PurposeIn this study, a dynamic contracting model is developed between a venture capitalist (VC) and an entrepreneur (EN) to explore the influence of asymmetric beliefs regarding output-relevant parameters, agency conflicts and complementarity on the VC's posterior beliefs through the EN's unobservable effort choices to influence the optimal dynamic contract.Design/methodology/approachThe authors construct the contracting model by incorporating the VC's effort, which is ignored in most studies. Using backward induction and a discrete-time approximation approach, the authors solve the continuous-time contract design problem, which evolves into a nonlinear ordinary differential equation (ODE).FindingsThe optimal equity share that the VC provides to the EN decreases over time. In accordance with the empirical evidence, the EN's optimistic beliefs regarding the project's profitability positively affect its equity share. However, the interactions between the optimal equity share, project risk and both partners' degrees of risk aversion are not monotonic. Moreover, the authors find that the optimal equity share increases with the degree of complementarity, which indicates that the EN is willing to cooperate with the VC. This study’s results also show that the optimal equity shares at each time are interdependent if the VC is risk-averse and independent if the VC is risk-neutral.Research limitations/implicationsIn conclusion, the authors highlight two potential directions for future research. First, the authors only considered a single VC, whereas in practice, a risk project may be carried out by multiple VCs, and it is interesting to discuss how the degree of complementarity affects the number of VCs that ENs contract. Second, the authors may introduce jumps and consider more general multivariate stochastic volatility models for output dynamics and analyze the characteristics of the optimal contracts. Third, further research can deal with other forms of discretionary output functions concerning complementarity, such as Cobb–Douglas and constant elasticity of substitution (See Varian, 1992).Social implicationsThe results of this study have several implications. First, it offers a novel approach to designing dynamic contracts that are specific and easy to operate. To improve the complicated venture investment situation and abate conflict between contractual parties, this study plays a good reference role. Second, the synergy effect proposed in this study provides a theoretical explanation for the executive compensation puzzle in economics, in which managers are often “rewarded for luck” (Bertrand and Mullainathan, 2001; Wu et al., 2018). This result indicates a realistic perspective on financing and establishing cooperative relationships, which enhances the efficiency of venture investment. Third, from an empirical standpoint, one can apply this framework to study research and development (R&D) problems.Originality/valueFirst, the authors introduce asymmetric beliefs and Bayesian learning to study the dynamic contract design problem and discuss their effects on equity share. Second, the authors incorporate the VC's effort into the contracting problem, and analyze the synergistic effect of effort complementarity on the optimal dynamic contract.
PurposeThis study aims to investigate the effects and implications of overconfidence in a competitive game involving multiple newsvendors. This study explores how overconfidence influences system coordination, optimal stocking strategies and competition among newsvendors in the context of the well-known newsvendor stocking problem.Design/methodology/approachThe study applies robust optimization theory and the absolute regret minimization criterion to analyze the competitive game of overconfident newsvendors. This study considers the asymmetric information held by newsvendors regarding market demand and obtains a closed-form solution for the competing game. The effects of overconfidence on system coordination and optimal stocking strategies are examined.FindingsThe results of the study indicate that overconfidence can act as a positive force in reducing the effects of overstocking caused by competition and asymmetric information among newsvendors. The analysis reveals that there exists an optimal level of overconfidence that coordinates the ordering system of multiple overconfident newsvendors, leading to first-best outcomes under certain conditions. Additionally, numerical examples confirm the obtained results. Furthermore, considering newsvendors' expected profit, the study finds that a higher degree of overconfidence does not necessarily result in lower actual expected profit.Research limitations/implicationsDespite the significant contributions of this study to theoretical and managerial insights, this study does have certain limitations. First, in the establishment of the belief demand function, the substitution ratio, which quantifies the transfer, is assumed to be an exogenous variable. However, in reality, this is often influenced by factors such as the price of goods and the distance between stores. Therefore, one direction worth studying in the future is to explore the uncertainty associated with the demand substitution ratio and integrate that as an endogenous variable into the optimization model. Second, this study does not address the type of product and solely focuses on quantitatively analyzing the effect of salvage value on the optimal stocking strategy. Future studies can explore the effect of degree of perishability and selling period of the product on the stocking. Third, the focus of uncertainty in this study revolves around market demand, and the implications of this uncertainty are significant. A recent study (Rahbari et al., 2023) addressed an innovative robust optimization problem related to canned foods during pandemic crises. The recent study's findings highlighted the effectiveness of expanding canned food exports to neighboring countries with economic justification as the best strategy for companies amidst the disruptions caused by the coronavirus disease 2019 (COVID-19) pandemic. Incorporating the issue of disruptions into the authors' research would be interesting and challenging.Practical implicationsFrom a managerial perspective, the authors' study provides a research paradigm for game-theoretic inventory problems in scenarios where the market demand distribution is unknown. While most inventory problems are analyzed and solved based on expectation-based optimization criteria, which rely on an accurate distribution of market demand, obtaining this information in practice can often be challenging or expensive for decision-makers. Consequently, a discrepancy arises between real-world observations and theoretical identifications. This study aimed to complement previous research and address the inconsistency between observations and theoretical identification.Social implicationsThe authors' research contributes to the existing understanding of overconfidence and assists individuals in making appropriate stocking strategies based on the individuals' level of overconfidence. Diverging significantly from the traditional view of overconfidence as a negative bias, the authors' results show the view's potential positive impact within a competitive environment, resulting in greater actual expected profits for newsvendors.Originality/valueThis study contributes to the existing literature by examining the effects of overconfidence in a competitive game of newsvendors. This study extends the analysis of the well-known newsvendor stocking problem by incorporating overconfidence and considering the implications for system coordination and competition. The application of robust optimization theory and the absolute regret minimization criterion provides a novel approach to studying overconfidence in this context.
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