Tenable Strategy Blocks and Settled Equilibria

When people interact in familiar settings, social conventions usually develop so that people tend to disregard alternatives outside the convention. For rational players to usually restrict attention to a block of conventional strategies, no player should prefer to deviate from the block when others are likely to act conventionally and rationally inside the block. We explore two set‐valued concepts, coarsely and finely tenable blocks, that formalize this notion for finite normal‐form games. We then identify settled equilibria, which are Nash equilibria with support in minimal tenable blocks. For a generic class of normal‐form games, our coarse and fine concepts are equivalent, and yet they differ from standard solution concepts on open sets of games. We demonstrate the nature and power of the solutions by way of examples. Settled equilibria are closely related to persistent equilibria but are strictly more selective on an open set of games. With fine tenability, we obtain invariance under the insertion of a subgame with a unique totally mixed payoff‐equivalent equilibrium, a property that other related concepts have not satisfied.     

COMPETITIVE MARKETS WITH ENDOGENOUS HEALTH RISKS

We study an economy where agents' productivity and labor endowment depend on their health status, and indivisible occupational choices affect individual health distributions. We show that Pareto efficiency requires cross‐transfers across occupations. Moreover, workers with relatively less safe jobs must get positive transfers whenever labor supply is not very reactive to wages, a condition in line with the findings of a large empirical literature. In these instances, compensating wage differentials equalizing the utilities of ex‐ante identical workers in different jobs undermine ex‐ante efficiency. Moreover, competitive equilibria where only assets with deterministic payoffs are traded are not first‐best. Finally, we show that simple transfer schemes, implemented through linear subsidies to health insurance, enhance efficiency.     

Coordination of Supply Chains with Risk‐Averse Agents

The extant supply chain management literature has not addressed the issue of coordination in supply chains involving risk‐averse agents. We take up this issue and begin with defining a coordinating contract as one that results in a Pareto‐optimal solution acceptable to each agent. Our definition generalizes the standard one in the risk‐neutral case. We then develop coordinating contracts in three specific cases: (i) the supplier is risk neutral and the retailer maximizes his expected profit subject to a downside risk constraint; (ii) the supplier and the retailer each maximizes his own mean‐variance trade‐off; and (iii) the supplier and the retailer each maximizes his own expected utility. Moreover, in case (iii), we show that our contract yields the Nash Bargaining solution. In each case, we show how we can find the set of Pareto‐optimal solutions, and then design a contract to achieve the solutions. We also exhibit a case in which we obtain Pareto‐optimal sharing rules explicitly, and outline a procedure to obtain Pareto‐optimal solutions.     

Coordinating a Supply Chain System with Retailers Under Both Price and Inventory Competition

We investigate a supply chain system with a common supplier selling to downstream retailers who are engaged in both price and inventory competition. We establish the existence and uniqueness of the pure‐strategy Nash equilibrium for the retailer game and study how a supplier can coordinate the system to achieve the best performance. Our main conclusions are as follows: First, a buyback contract can be used to coordinate retailers competing on both price and inventory in a sense that optimal retail prices and inventory levels arise as the Pareto‐dominant equilibrium. With symmetric retailers, the system optimum arises as the unique symmetric equilibrium. Second, the particular type of competition experienced by retailers (price versus inventory competition) affects the characteristics of the contract. Specifically, strong price competition leads to a coordination mechanism with a positive buyback rate, where the supplier subsidizes retailers for leftover inventories; however, strong inventory competition leads to a negative buyback rate, where retailers are punished for overstocking. Using a linear expected demand function, we further explore the impact of system parameters on the coordination contract and the competitive equilibrium. We also find that the performance of the supplier's optimal contract is asymptotic to the system optimal coordination contract as competition becomes fierce.     

No‐Betting‐Pareto Dominance

We argue that the notion of Pareto dominance is not as compelling in the presence of uncertainty as it is under certainty. In particular, voluntary trade based on differences in tastes is commonly accepted as desirable, because tastes cannot be wrong. By contrast, voluntary trade based on incompatible beliefs may indicate that at least one agent entertains mistaken beliefs. We propose and characterize a weaker, No‐Betting, notion of Pareto domination which requires, on top of unanimity of preference, the existence of shared beliefs that can rationalize such preference for each agent.     

Informational Size and Incentive Compatibility

We examine a general equilibrium model with asymmetrically informed agents. The presence of asymmetric information generally presents a conflict between incentive compatibility and Pareto efficiency. We present a notion of informational size and show that the conflict between incentive compatibility and efficiency can be made arbitrarily small if agents are of sufficiently small informational size.     

消费者“搭便车”行为影响下的双渠道供应链定价和促销策略研究

在制造商主导的二层双渠道供应链背景下,考察由于实体店促销努力而新进入市场消费者的“搭便车”行为,刻画供应链定价和促销策略发生的变化,并设计一个制造商分担实体店促销努力成本的协调机制来改善供应链运作效率。研究发现：（1）促销成本分担机制的介入将同时提高实体店零售价格和网店直销价格,但无论是否存在促销成本分担机制,网店直销价格均显著低于实体店零售价格;（2）新进入市场消费者的“搭便车”行为将会显著降低实体店促销努力水平和供应链整体利润水平;（3）促销成本分担机制可以实现制造商和实体店双方利润水平的Pareto改进。最后用数值仿真验证了促销成本分担机制作为供应链协调机制的可行性。     

Coordinating Supply Chains via Advance‐Order Discounts,Minimum Order Quantities,and Delegations

To avoid inventory risks, manufacturers often place rush orders with suppliers only after they receive firm orders from their customers (retailers). Rush orders are costly to both parties because the supplier incurs higher production costs. We consider a situation where the supplier's production cost is reduced if the manufacturer can place some of its order in advance. In addition to the rush order contract with a pre‐established price, we examine whether the supplier should offer advance‐order discounts to encourage the manufacturer to place a portion of its order in advance, even though the manufacturer incurs some inventory risk. While the advance‐order discount contract is Pareto‐improving, our analysis shows that the discount contract cannot coordinate the supply chain. However, if the supplier imposes a pre‐specified minimum order quantity requirement as a qualifier for the manufacturer to receive the advance‐order discount, then such a combined contract can coordinate the supply chain. Furthermore, the combined contract enables the supplier to attain the first‐best solution. We also explore a delegation contract that either party could propose. Under this contract, the manufacturer delegates the ordering and salvaging activities to the supplier in return for a discounted price on all units procured. We find the delegation contract coordinates the supply chain and is Pareto‐improving. We extend our analysis to a setting where the suppliers capacity is limited for advance production but unlimited for rush orders. Our structural results obtained for the one‐supplier‐one‐manufacturer case continue to hold when we have two manufacturers.     

考虑利他主义的古诺模型研究

针对完全利己和(或)完全利他可能不具有集体帕累托效率这些经济现象,利用文献[1]建立的GR博弈模型和GR均衡,建立了基于GR(黄金规则)的古诺模型,研究了GR均衡的集体帕累托效率性质与GR博弈中权重系统(描述厂商关心自己和他人的程度)之间的关系.结果表明,(1)对于N-厂商的情形,GR均衡集合与具有集体帕累托效率的策略组合构成的集合一致的充分必要条件是每个厂商都均等地关心自己和他人的利润;(2)对于两厂商的情形,GR均衡都具有集体帕累托效率的充分必要条件是,存在一个厂商均等地关心自己和他人的利润.这些结果一方面在古诺竞争的背景下加强了文献[1]的结果;另一方面表明.一个"平等地看待竞争对手利益"的古诺竞争将会获得集体有效率的竞争均衡.     

A Model for Partial Product Complementarity and Strategic Production Decisions under Demand Uncertainty

This paper considers a general industrial setting where multiple manufacturers each produce a different product and sell it to the markets. These products are partially complementary in the sense that there is a common demand stream that requests all these products as complementary sets and there are streams of individual demands each requesting only one of the products. All demands are uncertain and may follow any general, joint distributions. Facing demand uncertainties, the manufacturers each choose a production quantity for its product with an objective to maximize its own expected profit. We formulate the problem as a non‐cooperative game to study the strategic interactions of such firms and their implications to supply chain performance. We show that such a game may have numerous equilibria. Among all the possible equilibria, however, we prove that there always exists a unique one that maximizes each and every manufacturer's profit, and we derive an explicit solution for this Pareto‐optimal equilibrium point. We further study the optimal solution for a centralized system and compare it with the decentralized solution. Managerial insights are drawn as to how system parameters and control mechanisms affect firms' decisions and performance.     

Pathological Outcomes of Observational Learning

This paper explores how Bayes‐rational individuals learn sequentially from the discrete actions of others. Unlike earlier informational herding papers, we admit heterogeneous preferences. Not only may type‐specific ‘herds’ eventually arise, but a new robust possibility emerges: confounded learning. Beliefs may converge to a limit point where history offers no decisive lessons for anyone, and each type's actions forever nontrivially split between two actions. To verify that our identified limit outcomes do arise, we exploit the Markov‐martingale character of beliefs. Learning dynamics are stochastically stable near a fixed point in many Bayesian learning models like this one.     

TRANSFERABLE CONTROL

In this paper, we introduce the notion of transferable control, defined as a situation where one party (the principal, say) can transfer control to another party (the agent) but cannot commit herself to do so. One theoretical foundation for this notion builds on the distinction between formal and real authority introduced by Aghion and Tirole, in which the actual exercise of authority may require noncontractible information, absent which formal control rights are vacuous. We use this notion to study the extent to which control transfers may allow an agent to reveal information regarding his ability or willingness to cooperate with the principal in the future. We show that the distinction between contractible and transferable control can drastically influence how learning takes place: with contractible control, information about the agent can often be acquired through revelation mechanisms that involve communication and message‐contingent control allocations; in contrast, when control is transferable but not contractible, it can be optimal to transfer control unconditionally and learn instead from the way in which the agent exercises control. (JEL: C70, C72, D23, L2)     

Waiting for News in the Market for Lemons

We study a dynamic setting in which stochastic information (news) about the value of a privately informed seller's asset is gradually revealed to a market of buyers. We construct an equilibrium that involves periods of no trade or market failure. The no‐trade period ends in one of two ways: either enough good news arrives, restoring confidence and markets reopen, or bad news arrives, making buyers more pessimistic and forcing capitulation that is, a partial sell‐off of low‐value assets. Conditions under which the equilibrium is unique are provided. We analyze welfare and efficiency as they depend on the quality of the news. Higher quality news can lead to more inefficient outcomes. Our model encompasses settings with or without a standard static adverse selection problem—in a dynamic setting with sufficiently informative news, reservation values arise endogenously from the option to sell in the future and the two environments have the same equilibrium structure.     

Product Assortment and Price Competition under Multinomial Logit Demand

The role of assortment planning and pricing in shaping sales and profits of retailers is well documented and studied in monopolistic settings. However, such a role remains relatively unexplored in competitive environments. In this study, we study equilibrium behavior of competing retailers in two settings: (i) when prices are exogenously fixed, and retailers compete in assortments only; and (ii) when retailers compete jointly in assortment and prices. For this, we model consumer choice using a multinomial Logit, and assume that each retailer selects products from a predefined set, and faces a display constraint. We show that when the sets of products available to retailers do not overlap, there always exists one equilibrium that Pareto‐dominates all others, and that such an outcome can be reached through an iterative process of best responses. A direct corollary of our results is that competition leads a firm to offer a broader set of products compared to when it is operating as a monopolist, and to broader offerings in the market compared to a centralized planner. When some products are available to all retailers, that is, assortments might overlap, we show that display constraints drive equilibrium existence properties.     

PROPERTY RIGHTS AND THE EFFICIENCY OF BARGAINING

We show that efficient bargaining is impossible for a wide class of economic settings and property rights. These settings are characterized by (i) the existence of “adverse efficient opt‐out types”, whose participation does not change the efficient allocation and who, when they opt out, are the worst type other agents can face, and (ii) non‐existence of the “marginal core”, and its multivaluedness with a positive probability. We also examine the optimal allocation of property rights within a given class that satisfies (i), such as simple property rights, liability rules, and dual‐chooser rules. We characterize property rights that minimize the expected subsidy required to implement efficiency. With two agents, simple property rights that are optimal in this way maximize the expected surplus at the status quo allocation, but this no longer holds with more agents. We also study “second‐best” budget‐balanced bargaining under a liability rule. The optimal “second‐best” liability rule may differ from, but is often close to, the expectation of the victim's harm, which would be optimal if there were no bargaining. However, liability rules that are close to a simple property right result in a lower expected surplus than the simple property right they are near.     

Optimal Inventory Control with Dual‐Sourcing,Heterogeneous Ordering Costs and Order Size Constraints

We consider a dual‐sourcing inventory system, where procuring from one supplier involves a high variable cost but negligible fixed cost whereas procuring from the other supplier involves a low variable cost but high fixed cost, as well as an order size constraint. We show that the problem can be reduced to an equivalent single‐sourcing problem. However, the corresponding ordering cost is neither concave nor convex. Using the notion of quasi‐convexity, we partially characterize the structure of the optimal policy and show that it can be specified by multiple thresholds which determine when to order from each supplier and how much. In contrast to previous research, which does not consider order size constraints, we show that it is optimal to simultaneously source from both suppliers when the beginning inventory level is sufficiently low. We also show that the decision to source from the low‐cost supplier is not monotonic in the inventory level. Our results require that the variable costs satisfy a certain condition which guarantees quasi‐convexity. However, extensive numerical results suggest that our policy is almost always optimal when the condition is not satisfied. We also show how the results can be extended to systems with multiple capacitated suppliers.     

Shop Floor Control When Tacit Worker Knowledge is Important

We investigate a shop where the workers and supervisors have tacit knowledge of how to operate efficiently and where efficiency is important to providing capacity to meet demand. This tacit knowledge includes setup dependencies between products as well as which worker or machine is best suited for a particular product. We discuss a real‐world shop where this is the case. Management expects workers and supervisors to use their knowledge to schedule efficiently by monitoring their performance based on standards. The question that we explore is how management should control for due date performance in light of the discretion given to the workers and supervisors to sequence jobs on the basis of efficiency. We explore management control of due date performance through the use of order review and release (ORR) and management expediting. We find that although ORR is quite effective at reducing work‐in‐process (WIP) inventories, it may foster very late deliveries in a shop such as this. In fact, under such conditions, deftly executed expediting with no ORR at all can be far more effective at supporting all deliveries. Even improving ORR into a hybrid by actively updating path efficiencies (observed from supervisor/worker scheduling) did not support a change to this conclusion. Conversely, when conditions are created where tacit knowledge plays a reduced role or utilization is decreased, ORR delivers in a timely manner. The interaction between utilization, WIP levels, and worker knowledge all help dictate the appropriate control methodology.     

Capacity Sharing and Cost Allocation among Independent Firms with Congestion

We analyze the benefit of production/service capacity sharing for a set of independent firms. Firms have the choice of either operating their own production/service facilities or investing in a facility that is shared. Facilities are modeled as queueing systems with finite service rates. Firms decide on capacity levels (the service rate) to minimize delay costs and capacity investment costs possibly subject to service‐level constraints on delay. If firms decide to operate a shared facility they must also decide on a scheme for sharing the capacity cost. We formulate the problem as a cooperative game and identify settings under which capacity sharing is beneficial and there is a cost allocation that is in the core under either the first‐come, first‐served policy or an optimal priority policy. We show that capacity sharing may not be beneficial in settings where firms have heterogeneous work contents and service variabilities. In such cases, we specify conditions under which capacity sharing may still be beneficial for a subset of the firms.     

The Promise of Strategic Customer Behavior: On the Value of Click Tracking

Click tracking is gaining in popularity, and the practice of web analytics is growing fast. Whether strategic customers are willing to visit a website when they know their clicks may be tracked is an important yet complex problem, which depends on various factors. Using a newsvendor framework, we examine this problem by focusing on the operational factor: how product availability induces strategic customers to voluntarily provide advance demand information. We find that a strong Nash equilibrium exists where every customer is willing to click, and customer incentives to click are robust to noise. Hence, we demonstrate the promise of strategic customer behavior in the context of click tracking, contrary to the conventional wisdom that it is typically a peril for the firm. Notably, click tracking is typically advantageous to both the firm and its customers, compared with other strategies such as advance selling, quantity commitment, availability guarantees, and quick response. Lastly, we extend to two settings by including marketing decisions, price‐sensitive demand and markdown pricing, and discuss how operations and marketing decisions interact in influencing the value of click tracking.     

Games and Mechanism Design in Machine Scheduling—An Introduction

We survey different models, techniques, and some recent results to tackle machine scheduling problems within a distributed setting. In traditional optimization, a central authority is asked to solve a (computationally hard) optimization problem. In contrast, in distributed settings there are several agents, possibly equipped with private information that is not publicly known, and these agents must interact to derive a solution to the problem. Usually the agents have their individual preferences, which induces them to behave strategically to manipulate the resulting solution. Nevertheless, one is often interested in the global performance of such systems. The analysis of such distributed settings requires techniques from classical optimization, game theory, and economic theory. The paper therefore briefly introduces the most important of the underlying concepts and gives a selection of typical research questions and recent results, focusing on applications to machine scheduling problems. This includes the study of the so‐called price of anarchy for settings where the agents do not possess private information, as well as the design and analysis of (truthful) mechanisms in settings where the agents do possess private information.