Dynamic Probabilistic Selling When Customers Have Boundedly Rational Expectations

2020 ◽  
Author(s):  
Tingliang Huang ◽  
Zhe Yin
Keyword(s):  
Rational Expectations ◽  
Programming Model ◽  
Simple Game ◽  
Problem Definition ◽  
Lower Probability ◽  
Purchasing Decisions ◽  
Managerial Implications ◽  
Total Profit ◽  
Game Theoretic ◽  
Over Time

Problem definition: The existing literature on probabilistic or opaque selling has largely focused on understanding why it is attractive to firms. In this paper, we intend to answer a follow-up question: How should opaque selling be managed in a firm’s operations over time? Academic/practical relevance: Answering this question is relevant yet complex, because in practice (i) the profitability of opaque selling depends on how customers respond to the firm’s product-offering strategies and (ii) the firm’s strategies have to be responsive to customers’ purchasing decisions to maximize its total profit. Methodology: We develop a simple game-theoretic framework to capture the dynamic nature of the problem in multiple periods when customers boundedly rationally expect the firm’s strategies through anecdotal reasoning. We characterize the firm’s optimal pricing and product-offering policy. Results: We find that offering the high-value product with a high probability followed by a lower probability is typically optimal over time. We finally analyze several model extensions, such as different numbers of customers, multiple anecdotes, infinitely many periods, and limited inventory, and show the robustness of our results. Managerial implications: We demonstrate the value of using a dynamic probabilistic selling policy and prove that our dynamic policy can double the firm’s profit compared with using the static policy proposed in the existing literature. In a dynamic programming model, we prove that a cycle policy oscillating between two product-offering probabilities is typically optimal in the steady state over infinitely many periods.

scholarly journals Optimal Duration of Innovation Contests

2020 ◽  
Author(s):  
C. Gizem Korpeoglu ◽  
Ersin Körpeoğlu ◽  
Sıdıka Tunç
Keyword(s):  
Problem Definition ◽  
Theory And Practice ◽  
Theoretic Model ◽  
Output Uncertainty ◽  
Support Tools ◽  
Managerial Implications ◽  
Game Theoretic ◽  
Award Scheme ◽  
Over Time

Problem definition: We study the contest duration and the award scheme of an innovation contest where an organizer elicits solutions to an innovation-related problem from a group of agents. Academic/practical relevance: Our interviews with practitioners at crowdsourcing platforms have revealed that the duration of a contest is an important operational decision. Yet, the theoretical literature has long overlooked this decision. Also, the literature fails to adequately explain why giving multiple unequal awards is so common in crowdsourcing platforms. We aim to fill these gaps between the theory and practice. We generate insights that seem consistent with both practice and empirical evidence. Methodology: We use a game-theoretic model where the organizer decides on the contest duration and the award scheme while each agent decides on her participation and determines her effort over the contest duration by considering potential changes in her productivity over time. The quality of an agent’s solution improves with her effort, but it is also subject to an output uncertainty. Results: We show that the optimal contest duration increases as the relative impact of the agent uncertainty on her output increases, and it decreases if the agent productivity increases over time. We characterize an optimal award scheme and show that giving multiple (almost always) unequal awards is optimal when the organizer’s urgency in obtaining solutions is below a certain threshold. We also show that this threshold is larger when the agent productivity increases over time. Finally, consistent with empirical findings, we show that there is a positive correlation between the optimal contest duration and the optimal total award. Managerial implications: Our results suggest that the optimal contest duration increases with the novelty or sophistication of solutions that the organizer seeks, and it decreases when the organizer can offer support tools that can increase the agent productivity over time. These insights and their drivers seem consistent with practice. Our findings also suggest that giving multiple unequal awards is advisable for an organizer who has low urgency in obtaining solutions. Finally, giving multiple awards goes hand in hand with offering support tools that increase the agent productivity over time. These results help explain why many contests on crowdsourcing platforms give multiple unequal awards.

Managing Congestion in Matching Markets

2021 ◽  
Author(s):  
Nick Arnosti ◽  
Ramesh Johari ◽  
Yash Kanoria
Keyword(s):  
Problem Definition ◽  
Theoretic Model ◽  
Matching Markets ◽  
Contact Potential ◽  
Managerial Implications ◽  
The Commons ◽  
Game Theoretic ◽  
Face Search ◽  
Uniqueness Of Equilibrium ◽  
Never Screened

Problem definition: Participants in matching markets face search and screening costs when seeking a match. We study how platform design can reduce the effort required to find a suitable partner. Practical/academic relevance: The success of matching platforms requires designs that minimize search effort and facilitate efficient market clearing. Methodology: We study a game-theoretic model in which “applicants” and “employers” pay costs to search and screen. An important feature of our model is that both sides may waste effort: Some applications are never screened, and employers screen applicants who may have already matched. We prove existence and uniqueness of equilibrium and characterize welfare for participants on both sides of the market. Results: We identify that the market operates in one of two regimes: It is either screening-limited or application-limited. In screening-limited markets, employer welfare is low, and some employers choose not to participate. This occurs when application costs are low and there are enough employers that most applicants match, implying that many screened applicants are unavailable. In application-limited markets, applicants face a “tragedy of the commons” and send many applications that are never read. The resulting inefficiency is worst when there is a shortage of employers. We show that simple interventions—such as limiting the number of applications that an individual can send, making it more costly to apply, or setting an appropriate market-wide wage—can significantly improve the welfare of agents on one or both sides of the market. Managerial implications: Our results suggest that platforms cannot focus exclusively on attracting participants and making it easy to contact potential match partners. A good user experience requires that participants not waste effort considering possibilities that are unlikely to be available. The operational interventions we study alleviate congestion by ensuring that potential match partners are likely to be available.

Expecting the Unexpected: Disaster Risks and Conflict

2020 ◽  
pp. 106591292091120
Author(s):  
Muhammet A. Bas ◽  
Elena V. McLean
Keyword(s):  
Rational Expectations ◽  
Simple Game ◽  
Interstate Conflict ◽  
Theoretic Model ◽  
Commitment Problem ◽  
Future Events ◽  
Game Theoretic ◽  
Game Theoretic Model ◽  
The Relationship ◽  
Commitment Problems

This study examines the relationship between disaster risks and interstate conflict. We argue that in disaster-prone areas actors’ rational expectations about the likelihood and magnitude of potential future disasters can make conflict more likely. The relationship emerges when future disasters are viewed as shocks that are expected to shift the relative power balance among states. If large enough, such expected shifts can generate commitment problems and cause conflict even before any disasters take place. Our approach represents a shift of focus from previous research, which investigates the effect of actual disasters and ignores rational expectations regarding future events. We use a simple game-theoretic model to highlight the commitment problem caused by disaster risks. We then discuss and apply an empirical strategy enabling us to disentangle effects of disaster proneness from effects of actual disaster events. Our results indicate that greater disaster risks are indeed associated with a higher likelihood of interstate conflict.

Supplier Centrality and Auditing Priority in Socially Responsible Supply Chains

2020 ◽  
Vol 22 (6) ◽  
pp. 1199-1214 ◽  
Author(s):  
Jiayu Chen ◽  
Anyan Qi ◽  
Milind Dawande
Keyword(s):  
Child Labor ◽  
Problem Definition ◽  
Socially Responsible ◽  
Supply Networks ◽  
Game Theoretic Analysis ◽  
Managerial Implications ◽  
Game Theoretic ◽  
Negative Publicity ◽  
The Impact ◽  
Number Of Firms

Problem definition: A key question in socially responsible supply networks is as follows: When firms audit some, but not all, of their respective suppliers, how do the degree centralities of the suppliers (i.e., the number of firms to which they supply) affect their auditing priority from the viewpoint of the firms? To investigate, we consider an assembly network consisting of two firms and three suppliers; each firm has one independent supplier that uniquely supplies to that firm and one common supplier that supplies to both. Academic/practical relevance: Most supply networks are characterized by firms that source from multiple suppliers and suppliers that serve multiple firms, thus resulting in suppliers who differ in their degree centrality. In such networks, any negative publicity from suppliers’ noncompliance with socially responsible practices—for example, employment of child labor, unsafe working conditions, and excessive pollution—can significantly damage the reputation of the buying firms. To mitigate this impact, firms preemptively audit suppliers although resource and time considerations typically restrict the number of suppliers a firm can audit. Consequently, it becomes important to understand the impact of the degree centralities of the suppliers on the priority with which firms audit them. Methodology: Game-theoretic analysis. Results: Downstream competition between the firms drives them away from auditing the supplier with higher centrality, that is, the common supplier, in equilibrium, despite the fact that auditing this supplier is better for the aggregate profit of the firms. We show that this inefficiency is corrected when the firms cooperate (via a stable coalition) to jointly audit the suppliers and share the auditing cost in a fair manner. We also identify conditions under which joint auditing improves social welfare. Managerial implications: We have two main messages: (i) individual incentives can lead firms to deprioritize the auditing of structurally important suppliers, which is inefficient; (ii) the practice of joint auditing can correct this inefficiency.

Intertemporal Content Variation with Customer Learning

2021 ◽  
Author(s):  
Fernando Bernstein ◽  
Soudipta Chakraborty ◽  
Robert Swinney
Keyword(s):  
Lower Bound ◽  
Dynamic Pricing ◽  
Business Models ◽  
Optimal Allocation ◽  
Planning Horizon ◽  
Problem Definition ◽  
Allocation Policy ◽  
Content Variation ◽  
Managerial Implications ◽  
Over Time

Problem definition: We analyze a firm that sells repeatedly to a customer population over multiple periods. Although this setting has been studied extensively in the context of dynamic pricing—selling the same product in each period at a varying price—we consider intertemporal content variation, wherein the price is the same in every period, but the firm varies the content available over time. Customers learn their utility on purchasing and decide whether to purchase again in subsequent periods. The firm faces a budget for the total amount of content available during a finite planning horizon, and allocates content to maximize revenue. Academic/practical relevance: A number of new business models, including video streaming services and curated subscription boxes, face the situation we model. Our results show how such firms can use content variation to increase their revenues. Methodology: We employ an analytical model in which customers decide to purchase in multiple successive periods and a firm determines a content allocation policy to maximize revenue. Results: Using a lower bound approximation to the problem for a horizon of general length T, we show that, although the optimal allocation policy is not, in general, constant over time, it is monotone: content value increases over time if customer heterogeneity is low and decreases otherwise. We demonstrate that the optimal policy for this lower bound problem is either optimal or very close to optimal for the general T period problem. Furthermore, for the case of T = 2 periods, we show how two critical factors—the fraction of “new” versus “repeat” customers in the population and the size of the content budget—affect the optimal allocation policy and the importance of varying content value over time. Managerial implications: We show how firms that sell at a fixed price over multiple periods can vary content value over time to increase revenues.

scholarly journals The Role of Problem Specification in Crowdsourcing Contests for Design Problems: A Theoretical and Empirical Analysis

2020 ◽  
Author(s):  
Zhaohui (Zoey) Jiang ◽  
Yan Huang ◽  
Damian R. Beil
Keyword(s):  
Problem Definition ◽  
Empirical Literature ◽  
Theoretic Model ◽  
Real World Data ◽  
Solution Quality ◽  
Design Problems ◽  
Managerial Implications ◽  
Game Theoretic ◽  
Types Of Information

Problem definition: This paper studies the role of seekers’ problem specification in crowdsourcing contests for design problems. Academic/practical relevance: Platforms hosting design contests offer detailed guidance for seekers to specify their problems when launching a contest. Yet problem specification in such crowdsourcing contests is something the theoretical and empirical literature has largely overlooked. We aim to fill this gap by offering an empirically validated model to generate insights for the provision of information at contest launch. Methodology: We develop a game-theoretic model featuring different types of information (categorized as “conceptual objectives” or “execution guidelines”) in problem specifications and assess their impact on design processes and submission qualities. Real-world data are used to empirically test hypotheses and policy recommendations generated from the model, and a quasi-natural experiment provides further empirical validation. Results: We show theoretically and verify empirically that with more conceptual objectives disclosed in the problem specification, the number of participants in a contest eventually decreases; with more execution guidelines in the problem specification, the trial effort provision by each participant increases; and the best solution quality always increases with more execution guidelines but eventually decreases with more conceptual objectives. Managerial implications: To maximize the best solution quality in crowdsourced design problems, seekers should always provide more execution guidelines and only a moderate number of conceptual objectives.

scholarly journals Motivating Supplier Social Responsibility Under Incomplete Visibility

2020 ◽  
Vol 22 (6) ◽  
pp. 1268-1286 ◽  
Author(s):  
Tim Kraft ◽  
León Valdés ◽  
Yanchong Zheng
Keyword(s):  
Supply Chain ◽  
Social Responsibility ◽  
Investment Decision ◽  
Problem Definition ◽  
Third Party ◽  
Theoretic Model ◽  
Practical Relevance ◽  
Managerial Implications ◽  
Game Theoretic ◽  
Game Theoretic Model

Problem definition: We examine how a profit-driven firm (she) can motivate better social responsibility (SR) practices by a supplier (he) when these practices cannot be perfectly observed by the firm. We focus on the firm’s investment in the supplier’s SR capabilities. To capture the influence of consumer demands, we incorporate the potential for SR information to be disclosed by the firm or revealed by a third party. Academic/practical relevance: Most firms have limited visibility into the SR practices of their suppliers. However, there is little research on how a firm under incomplete visibility should (i) invest to improve a supplier’s SR practices and (ii) disclose SR information to consumers. We address this gap. Methodology: We develop a game-theoretic model with asymmetric information to study a supply chain with one supplier and one firm. The firm makes her investment decision given incomplete information about the supplier’s current SR practices. We analyze and compare two settings: the firm does not disclose versus she discloses SR information to the consumers. Results: The firm should invest a high (low) amount in the supplier’s capabilities if the information she observes suggests the supplier’s current SR practices are poor (good). She should always be more aggressive with her investment when disclosing (versus not disclosing). This more aggressive strategy ensures better supplier SR practices under disclosure. When choosing between disclosing and not disclosing, the firm most likely prefers not to disclose when the supplier’s current SR practices seem to be average. Managerial implications: (i) Greater visibility helps the firm to better tailor her investment to the level of support needed. (ii) Better visibility also makes the firm more “truthful” in her disclosure, whereas increased third-party scrutiny makes her more “cautious.” (iii) Mandating disclosure is most beneficial for SR when the suppliers’ current practices seem to be average.

Intertemporal Segmentation via Flexible-Duration Group Buying

2020 ◽  
Author(s):  
Ming Hu ◽  
Jingchen Liu ◽  
Xin Zhai
Keyword(s):  
Rational Expectations ◽  
Customer Segmentation ◽  
Product Line ◽  
Problem Definition ◽  
Batch Size ◽  
Group Buying ◽  
Economic Production ◽  
Managerial Implications ◽  
Expected Waiting Time ◽  
Line Design

Problem definition: We study a special form of group buying: the group buying succeeds only if the number of sign-ups reaches a preset threshold, with no duration constraint. Customers with heterogeneous valuations arrive sequentially and decide between signing up for the group buying or purchasing a regular product. To decide whether to join the group buying, customers need to estimate their expected waiting time, which varies depending on the cumulative sign-ups by the time of their arrival. The firm decides on the prices for the group-buying product and regular product, with the product quality levels and group-buying size exogenously determined. Academic/practical relevance: This type of group buying is often adopted for a special edition of the product and offered alongside a constantly available regular product. Methodology: We study the product line design with the group-buying sign-up behavior of customers characterized by the rational expectations equilibrium in a random pledging process. Results: We show that group buying with flexible duration can result in intertemporal customer segmentation, as different segments might be admitted at different times in the dynamic sign-up process. Such intertemporal segmentation is a natural discrimination scheme and has nontrivial implications. First, the efficiency loss due to waiting for enough sign-ups may decrease when a larger batch size is required for economic production. Second, as valuation heterogeneity in the market increases, the firm may not always benefit from offering group buying along with the regular product. Third, group buying can achieve a win-win-win situation for both high-end and low-end customers as well as the firm. Managerial implications: In addition to demonstrating the profitability of flexible-duration group buying, we show that the firm can strengthen its profitability by contingently setting prices or concealing sign-up information in group buying. We also confirm the robustness of our main insights by considering customers’ heterogeneous patience levels and horizontally differentiated products, among other factors.

scholarly journals An Empirical Study of Holiday Season Discounts: A Comparison Between Third-Party Marketplace Sellers and Fulfilled by Walmart Sellers

SAGE Open ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 215824402110241
Author(s):  
Ya-Ling Chiu ◽  
Yuan-Teng Hsu ◽  
Xiaoyu Mao ◽  
Jying-Nan Wang
Keyword(s):  
Empirical Study ◽  
Third Party ◽  
Purchasing Decisions ◽  
Product Categories ◽  
Price Discounts ◽  
Online Retailers ◽  
Holiday Season ◽  
Over Time

When online retailers allow third-party sellers to place certain products on their platforms, these sellers become not only collaborators but also competitors. The purpose of this study is to compare the differences in price discounts between Third-Party Marketplace (3PM) sellers and Fulfilled by Walmart (FBW) sellers on Walmart.com over time. The results, based on data collected in the form of the daily prices of 54,162 products offered by Walmart during the holiday season, show that the average discount for 3PM sellers is significantly lower than that for FBW sellers. In addition, across product categories, FBW sellers had significantly higher average discounts than 3PM sellers in the electronics, housewares, and toys categories. Furthermore, the level of discount began to increase in early November and peaked around Christmas. Our findings may help retailers manage their dealings with these third-party sellers while also helping consumers to optimize their purchasing decisions.

scholarly journals Evolving user needs and late-mover advantage

2016 ◽  
Vol 15 (1) ◽  
pp. 67-90 ◽  
Author(s):  
Adrien Querbes ◽  
Koen Frenken
Keyword(s):  
User Needs ◽  
Nk Model ◽  
Trade Offs ◽  
Managerial Implications ◽  
First Mover ◽  
Over Time ◽  
Late Movers

We propose a generalized NK-model of late-mover advantage where late-mover firms leapfrog first-mover firms as user needs evolve over time. First movers face severe trade-offs between the provision of functionalities in which their products already excel and the additional functionalities requested by users later on. Late movers, by contrast, start searching when more functionalities are already known and typically come up with superior product designs. We also show that late-mover advantage is more probable for more complex technologies. Managerial implications follow.

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