The Role of Reputation in Sequel Production

Abstract

This paper develops a simple model of sequel production for experience goods, showing how reputation shapes a producer’s incentives. Producers differ in productivity, which determines how much effort they invest. A sequel is made only if the previous installment exceeds a quality threshold, capturing the idea that consumers base future consumption on past success. Although high-productivity producers create higher-quality originals and sequels, the conditioning on successful originals still makes sequels, on average, worse than their predecessors. This aligns with evidence of sequel underperformance in media markets.

1. Introduction

This paper aims to develop a simple model of the role of reputation in producing sequels. In particular, we show why there may be incentives for a producer to create a sequel of lower quality. Our motivation stems from the evidence that many movie sequels tend to be worse than their original counterparts. Helmer (2011) compares the scores of selected original and sequel movies (taken from the review aggregator Rotten Tomatoes) against each other. He finds that there are only a few examples where the sequel outperforms the original, such as Star Trek II or The Dark Knight, which are usually considered as the best movies in the respective series. But the vast majority of sequels perform worse than the respective originals. In this paper, we provide a model to explain this fact.

Nelson (1970) introduced the concept of experience goods, which are goods for which the consumer is not fully informed about quality before purchase or consumption. Because it is unclear how much utility the consumer will derive before making the decision to acquire or consume the good, the consumer only learns this ex post.

In the literature, goods such as books and movies are often modeled as experience goods. In theory, consumer “tastes” can differ, leading each consumer to derive different utility from the same good. Since consumers do not know ex ante how much utility they will gain, they only discover it ex post. As a result, reputation may influence the consumption of a sequel, since it provides consumers with information about the expected utility of the product. Among other factors, this reputation can be derived from the quality of earlier installments that the consumer has already experienced.

This paper develops a simple theoretical model to explain why sequels of experience goods often end up with lower quality than their predecessors despite being produced by the same firm. We consider a risk-neutral producer whose productivity can be either high or low and is known only to themselves. The producer’s effort and an exogenous shock jointly determine a product’s realized quality. Crucially, a sequel is only viable if the quality of the original surpasses a certain threshold, creating a reputation for the producer. It increases buyers’ willingness to consume the sequel. Since the producer’s type is not known to the consumers and the qualities of products are the only variables observable by consumers, the reputation of a producer in our model is related only to the quality of their past products.

Our analysis shows that high-productivity producers exert higher effort and thus deliver higher expected quality for both original and sequel productions (Proposition 1). The higher effort of producers of a higher type results in a higher expected quality of their goods (Proposition 2). Besides that, they produce sequels more often (Proposition 3). However, even these producers cannot fully escape the sequel-quality drop, because only sufficiently successful originals move on to a sequel. This selection effect implies that once a producer decides to make a sequel, the conditioning on the original’s successful outcome renders the expected sequel quality lower than the expected quality of the original (Proposition 4). These findings align with observed tendencies in the movie industry, offering a formal explanation for why many sequels underperform relative to their originals despite a clear reputation-based incentive to sustain high quality.

Our motivation for adopting a two-type framework is to keep the model analytically tractable and to clearly illustrate the core mechanisms by which reputation affects sequel production incentives. The main qualitative insights—such as the reputation threshold inducing higher effort from high-productivity producers, the selection effect behind sequel underperformance, and the persistence of quality gaps—are robust to richer settings. In particular, the comparative statics and selection effects would extend to environments with a continuous productivity distribution.

The paper is structured as follows. In the next section, we provide a review of the related literature. In Section 3, we formulate the model. Section 4 presents our analysis and the main results. Section 5 concludes the paper.

2. Related Literature

Building on Nelson’s insights, Shapiro (1983) formalized how reputational premiums emerge. Firms that continually provide higher quality can command price premiums because consumers trust their reputation. This reputational signaling dynamic underpins incentives to maintain quality across multiple “installments” or product lines.

Extending these foundational ideas, Mailath and Samuelson (2001) examined how reputation evolves in repeated interactions. They showed that maintaining a good reputation can yield long-term benefits, but incentives to deviate—and produce lower quality at times—may also exist if near-term gains outweigh future losses. This tension resonates with the puzzle of sequel quality: a producer might see short-run profit benefits from lowering production costs, even if doing so risks harming the franchise’s long-term reputation.

Tadelis (2002) studied a market for reputations, providing further insight into how brand names (or “reputation capital”) can be traded or inherited, potentially encouraging or discouraging effort. While his analysis is more general, it clarifies how reputational considerations might vary with different producer types (e.g., high- vs. low-productivity firms) and over time.

There is also literature on how the experience of one consumer can influence others. For instance, Reinstein and Snyder (2005) examine the role of expert reviews on the consumption of experience goods in the context of movie releases. They find some evidence that positive reviews correlate with higher earnings, although the effect’s significance varies with the scope of release and movie genre. Gemser et al. (2007) build on these findings, comparing the impact of expert reviews on small-release art-house movies and wide-release mainstream movies. While reviews significantly affect revenues for smaller releases, they do not have the same measurable impact on wider-release mainstream movies, supporting the findings by Reinstein and Snyder (2005). Moretti (2011) further shows that social learning from non-professional opinions also affects movie revenues.

Relatively little literature addresses the impact of an original on subsequent sequel consumption. For example, Karniouchina (2011) provides evidence that being a sequel can positively affect a movie’s revenues. Similarly, B. I. Situmeang et al. (2014) show that originals can influence sequel consumption in video games, with both the quality of past editions and the variance in reviews playing a role.

3. Model

There is a risk-neutral producer who may provide a good at period $t\ge 0$ with quality $q_t$ by choosing effort level $x_t$. The good produced at $t=0$ is referred to as original and the good produced at any $t>0$ as sequel. Producer is characterized by type ${\theta }^i$, where i indicates whether they have high productivity ${\theta }^h$ or low productivity ${\theta }^l$, such that ${\theta }^i\in \{{\theta }^l;{\theta }^h\}$ and ${\theta }^l<{\theta }^h$. Only the producer knows its own productivity type. We further assume that some error term ${ϵ}_t^i$ affects the good’s quality in addition to the producer’s effort. This error term is uniformly distributed on the interval $[-a,a]$, ${ϵ}_t^i\sim U[-a,a]$, and is independent and identically distributed over time. The quality of the good produced in period t is $q_t={\theta }^i{x}_t+{ϵ}_t^i.$ As a result of exerting effort $x_t$, the producer incurs a cost given by the quadratic cost function ${\displaystyle \frac{c{x}_t^2}{2}}.$

Consumers do not know the quality ex ante. They cannot observe the producer’s type or effort. They only observe the realized quality $q_t$ after consumption. We assume that the consumers will be willing to consume the sequel only if its predecessor is of sufficiently high quality. Namely, a sequel at any $t>0$ can be produced only if the quality $q_{t-1}$ in period $t-1$ exceeds a constant over time threshold $\overline{q}$. If $q_{t-1}\le \overline{q}$, a sequel at period t cannot be produced. We assume that the threshold $\overline{q}$ is substantially low to ensure a positive optimal level of effort. In particular, we assume:

$$\overline{q}<{\displaystyle \frac{2{{\theta }^l}^2}{c}}.$$

(1)

We also assume that the error term ${ϵ}^i$ is sufficiently noisy to ensure that the solution is well behaved, i.e.,

$$a>{\displaystyle \frac{2{{\theta }^l}^2}{c}}-\overline{q}.$$

(2)

We assume that the earnings from selling the good are proportional to its quality $q_t$. Thus, producer’s profit ${\mathsf{\Pi }}_t$ in period $t>0$ is the following:

$${\mathsf{\Pi }}_t^i=q_t-{\displaystyle \frac{c{x}_t^2}{2}}.$$

The producer discounts the future value of $t+1$ by a discount factor $\beta$, $\beta \in [0,1]$. Hence, the effort chosen in period t affects potential revenue in period $t+1$.

4. Analysis

First, we obtain the following value for the producer in period t:

$$\begin{array}{cc}\hfill V_t& =\underset{x_t\ge 0}{max}\left\{\mathbb{E}{\mathsf{\Pi }}_t+\beta V_{t+1}Pr({\theta }^i{x}_t+{ϵ}_t^i>\overline{q})\right\}.\hfill \end{array}$$

The term $Pr({\theta }^i{x}_t+{ϵ}_t>\overline{q})$ represents the probability that a sequel can be produced. If this event does not occur, its contribution to the expected value is zero. Thus, we obtain the following Bellman equation:

$$\begin{array}{c}\hfill V_t=\underset{x_t\ge 0}{max}\left\{{\theta }^i{x}_t-{\displaystyle \frac{c{x}_t^2}{2}}+\beta V_{t+1}\left(1-{\displaystyle \frac{\overline{q}-{\theta }^i{x}_t+a}{2a}}\right)\right\}.\end{array}$$

(3)

We solve for the optimum effort level by computing the first-order condition:

$$\begin{array}{cc}\hfill {\displaystyle \frac{d{V}_t}{d{x}_t}}=& {\theta }^i-c{x}_t+{\displaystyle \frac{\beta {\theta }^i{V}_{t+1}}{2a}}=0\hfill \\ \hfill \Rightarrow x_t=& {\displaystyle \frac{{\theta }^i}{c}}+{\displaystyle \frac{\beta {\theta }^i{V}_{t+1}}{2ac}}.\hfill \end{array}$$

(4)

The second-order condition is fulfilled because

$${\displaystyle \frac{d^2{V}_t}{d{x}_t^2}}=-c<0,$$

which indicates that condition (4) indeed determines the optimal effort.

Notice that the problem is stationary in time. Hence, for every type ${\theta }^i$, the value and the optimal effort are constant over time. Denote $V^i$ and $x^i$ as the value and the optimal level of effort for the producer of type ${\theta }^i$. Thus,

$$\begin{array}{c}\hfill x^i={\displaystyle \frac{{\theta }^i}{c}}+{\displaystyle \frac{\beta {\theta }^i{V}^i}{2ac}}.\end{array}$$

(5)

Plugging it back into Bellman Equation (3), we obtain

$$\begin{array}{cc}\hfill V^i& ={\theta }^i{x}^i-{\displaystyle \frac{c{\left(x^i\right)}^2}{2}}+\beta V^i\left(1-{\displaystyle \frac{\overline{q}-{\theta }^i{x}^i+a}{2a}}\right).\hfill \end{array}$$

(6)

$$\begin{array}{cc}\hfill & \iff V^i={\displaystyle \frac{2a{\theta }^i{x}^i-ac{\left(x^i\right)}^2}{2a-\beta (a-\overline{q}+{\theta }^i{x}^i)}}.\hfill \end{array}$$

(7)

Now, we are ready to provide the main results of our analysis. First, we show that the producers of higher type will supply a higher level of effort.

Proposition 1.

The optimal level of effort of the producer of a higher type is higher than the optimal level of effort of the producer of a lower type, i.e.,

$$x^h>x^l.$$

Proof. 

We show this by contradiction. First, assume that $x^l\ge x^h$. Since ${\theta }^l<{\theta }^h$, Equation (5) implies that to have $x^l\ge x^h$ it must be that $V^l>V^h$. Define function

$$\mathsf{\Phi }(x,\theta )={\displaystyle \frac{2a\theta x-ac{\left(x\right)}^2}{2a-\beta (a-\overline{q}+\theta x)}}.$$

Notice that for any $i\in \{h,l\}$

$$\mathsf{\Phi }(x^i,{\theta }^i)=V^i.$$

Since $V^l>V^h$, it follows that

$$\mathsf{\Phi }(x^l,{\theta }^l)>\mathsf{\Phi }(x^h,{\theta }^h).$$

By definition of $V^h$, it follows that

$$\mathsf{\Phi }(x^h,{\theta }^h)\ge \mathsf{\Phi }(x,{\theta }^h)$$

for any $x\in {\mathbb{R}}_{+}$. This implies that

$$\mathsf{\Phi }(x^h,{\theta }^h)\ge \mathsf{\Phi }(x^l,{\theta }^h).$$

Next, notice that function $\mathsf{\Phi }(x,\theta )$ is increasing in $\theta$ because its numerator is increasing, the denominator is decreasing in $\theta$, and the assumptions (1) and (2) guarantee that both the numerator and denominator of $\mathsf{\Phi }$ are positive for the respective parameter ranges. Hence,

$$\mathsf{\Phi }(x^l,{\theta }^h)\ge \mathsf{\Phi }(x^l,{\theta }^l).$$

Finally, combining the last two inequalities, we obtain

$$V^h=\mathsf{\Phi }(x^h,{\theta }^h)\ge \mathsf{\Phi }(x^l,{\theta }^h)\ge \mathsf{\Phi }(x^l,{\theta }^l)=V^l.$$

This is a contradiction to $V^l>V^h$. □

Next, we demonstrate that the expected quality of originals and sequels is higher for the producer with high type.

Proposition 2.

The expected quality of good of originals and all sequels is higher for the producer of a higher type than for the producer with a lower type, i.e., for any $t\ge 0$

$$\mathbb{E}{q}_t^h>\mathbb{E}{q}_t^l.$$

Proof. 

We show this by computing the expected value and comparing the results for the optimum effort levels.

$$\begin{array}{cc}\hfill \mathbb{E}{q}_t^i& ={\theta }^i{x}^i+\mathbb{E}{ϵ}_t^i={\theta }^i{x}^i.\hfill \end{array}$$

Since ${\theta }^h>{\theta }^l$ and from Proposition 1 we have $x^h>x^l$, it follows that

$${\theta }^h{x}^h>{\theta }^l{x}^l.$$

□

Besides that, we can demonstrate that the producer of the high type is more likely to produce a sequel than the producer of the low type.

Proposition 3.

The producer of the high type produces sequels more often than the producer of the low type.

Proof. 

The probability of producing a sequel for each good produced at t is equal to $Pr({ϵ}_t^i>\overline{q}-{\theta }^i{x}_t^i)$. From Proposition 2, we know that

$${\theta }^h{x}^h>{\theta }^l{x}^l.$$

Hence,

$$Pr({ϵ}_t^h>\overline{q}-{\theta }^h{x}^h)>Pr({ϵ}_t^l>\overline{q}-{\theta }^l{x}^l).$$

□

Our last result concerns the quality of each sequel compared to its predecessor.

Proposition 4.

The expected quality of each good that receives a sequel is higher than the expected quality of that sequel.

Proof. 

To prove this result, we just need to note that if some good produced at t receives a sequel, the expected quality of this good is $\mathbb{E}\left[q_t^i\right|q_t^i>\overline{q}]$. This conditional expectation is greater than the unconditional expectation, i.e.,

$$\mathbb{E}\left(q_t^i\right|q_t^i>\overline{q})>\mathbb{E}{q}_t^i.$$

Finally, from Proposition 2, it follows that

$$\mathbb{E}{q}_t^i={\theta }^i{x}^i=\mathbb{E}{q}_{t+1}^i.$$

Thus, we obtain that

$$\mathbb{E}\left(q_t^i\right|q_t^i>\overline{q})>\mathbb{E}{q}_{t+1}^i.$$

□

This result is consistent with the anecdotal evidence presented in the introduction. Intuitively, sequels are usually produced for goods of sufficiently high quality. Thus, even if the producer applies the same level of effort to producing a sequel, the fact that the decision was made to produce it means that the expected quality of the sequel will be lower than the expected quality of the original.

5. Conclusions

In this paper, we designed a model in which reputation in the form of the previous period’s quality influences the production of a sequel. Our model predicts that producers of higher types will apply higher effort, produce better originals and sequels, and produce sequels more often than the producers of lower types. However, for both types of producers, sequels will have a lower expected quality than their predecessors.

Reputation in our model is represented by the equality of the product developed in the previous period. The unobservability of the producer’s type to consumers is important because in the model with complete information, the consumers should make their consumption decisions based on the observable type of the producer and not on the quality of the good in the previous problem. Given the type of the producer, they would be also able to solve the optimization problem of the producer and compute the expected quality of the product. The analysis will be less interesting in this case, because any dynamics would disappear.