(\overline{x},\overline{y}\right) \) would correspond to a mixed-strategy Nash-equilibrium. When players have perfect foresight, they optimally play strategies C and M with equilibrium frequencies \( \overline{x} \) and \( \overline{y} \) respectively.
Indeed, when E < W < E/p, the Discipline equilibrium is repulsive but more efficient than the Conflict equilibrium. Similarly, when E − W < B < E, the Cooperation equilibrium is repulsive but more efficient than the Conflict equilibrium. In addition, when \( E-W\left(1+p\hat{x}-\hat{x}\right)<B<E \), the Cooperation equilibrium is repulsive but more efficient than the Quasi-Discipline equilibrium. Finally, the Cooperation equilibrium it is always more efficient than the Discipline equilibrium, regardless of its stability properties.
Indeed, when \( {R}^P\hat{x}+W\left[1-\hat{x}-\left(1-p\right)\left(\hat{x}-{\hat{x}}^2\right)\right]<{R}^C<{R}^P \), the Cooperation equilibrium is repulsive but more efficient for workers than the Quasi-Discipline equilibrium. In addition, the Cooperation equilibrium it is always more efficient than the Conflict equilibrium, regardless of its stability properties.
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Dughera, S. The evolution of workplace control leadership, obedience and organizational performance. J Evol Econ 32, 399–421 (2022). https://doi.org/10.1007/s00191-020-00720-5
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DOI: https://doi.org/10.1007/s00191-020-00720-5