A reference-based theory of motivation and effort allocation

Abstract

Motivation is key for performance in domains such as work, sport, and learning. Research has established that motivation and the willingness to invest effort generally increase as a function of reward. However, this view struggles to explain some empirical observations-for example, in the domain of sport, athletes sometimes appear to lose motivation when playing against weak opponents-this despite objective rewards being high. This and similar evidence highlight the role of subjective value in motivation and effort allocation. To capture this, here, we advance a novel theory and computational model where motivation and effort allocation arise from reference-based evaluation processes. Our proposal argues that motivation (and the ensuing willingness to exert effort) stems from subjective value, which in turns depends on one's standards about performance and on the confidence about these standards. In a series of simulations, we show that the model explains puzzling motivational dynamics and associated feelings. Crucially, the model identifies realistic standards (i.e., those matching one's own actual ability) as those more beneficial for motivation and performance. On this basis, the model establishes a normative solution to the problem of optimal allocation of effort, analogous to the optimal allocation of neural and computational resources as in efficient coding.

Keywords: Effort; Motivation; Reference-based model; Subjective value.

Fig. 1

Role of the standard parameter μ. This shows the motivational dynamics of four agents with different standard (15, 10, 5, 1, respectively) but equal uncertainty parameter (i.e., σ = 2). Each column describes a different agent and includes three panels. The top panel shows the subjective value (SV) associated with the outcome expected by exerting effort (red solid line) and expected without effort (green dashed line). The middle panel shows the motivation. The bottom panel shows the motivational valence. Data are shown for different positions (on the x-axis). (Colour figure online)

Fig. 2

Role of contextual factors. Each column describes an agent under different contextual situations (see main text for explanation). All agents have standard μ = 10 and uncertainty parameter σ = 2. The top panel shows the subjective value (SV) associated with the outcome expected by exerting effort (red solid line) and expected without effort (green dashed line). The middle panel shows the motivation. The bottom panel shows the motivational valence. Data are shown for different positions (on the x-axis). (Colour figure online)

Fig. 3

Role of the uncertainty parameter σ. This shows the motivational dynamics of four agents with equal standard (μ = 10) but different uncertainty parameter (1, 2, 4, 8, respectively). Each column describes a different agent and includes three panels. The top panel shows the subjective value (SV) associated with the outcome expected by exerting effort (red solid line) and expected without effort (green dashed line). The middle panel shows the motivation. The bottom panel shows the motivational valence. Data are shown for different positions (on the x-axis). (Colour figure online)

Fig. 4

Relationship between parameters and performance. This simulation shows the proportion of effort choices across trials during a race. For each trial, the agent’s position is randomly selected from a normal distribution having the 10th position as mean and three positions as SD. Four conditions are simulated, each shown on a different panel (10,000 trials are simulated for each panel) and characterized by a different range (i.e., the difference between the position expected with effort and the position expected without effort): 1.5, 2, 2.5 or 3, respectively. An effort choice occurs when motivation exceeds a threshold of 0.15. (Colour figure online)

Fig. 5

How the standard is learnt from experience. This shows the motivational dynamics of four agents with different learning rate (0, 0.3, 0,7, 1, respectively). All agents occupy the 15th position during the initial four time points, reaching the fifth position from Time Point 5 to 13, and moving back to the 15th position from Time 14 to 20 (agents start with the same standard μ₁ = 15). Each column describes a different agent and includes three panels. The top panel shows the subjective value (SV) associated with the outcome expected by exerting effort (red solid line) and expected without effort (green dashed line). The middle panel shows the motivation. The bottom panel shows the motivational valence. Data are shown for different time points (on the x-axis). (Colour figure online)