Timothy Van Zandt

Monotone equilibria in Bayesian games of strategic complementarities

For Bayesian games of strategic complementarities, we provide a constructive proof of the existence of a greatest and a least Bayes-Nash equilibrium - each one in strategies monotone in type - if the payoff to a player displays increasing differences in own action and the profile of types, and if the posteriors are increasing in type with respect to first-order stochastic dominance (e.g. if types are affiliated). The result holds for multidimensional action and type spaces and also for continuous and discrete type distributions. It uses an intermediate result on monotone comparative statics under uncertainty, which implies that the extremal equilibria increase when there is a first-order stochastic dominant shift in beliefs. We provide an application to strategic information revelation in games of voluntary disclosure.

Decentralized Information Processing in the Theory of Organizations

Although models with bounded rationality — defined broadly to mean those in which agent behaviour departs from the paradigm of effortless full rationality — are appearing in every field of economics, only in the theory of organizations has bounded rationality been an important theme throughout the history of the field. There is a reason for this difference. The classical model of rational choice has been a good approximation and powerful tool in studying consumer and producer theory, markets and price determination, imperfect competition, trading in financial markets, and most other topics in economics. Only recently have fields matured enough that some outstanding open questions require more accurate models of human decision-making. In the thoery of organizations, on the other hand, the rational model leads to uninteresting models of organizations, in which one manager or entrepreneur can run a firm or economy of arbitrary size. Without bounds on information processing capacity, it is impossible to explain the sharing of information processing tasks that is such an important part of the interaction between members of organizations, and to explain the existence and functioning of the administrative apparatus that are such important components of organizations (as documented for example by Chandler, 1966 and 1990).

Information Processing in Firms and Returns to Scale

The study of returns to scale in firms has traditionally focused on technological returns to scale in the production process. However, as the scale of a firm’s production grows, so does its administrative apparatus. The process of managing a firm, although not as well understood nor as extensively studied as the production process itself, uses significant resources and is important to the profitability of the other operations in the firm. Therefore, this process may also have a significant impact on returns to scale. The purpose of this paper is to explore this impact.

Real-Time Decentralized Information Processing and Returns to Scale

Abstract. We use a model of real-time decentralized information processing to understand how constraints on human information processing affect the returns to scale of organizations. We identify three informational (dis)economies of scale: diversification of heterogeneous risks (positive), sharing of information and of costs (positive), and crowding out of recent information due to information processing delay (negative). Because decision rules are endogenous, delay does not inexorably lead to decreasing returns to scale. However, returns are more likely to be decreasing when computation constraints, rather than sampling costs, limit the information upon which decisions are conditioned. The results illustrate how information processing constraints together with the requirement of informational integration cause a breakdown of the replication arguments that have been used to establish nondecreasing technological returns to scale.

The scheduling and organization of periodic associative computation: Essential networks

Abstract. This paper characterizes the efficient decentralized networks for calculating the associative aggregate of cohorts of data of a fixed size that arrive periodically. Radner (1993) proposed this problem of periodic parallel associative computation as a model of the ongoing information processing and communication by the administrative staff of a large organization. For a simpler model in which the organization processes a single cohort of data – which is equivalent to the periodic model when the agents are paid only when busy – he found that the efficient networks are hierarchical but quite irregular, even though the computation problem and technology are each symmetric. In the periodic model in which managers are paid even when idle, it becomes important to minimize idle time when scheduling managers to processing tasks. Such scheduling appears more difficult when each problem is processed by an irregular hierarchy, which suggest that hierarchies might be more regular in the periodic model. However, we show that in a class of efficient networks for periodic computation that spans the efficiency frontier, the processing of each cohort is similar to the efficient processing of a single cohort, and the overall organizational structure is not even hierarchical.

Does WTO Matter for the Extensive and the Intensive Margins of Trade

We use 6-digit bilateral trade data to document the effect of WTO/GATT membership on the extensive and intensive product margins of trade. We construct gravity equations for the two product margins where the specifications of these gravity equations are motivated by the model of Eaton and Kortum (2002). The data show that the puzzle of no significant impact of WTO membership on trade documented by Rose (2004) manifests itself differently at the product margins of trade. We show that the impact of the WTO is almost exclusively on the extensive product margin of trade, i.e. trade in goods that were not previously traded. In our preferred specification, WTO membership increases the extensive margin of exports by 31%. At the same time, WTO membership has a negligible or even a negative impact on the intensive margin (the volume of already-traded goods). Incidentally, we also document that standard gravity variables provide good explanatory power for bilateral trade on both margins.

The effect of WTO on the extensive and the intensive margins of trade

We use 6-digit bilateral trade data to document the effect of WTO/GATT membership on the extensive and intensive product margins of trade.We construct gravity equations for the two product margins motivated by Chaney (2008). The empirical results show that standard gravity variables provide good explanatory power for bilateral trade on both margins. Importantly, we show that the impact of the WTO is concentrated almost exclusively on the extensive product margin of trade, i.e. trade in goods that were not previously traded. In our preferred specification, WTO membership increases the extensive margin of exports by 25%. At the same time, WTO membership has a negative impact on the intensive margin. Based on novel comparative statics results about how fixed and variable trade costs impact the product margins of trade, our results suggest that WTO membership works by reducing primarily the fixed rather than the variable costs of trade.

Interim Bayesian Nash Equilibrium on Universal Type Spaces for Supermodular Games

We prove the existence of a greatest and a least interim Bayesian Nash equilibrium for supermodular games of incomplete information. There are two main differences from the earlier proofs in Vives (1990) and Milgrom and Roberts (1990): we use the interim formulation of a Bayesian game, in which each players beliefs are part of his or her type rather than being derived from a prior; we use the interim formulation of a Bayesian Nash equilibrium, in which each player and every type (rather than almost every type) chooses a best response to the strategy profile of the other players. Given also the mild restrictions on the type spaces, we have a proof of interim Bayesian Nash equilibrium for universal type spaces (for the class of supermodular utilities), as constructed, for example, by Mertens and Zami (1985)? We also weaken restrictions on the set of actions.

Hierarchical computation of the resource allocation problem

Some recent research on information processing in organizations has treated the agents who process information as endogenous. This paper discusses a sample of models in this area, which differ in their methodology but are unified by the fact that they study the resource allocation problem. Computational constraints are related to the structure and returns to scale of hierarchies.

Hierarchy Size and Environmental Uncertainty

We examine how a firms changing environment and the information constraints of its managers interact as determinants of the size of the firms administration. Following the recent decentralised information processing literature, we assume that it takes individual managers time to process information. A consequence is that it takes time for a firm to aggregate information, even when this task is shared. This delay increases with the amount of information that is aggregated, leading to the following trade-off: the more data the firm samples each period (and hence the larger its managerial staff), the more precisely it can estimate the state that its environment was in when the sample was taken but the more the environment has changed by the time these data are used to estimate the current state. We explore this trade-off for two computation models and for both a benchmark case of costless managers and the case of costly managers. When managers are costless, the size of the administrative staff increases monotonically, as the environment becomes more stable. In contrast, when managers are costly, optimal managerial size first increases and then decreases as a function of environmental stability.