This paper studies the endogenous formation of supply chain networks when procurement is subject to disruption risk. We argue that the presence of non-convexities in the chain (e.g., due to non-convex production technologies or financial constraints) may create a wedge in the sourcing incentives of firms at different tiers, leading to the formation of overly fragile supply chains. More specifically, we show that even though upstream firms may find it optimal to employ multi-sourcing strategies as a way of mitigating supply disruption risks, such strategies lead to a more intertwined supply chain, which may exacerbate the extent of risk propagation further downstream: multi-sourcing by upstream firms may increase the likelihood of simultaneous disruptions in all procurement channels available to the downstream firms. We establish that under fairly general conditions, the losses due to such system-wide disruptions outweigh the benefits of multi-sourcing, thus, implying that the endogenously formed supply networks may be excessively interconnected.
We consider a single-period, multi-location newsvendor problem, where different locations face independent and identically distributed demands and linear holding and backorder costs. It is well-known that when demands are normally distributed, centralized inventory management leads to savings in expected costs that increase with the square root of the number of locations. Motivated by empirical evidence of significantly higher variability compared to that of normal distributions, e.g., in online retailing, we revisit this classical setting and examine the impact of high demand variability on both the expected cost savings and the optimal inventory levels of centralized inventory management. For the general class of stable distributions we provide closed-form expressions that characterize the benefits from inventory pooling as a function of the number of locations and a single parameter that captures the variability of the underlying demand distribution. The managerial insight derived from our analysis is that pooling is considerably less appealing in the case of heavy-tailed demands and, furthermore, its value decreases as the variability of the underlying demand increases. This could potentially make decentralized inventory management preferable in certain cases. Finally, we extend our findings to inventory systems with service-level constraints, e.g., in-stock probability, and discuss their implications on the performance of periodic-review policies, in the context of a single-location, multi-period newsvendor problem with fixed ordering costs.
Recent advances in information technology have allowed firms to gather vast amounts of data regarding consumers' preferences and the structure and intensity of their social interactions. This paper examines a game-theoretic model of competition between firms, which can target their marketing budgets to individuals embedded in a social network. We provide a sharp characterization of the optimal targeted marketing strategies and highlight their dependence on the underlying social network structure. Furthermore, we identify network structures for which the returns to targeting are maximized, and we provide conditions under which it is optimal for the firms to asymmetrically target a subset of the individuals. Finally, we provide a lower bound on the extent of asymmetry in these asymmetric equilibria and therefore shed light on the effect of the network structure to the outcome of marketing competition between firms.
This paper argues that in the presence of liquidation costs, portfolio diversification by financial institutions may be socially inefficient. We propose a stylized model in which individual banks have an incentive to diversify their risks. Yet, at the same time, diversification may increase the aggregate risk faced by the banks' depositors, creating a negative externality. The increase in systemic risk is due to the fact that even though diversification decreases the probability of each bank's failure, it may increase the probability of joint failures, which may be socially inefficient when the depositors are risk-averse. The presence of such externalities suggests that financial innovations that enable banks to engineer more diversified portfolios have non-trivial welfare implications.
We develop a model of information exchange through communication and investigate its implications for information aggregation in large societies. An underlying state determines payoffs from different actions. Agents decide which others to form a costly communication link with incurring the associated cost. After receiving a private signal correlated with the underlying state, they exchange information over the induced communication network until taking an (irreversible) action. We define asymptotic learning as the fraction of agents taking the correct action converging to one as a society grows large.
Under truthful communication, we show that asymptotic learning occurs if (and under some additional conditions, also only if) in the induced communication network most agents are a short distance away from information hubs, which receive and distribute a large amount of information. Asymptotic learning therefore requires information to be aggregated in the hands of a few agents. We also show that while truthful communication may not always be a best response, it is an equilibrium when the communication network induces asymptotic learning. Moreover, we contrast equilibrium behavior with a socially optimal strategy profile, i.e., a profile that maximizes aggregate welfare. We show that when the network induces asymptotic learning, equilibrium behavior leads to maximum aggregate welfare, but this may not be the case when asymptotic learning does not occur.
We then provide a systematic investigation of what types of cost structures and associated social cliques (consisting of groups of individuals linked to each other at zero cost, such as friendship networks) ensure the emergence of communication networks that lead to asymptotic learning. Our result shows that societies with too many and sufficiently large social cliques do not induce asymptotic learning, because each social clique would have sufficient information by itself, making communication with others relatively unattractive. Asymptotic learning results either if social cliques are not too large, in which case communication across cliques is encouraged, or if there exist very large cliques that act as information hubs.
We study the optimal pricing strategies of a monopolist selling a divisible good (service) to consumers that are embedded in a social network. A key feature of our model is that consumers experience a (positive) local network effect. In particular, each consumer's usage level depends directly on the usage of her neighbors in the social network structure. Thus, the monopolist's optimal pricing strategy may involve offering discounts to certain agents, who have a central position in the underlying network.
Our results can be summarized as follows. First, we consider a setting where the monopolist can offer individualized prices and derive an explicit characterization of the optimal price for each consumer as a function of her network position. In particular, we show that it is optimal for the monopolist to charge each agent a price that is proportional to her Bonacich centrality in the social network. In the second part of the paper, we discuss the optimal strategy of a monopolist that can only choose a single uniform price for the good and derive an algorithm polynomial in the number of agents to compute such a price.
Thirdly, we assume that the monopolist can offer the good in two prices, full and discounted, and study the problem of determining which set of consumers should be given the discount. We show that the problem is NP-hard, however we provide an explicit characterization of the set of agents that should be offered the discounted price. Next, we describe an approximation algorithm for finding the optimal set of agents. We show that if the profit is nonnegative under any feasible price allocation, the algorithm guarantees at least 88% of the optimal profit. Finally, we highlight the value of network information by comparing the profits of a monopolist that does not take into account the network effects when choosing her pricing policy to those of a monopolist that uses this information optimally.
This paper studies a simple model of experimentation and innovation. Our analysis suggests that patents improve the allocation of resources by encouraging rapid experimentation and efficient ex post transfer of knowledge. Each firm receives a signal on the success probability of a project and decides when to experiment. Successes can be copied. First, we assume that signal qualities are the same. Symmetric equilibria involve delayed and staggered experimentation, whereas the optimal allocation never involves delays and may involve simultaneous experimentation. Appropriately designed patents implement the optimal allocation. Finally, we discuss the case when signals differ and are private information.
We study the efficiency of oligopoly equilibria in a model where firms compete over capacities and prices. Our model economy corresponds to a two-stage game. First, firms choose their capacity levels. Second, after the capacity levels are observed, they set prices. Given the capacities and prices, consumers allocate their demands across the firms. We establish the existence of pure strategy oligopoly equilibria and characterize the set of equilibria. We then investigate the efficiency properties of these equilibria, where "efficiency" is defined as the ratio of surplus in equilibrium relative to the first best. We show that efficiency in the worst oligopoly equilibria can be arbitrarily low. However, if the best oligopoly equilibrium is selected (among multiple equilibria), the worst-case efficiency loss is 2(√N-1)/(N-1) with N firms, and this bound is tight. We also suggest a simple way of implementing the best oligopoly equilibrium.
Optimal Pricing in the Presence
of Local Network Effects, with O. Candogan and
A. Ozdaglar, WINE 2010.
Forming Information Networks,
with D. Acemoglu and A. Ozdaglar, Allerton,
Communication and Learning in
Social Networks: Partial Results, with
D. Acemoglu and A. Ozdaglar, Allerton,
Competition with Atomic Users, with A. Ozdaglar, Asilomar, 2007.
Partial Results on Capacity
Competition, with D. Acemoglu and A. Ozdaglar,