Multiscale decision-making: Bridging organizational scales in systems with distributed decision-makers

Decision-making in organizations is complex due to interdependencies among decision-makers (agents) within and across organizational hierarchies. We propose a multiscale decision-making model that captures and analyzes multiscale agent interactions in large, distributed decision-making systems. In general, multiscale systems exhibit phenomena that are coupled through various temporal, spatial and organizational scales. Our model focuses on the organizational scale and provides analytic, closed-form solutions which enable agents across all organizational scales to select a best course of action. By setting an optimal intensity level for agent interactions, an organizational designer can align the choices of self-interested agents with the overall goals of the organization. Moreover, our results demonstrate when local and aggregate information exchange is sufficient for system-wide optimal decision-making. We motivate the model and illustrate its capabilities using a manufacturing enterprise example.     

Optimal incentive contracts under relative income concerns

We are studying in this article an interplay between workers in organizations under the assumption that workers exhibit behavioral biases: envy, jealousy, or admiration toward the other coworkers’ compensation. We assume workers care about their relative position, and we study the impact of this assumption on their efforts and on their optimal incentive contracts. We explicitly solve for the optimal incentive contract of moral hazard a la Holmstrom and Milgrom (Econometrica 55:303–328, 1987). We model team production by agents in which each agent’s effort generates an observable signal and depends on efforts of other agents. One of the important findings is that an agent’s optimal effort is negatively impacted by the behavioral biases in other agents’ judgments. We also show envious behavior is destructive for organizations. Consistent with Tirole (Econometrica 69(1):1–35, 2001), our findings suggest that in the presence of agency problems induced by envy or jealousy, the optimal compensation exhibits high pay-for-performance sensitivity.     

On Finite-Difference Approximations for Normalized Bellman Equations

A class of stochastic optimal control problems involving optimal stopping is considered. Methods of Krylov (Appl. Math. Optim. 52(3):365–399, 2005) are adapted to investigate the numerical solutions of the corresponding normalized Bellman equations and to estimate the rate of convergence of finite difference approximations for the optimal reward functions.     

Managing decentralized inventory and transshipment

Any decentralized retail or wholesale system of competing entities requires a benefit sharing arrangement when competing entities collaborate after their demands are realized. For instance, consider a distribution system similar to the observed behavior of independent car dealerships. If a dealership does not have in stock the car requested by a customer, it might consider acquiring it from a competing dealer. Such behavior raises questions about procurement strategies that achieve system optimal (first-best) outcomes. In this paper, we examine the existence and uniqueness of pure strategy Nash equilibrium (PSNE) for a decentralized system that adopts a transfer payment approach proposed by Anupindi et al. (Manuf. Serv. Oper. Manag. 4(3):349–368, 2001). In particular, we state a set of conditions on cost parameters and distributions that guarantee uniqueness of PSNE and discuss its consequences. We also examine a situation with incomplete information and expand the scope of the earlier models by relaxing the assumption of satisfying local demand first. That is, we allow the retailers to transship their inventory regardless of the local demand status if such transshipment increases retailer’s profit, and observe that this model extension does not affect our results relative to the more restrictive case. In short, our results provide important insights, clarifications, and strategic limitations regarding collaborations in decentralized distribution system.     

Bidding and sequential coalition formation with externalities

We study coalition formation games with externalities where each agent’s payoff depends on the entire partition. As in Bloch (Games Econ Behav 14:90–123, 1996) and Ray and Vohra (Games Econ Behav 26:268–336, 1999), we assume that coalitions form sequentially and agreements are irreversible. Instead of a fixed order protocol, we use a “bidding mechanism” (see Pérez-Castrillo and Wettstein in Am Econ Rev 92(5):1577–1587, 2002) to determine proposals and transfers among the agents. We show that such a mechanism facilitates the attainment of efficiency; in particular, our game admits a Markov perfect equilibrium with the property of full dynamic efficiency. In addition, the aggregate equilibrium payoffs of our game exhibit monotonicity in time. Nevertheless, inefficient equilibria can also emerge.     

A simple model of corporate international investment under incomplete information and taxes

This paper extends the theory of corporate international investment in Choi (J. Int. Bus. Stud. 20: 145–155, 1989) in an environment where the segmentation of international capital markets for investors or the presence of agency costs provide some independence to corporate decisions. The model shows that the real exchange risk, the competition between firms in different markets and diversification gains affect corporate international investment. By accounting for the role of information as defined in the models of Merton (J. Finance 42: 483–510, 1987), Bellalah (Int. J. Finance Econ. 6: 59–67, 2001a) and Bellalah and Wu (Int. J. Theor. Appl. Finance 5(5): 479–495, 2002), the model embodies different existing explanations based on economic and behavioral variables. We show in a “two-country” firm model that real exchange risk, diversification motives and information costs are important elements in the determination of corporate international investment decisions. The dynamic portfolio model reflects the main results in several theories of foreign direct investment. Our model accounts for the role of information in explaining foreign investments. It provides simple explanations which are useful in explaining the home bias puzzle in international finance. Using the dynamical programming principle method, we provide the general solution for the proportion of firm’s total capital budget. We also use a new method to get explicit solutions in some special cases. This new method can be applied to solve other financial control problems. The simulating results are given to show our conclusion and the influence of some parameters to the optimal solution. The economic results can be seen as a generalization of the model in Solnik (J. Econ. Theory 8: 500–524, 1974).     

How behaviors spread in dynamic social networks

In this paper, we explore how decentralized local interactions of autonomous agents in a network relate to collective behaviors. Earlier work in this area has modeled social networks with fixed agent relations. We instead focus on dynamic social networks in which agents can rationally adjust their neighborhoods based on their individual interests. We propose a new connection evaluation theory, the Highest Weighted Reward (HWR) rule: agents dynamically choose their neighbors in order to maximize their own utilities based on rewards from previous interactions. We prove that, in the two-action pure coordination game, our system would stabilize to a clustering state in which all relationships in the network are rewarded with an optimal payoff. Our experiments verify this theory and also reveal additional interesting patterns in the network.     

On Controlled Linear Diffusions with Delay in a Model of Optimal Advertising under Uncertainty with Memory Effects

We consider a class of dynamic advertising problems under uncertainty in the presence of carryover and distributed forgetting effects, generalizing the classical model of Nerlove and Arrow (Economica 29:129–142, 1962). In particular, we allow the dynamics of the product goodwill to depend on its past values, as well as previous advertising levels. Building on previous work (Gozzi and Marinelli in Lect. Notes Pure Appl. Math., vol. 245, pp. 133–148, 2006), the optimal advertising model is formulated as an infinite-dimensional stochastic control problem. We obtain (partial) regularity as well as approximation results for the corresponding value function. Under specific structural assumptions, we study the effects of delays on the value function and optimal strategy. In the absence of carryover effects, since the value function and the optimal advertising policy can be characterized in terms of the solution of the associated HJB equation, we obtain sharper characterizations of the optimal policy.     

A hybrid method for quantum global optimization

This paper gives a quantum algorithm for global optimization. The heart of such approaches employ Grover’s database search (1996; Phys Rev Lett 79(23):4709–4712, 1997a; 79(2):325–328, 1997b). Chi and Kim (1998) show that when the phases of the generalized Grover database search operator are optimally chosen, it is capable of finding a solution by a single query. To apply this method to global optimization requires knowledge of the number of marked points m to calculate the optimal phases, but this value is seldom known. This paper focuses on overcoming this hurdle by showing that an estimate of the optimal phases can be found and used to replace the optimal phases while maintaining a high probability of finding a solution. Merging this finding with a recently discovered dynamic quantum global optimization algorithm (BBW2D) that reduces the problem to finding successively improving regions using Grover’s search, we present a hybrid method that improves the efficiency and reduces the variance of the search algorithm when empirically compared to other existing quantum search algorithms.     

Effects of sourcing structure on performance in a multiple-product assemble-to-order supply chain

This paper addresses the strategic pricing decisions of a decentralized assemble-to-order system, and the effects of sourcing structure on system performance. We consider an assemble-to-order system consisting of two substitute products and three components manufactured by different suppliers. Demand for the products is price-sensitive. The selling prices for the products are jointly determined by firms in the system. We study the system under both centralized and decentralized decision-making situations. For the centralized system, we demonstrate that there exists a unique optimal pricing solution. For the decentralized system, we show that there exists a unique Nash equilibrium in the players’ pricing game. We further analyze the effects of different sourcing structures on the system performance and the assembler’s performance. We find that reduction of suppliers in the system does not guarantee improvement of system performance. Different sourcing structures have different impacts on performance. When the two dedicated components are sourced from a single supplier and the common component is sourced from another independent supplier, the system and the assembler’s performance become worse. We show that the decentralized system can be effectively coordinated and the system performance can be improved with a simple profit-sharing contract. Finally, we provide comprehensive numerical examples to demonstrate some important managerial insights.     

Market selection: hungry misers and bloated bankrupts

The Market Selection Hypothesis is a principle which (informally) proposes that ‘less knowledgeable’ agents are eventually eliminated from the market. This elimination may take the form of starvation (the proportion of output consumed drops to zero), or may take the form of going broke (the proportion of asset held drops to zero), and these are not the same thing. Starvation may result from several causes, diverse beliefs being only one. We firstly identify and exclude these other possible causes, and then prove that starvation is equivalent to inferior belief, under suitable technical conditions. On the other hand, going broke cannot be characterized solely in terms of beliefs, as we show. We next present a remarkable example with two agents with different beliefs, in which one agent starves yet amasses all the capital, and the other goes broke yet consumes all the output—the hungry miser and the bloated bankrupt. This example also serves to show that although an agent may starve, he may have long-term impact on the prices. This relates to the notion of price impact introduced by Kogan et al. (Market selection, working paper, 2009), which we correct in the final section, and then use to characterize situations where asymptotically equivalent pricing holds.     

Well-posedness for a mean field model of Ginzburg–Landau vortices with opposite degrees

In this paper we analyze the hydrodynamic equations for Ginzburg–Landau vortices as derived by E (Phys. Rev. B. 50(3):1126–1135, 1994). In particular, we are interested in the mean field model describing the evolution of two patches of vortices with equal and opposite degrees. Many results are already available for the case of a single density of vortices with uniform degree. This model does not take into account the vortex annihilation, hence it can also be seen as a particular instance of the signed measures system obtained in Ambrosio et al. (Ann. Inst. H. Poincaré Anal. Non Linéaire 28(2):217–246, 2011) and related to the Chapman et al. (Eur. J. Appl. Math. 7(2):97–111, 1996) formulation. We establish global existence of L ^p solutions, exploiting some optimal transport techniques introduced in this context in Ambrosio and Serfaty (Commun. Pure Appl. Math. LXI(11):1495–1539, 2008). We prove uniqueness for L ^∞ solutions, as expected by analogy with the incompressible Euler equations in fluidodynamics. We also consider the corresponding Dirichlet problem in a bounded domain. Moreover, we show some simple examples of 1-dimensional dynamic.     

Centralized and decentralized management of groundwater with multiple users

In this work, we investigate two groundwater inventory management schemes with multiple users in a dynamic game-theoretic structure: (i) under the centralized management scheme, users are allowed to pump water from a common aquifer with the supervision of a social planner, and (ii) under the decentralized management scheme, each user is allowed to pump water from a common aquifer making usage decisions individually in a non-cooperative fashion. This work is motivated by the work of Saak and Peterson [14], which considers a model with two identical users sharing a common aquifer over a two-period planning horizon. In our work, the model and results of Saak and Peterson [14] are generalized in several directions. We first build on and extend their work to the case of n non-identical users distributed over a common aquifer region. Furthermore, we consider two different geometric configurations overlying the aquifer, namely, the strip and the ring configurations. In each configuration, general analytical results of the optimal groundwater usage are obtained and numerical examples are discussed for both centralized and decentralized problems.     

授权制造下碳交易对制造/再制造影响及协调机制研究

在授权制造下,为分析碳交易对制造/再制造供应链影响和研究供应链协调机制,基于授权制造分别构建由一个原始制造商和一个再制造商参与的分散决策博弈模型和集中决策博弈模型,对比分析政府碳交易政策对两种决策模式最优解影响,并针对制造商分散决策导致的边际损失问题,给出固定授权费的协调机制。研究主要得到:无论分散决策还是集中决策,当碳交易价格大于某一阈值时,碳交易不仅可以降低两种产品对环境的影响,还增加消费者剩余;分散决策时,在碳交易下原始制造商可以通过降低单位授权再制造费用来增加利润;原始制造商和再制造商可以签订固定授权费的契约来协调供应链利润。     

Efficient Coordination by Optimal Allocation of Decision Rights for Participants on Electronic Financial Services Markets

Information technology (IT) is enabling large companies and particularly banking firms to create new forms of organizations. Both globalization of markets and stronger regulation throughout the world puts pressure on banking firms to either spend more money coordinating business activities in the traditional hierarchical ways or to employ new forms of organizations enabled by (lower costs of) IT. When facing uncertain demand in multiple horizontal markets, resource allocation problems occur. Accordingly, the location of decision authority in a multilevel hierarchical organization has profound impact on the performance of the firm. The firm has to design its coordination structure, which determines who makes the resource allocation decisions. Considering the tradeoff between pooling effects in the case of centralized decision-making and better assessment of local markets in the case of decentralized decision-making, the decision problem where to locate decision rights to maximize total profits has to be solved. In this paper we investigate for both independent and dependent demands the total profits for each of the possible coordination mechanisms: centralized decision-making, decentralized decision-making, and intermediate-level decision-making. It turns out that—depending on the crucial parameters of the firm—decentralized decision-making or centralized decision-making may be optimal. But in many relevant cases the optimal location of decision rights is at an intermediate level of the hierarchy. We illustrate the findings by considering the banking firm coordinating equity capital allocation by granting alternative decision rights to their employees as participants on electronic financial markets. Finally we discuss the generality of the approach and its applicability in other areas such as inventory management.     

Equilibrium analysis of supply chain structures under power imbalance

This paper investigates the implications of channel power on supply chain stability in a setting where multiple suppliers sell substitutable products through a common retailer. Such supply chains have been traditionally analyzed as one- or two-stage Stackelberg non-cooperative games with all suppliers sharing balanced (equal) decision-making power. In this paper, we relax this assumption and formulate game-theoretic models to examine scenarios where one supplier can act as the Stackelberg leader. Consequently, we analyze new supply chain structures and introduce the notion of structure dominance, a novel approach to analyze the performance of supply chains that has practical implications. Thus, a decision maker can employ the concepts of structure dominance to determine whether there exist supply chain scenarios that are more stable than others, i.e., less prone to power reconfigurations, at both agent and group level. We find that power imbalance causes significant declines in supply chain profits, and the more balanced the agents are the higher their profits when demand is linear, regardless of product competition. It develops that neither the Manufacturer Stackelberg nor the Retailer Stackelberg supply chains are stable structures in our generalized setting, but that structures where power is equally split between agents provide for best stability and performance.     

Coordination in decentralized assembly systems with uncertain component yields

The literature on assembly systems with random component yields has focused on centralized systems, where a single decision maker chooses all components’ production quantities and incurs all the costs. We consider a decentralized setting where the component suppliers choose their production quantities based solely on their own cost/reward structure, and the assembly firm makes ordering decisions based on its own cost/reward structure. When the suppliers control their inputs but the outputs exhibit random yields, coordination in such systems becomes quite complex. In such situations, incentive alignment control mechanisms are needed so that the suppliers will choose production quantities as in the centralized system case. One such mechanism is to penalize the supplier with the worse delivery performance. We analyze the conditions under which system coordination is achieved while respecting participation constraints. Further, we determine the optimal component ordering policy for the assembly firm and derive the optimal coordinating penalties.     

面向网络外部性特征产品的供应链动态竞争策略研究

当产品具有网络外部性的特征时,该产品的规模收益特征对利润、产品价格和需求等因素都会产生重大影响。首先,通过将网络规模建立为网络成本投入的微分方程,分别构建了分散与集中式决策下的动态供应链模型。其次,以供应链的利润最大化为前提,利用微分博弈导出生产量、批发价、零售价和投入努力值的最优策略。结论表明:在生命周期的前部分,集中决策情形的供应链系统利润和产品价格低于分散决策情形,但越往后,其价格和利润都将逐步超过分散决策情形,且差距越来越大。     

Economic value of weather forecasting: the role of risk aversion

Extreme meteorological events have increased over the last decades and it is widely accepted that it is due to climate change (IPCC, Climate Change 2007, Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, Cambridge, 2007; Beniston et al., Clim. Change 81:71–95, 2007). Some of these extremes, like drought or frost episodes, largely affect agricultural outputs, and risk management becomes crucial. The goal of this paper it is to analyze farmers’ decisions about risk management, taking into account climatological and meteorological information. We consider a situation in which the farmer, as part of crop management, has available technology to protect the harvest from weather effects. This approach has been used by Murphy et al. (Mon. Weather Rev. 113:801–813, 1985), Katz and Murphy (J. Forecast. 9:75–86, 1990 and Economic Value of Weather and Climate Forecasts, pp. 183–217, Cambridge University Press, Cambridge, 1997) and others in the case when the farmer maximizes the expected returns. In our model, we introduce the attitude towards risk. Thus we can evaluate how the optimal decision is affected by the absolute risk aversion coefficient of Arrow and Pratt, and compute the economic value of the information in this context, while proposing a measure to estimate the amount of money that the farmer is willing to pay for this information in terms of the certainty equivalent.     

考虑决策者失望规避的供应链协同绿色创新动态优化与协调研究

针对决策者存在失望规避行为且产品绿色水平具有动态变化特征的情形,基于失望理论,运用微分博弈的方法研究了供应链协同绿色创新动态优化与协调问题,探讨了供应链成员失望规避程度对绿色创新决策及供应链绩效的影响,并提出双向成本分担契约对供应链进行协调。结果表明,供应链成员是否选择协同绿色创新及产品的绿色水平均与成员的失望规避程度密切相关;分散式决策下,若制造商选择分担供应商部分绿色创新成本,其分担比例与制造商失望规避程度负相关,与供应商失望规避程度正相关;集中式决策下,产品绿色水平、成员绿色创新水平及效用现值均高于协调前分散系统中的对应值;在一定条件下,双向成本分担契约的设计与实施,能有效提升供应链成员效用现值,实现供应链协调。