The 'Savage paradigm' of rational decision-making under uncertainty has become the dominant model of human behavior in mainstream economics and game theory. 'Bounded rationality' refers to the study of how human decision-makers deal with their cognitive limitations that may prevent them from fully applying the Savage paradigm to real problems without entirely abandoning the notion of rationality. This article sketches the historical roots and current developments of this topic, distinguishing between attempts to extend the Savage paradigm ('costly rationality') and the development of more radical departures.

We present a model of dynamic monopoly pricing for a good that displays network effects. In contrast with the standard notion of a rational-expectations equilibrium, we model consumers as boundedly rational and unable either to pay immediate attention to each price change or to make accurate forecasts of the adoption of the network good. Our analysis shows that the seller’s optimal price trajectory has the following structure: The price is low when the user base is below a target level, is high when the user base is above the target, and is set to keep the user base stationary once the target level has been attained. We show that this pricing policy is robust to a number of extensions, which include the product’s user base evolving over time and consumers basing their choices on a mixture of a myopic and a “stubborn” expectation of adoption. Our results differ significantly from those that would be predicted by a model based on rational-expectations equilibrium and are more consistent with the pricing of network goods observed in practice.

Global warming is now recognized as a significant threat to sustainable development on an international scale. One of the key challenges in mounting a global response to it is the seeming unwillingness of the fastest growing economies such as China and India to sign a treaty that limits their emissions. The aim of this paper is to examine the differential incentives of countries on different trajectories of capital growth. A benchmark dynamic game to study global warming, introduced in Dutta and Radner (J Econ Behav Organ, 2009 ), is generalized to allow for exogenous capital accumulation. It is shown that the presence of capital exacerbates the “tragedy of the common”. Furthermore, even with high discount factors, the threat of reverting to the inefficient “tragedy” equilibrium is not sufficient to deter the emissions growth of the fastest growing economies—in contrast to standard folk theorem like results. However, foreign aid can help. If the slower growth economies—like the United States and Western Europe—are willing to make transfers to China and India, then the latter can be incentivized to cut emissions. Such an outcome is Pareto improving for both slower and faster growth economies.

We model the global warming process as a dynamic commons game in which the players are countries, their actions at each date produce emissions of greenhouse gases, and the state variable is the current stock of greenhouse gases. The theoretical analysis is complemented by a calibration exercise. The first set of results establishes theoretically, and then with illustrative numbers, the over-emissions due to a “tragedy of the commons.” The power of simple sanctions to lower emissions and increase welfare is then examined as is the effect of cost asymmetry. Finally, a complete theoretical charactrization is provided for the best equilibrium, and it is shown that it has a very simple structure; it involves a constant emission rate through time.

This note reports part of a larger study of “petty corruption“ by government bureaucrats in the process of approving new business projects. Each bureaucrat may demand a bribe as a condition of approval. Entrepreneurs use the services of an intermediary who, for a fee, undertakes to obtain all of the required approvals. In a dynamic game model we investigate (1) the multiplicity of equilibria, (2) the equilibria that are “socially efficient”, and (3) the equilibria that maximize the total expected bureaucrats’ bribe income. We compare these results with those for the case in which entrepreneurs apply directly to the bureaucrats.

The paper explores a game-theoretic model of petty corruption involving a sequence of entrepreneurs and a track of bureaucrats. Each entrepreneur's project is approved if and only if it is cleared by each bureaucrat. The project value is stochastic; its value is observed only by the entrepreneur, but its distribution is common knowledge. Each bureaucrat clears the project only if a bribe is paid. The bribe for qualified projects (extortion) and unqualified projects (capture) may differ. We identify the nature and welfare implications of different types of equilibria under appropriate technical assumptions on the structure of the game.

This article reviews alternative approaches to incorporating uncertainty in Walrasian models. It begins with a sketch of the Arrow–Debreu model of complete markets. An extension of this framework allowing for economic agents to have different information about the environment is followed by a critique. When markets are incomplete and trades take place sequentially, several types of equilibrium concept arise according to the hypotheses we make about the way traders form their expectations. We present conditions for the existence of equilibria for two such equilibrium concepts, and discuss the possible failure to attain Paretian welfare optima.

This paper develops a game-theoretic model of petty by government officials. Such corruption is widespread, especially (but not only) in developing and transition economies. The model goes beyond the previously published studies in the way it describes the structure of bureaucratic tracks and the information among the participants. Entrepreneurs apply, in sequence, to a track of two or more bureaucrats in a prescribed order for approval of their projects. Our first result establishes that in a one-shot situation no project ever gets approved. This result leads us to consider a repeated interaction setting. In that context we characterize in more detail the trigger-strategy equilibria that minimize the social loss due to the system of bribes, and those that maximize the expected total bribe income of the bureaucrats. The results are used to shed some light on two much advocated anti-corruption policies: the single window policy and rotation of bureaucrats.

Flooded by a large number of variables found by modern business intelligence applications, pricing managers are perplexed by the task of selecting variables for price discrimination. However, relevant literature remains scarce. This dissertation attempts to investigate how sellers should determine the optimal or equilibrium combination of pricing metrics in a monopoly or duopoly industry. In the second chapter, I develop a model that closely resembles linear regression and probit regression to solve the pricing metrics selection problem. The criterion found is similar to the selection of independent variables for linear regression; it is revenue-maximizing to select the variable that best reduces the residual variance of buyer's willingness-to-pay. In the third chapter, I investigate the metrics selection problem by a general linear duopoly demand system. This model suggests that the value of information embedded in pricing metrics depends on two factors: (1) The explanatory power of product demands: equivalently, metrics that best reduce residual variance of demands are good candidates. (2) The price and demand coefficients: specifically, this study shows that when these two products are substitutes and the pricing metric affects two demand curves in the sauce direction (different directions), duopoly sellers should adopt that pricing metric simultaneously (unilaterally) in the equilibrium. When two products are complements, these effects are reversed. In the last chapter, a two-product monopoly model is examined in a setup that matches the second paper. The optimal metrics selection is qualitatively similar to the equilibrium metrics selection in the second paper. This model shows that it is more profitable for the centralized monopoly to use pricing metrics than decentralized duopoly.

In the absence of a world government, stopping the advance of global warming requires implementation of self-enforcing treaties among the countries of the world. In the language of game theory, such treaties are Nash equilibria of an underlying dynamic "climate change game." In this paper, we report on the progress of a project to formulate and analyze models of such a game. The players are the sovereign countries of the world (say the roughly 200 members of the United Nations). The rules of this game are determined by the laws of physics and chemistry, and by the economic resources of the various countries. An important property of our models is the large multiplicity of equilibria. Indeed, this property enables us to find "Pareto-improving" equilibria, i.e., that improve the outcome for every country relative to the "business-as-usual equilibrium" we seem to be in at the present time. In each model we describe the set of equilibria, the business-as-usual equilibrium, and equilibria that are Pareto-improving relative to business-as-usual. Since much of the global warming is caused by the accumulation of greenhouse gases (GHGs) in the earth's atmosphere, and the GHGs dissipate very slowly, an appropriate model must be in the form of a dynamic game, with state variables that change over time as a consequence of the actions of the individual countries. Thus, the state variables include the global stock of GHG and the state of the relevant technology in each country.

Price discrimination has been ubiquitous in the business world for decades. More recently, advances in information technologies have enabled sellers to collect and store customer information much more cost-e¤ectively. Equipped with analytical tools from burgeoning research in data mining, sellers learn more about each customer’s purchasing pattern, and have begun to personalize prices and product o¤erings to each customer. Amazon.com has experimented with o¤ering di¤erent customers di¤erent prices on DVD titles based on their purchase history. In another example, the Dell Latitude L400 ultralight laptop was listed at $2,307 on the company’s Web page catering to small businesses. On the Web page for sales to health-care companies, the same machine was listed at $2,228, or 3% less. For state and local governments, it was priced at $2,072.04, or 10% less than the price for small businesses. Stimulated by abundant business applications, economists have studied price discrimination extensively for years. Stole (2003) provides a recent survey of price discrimination in the economics literature. However, most of the economic studies focused on price discrimination with one pricing metric, which created a wide gap between the economics and data mining literatures. In the data mining literature, researchers designed various algorithms to discover purchase-decision patterns using a large number of variables. Our multidimensional model attempts to bridge this gap. Also, the economics literature has mainly concentrated on the welfare and consumer-surplus e¤ects of opening new markets or adopting personalized pricing technologies. Few articles discussed the selection of pricing metrics. This is becoming increasingly important, e.g., in the case of enterprise software licensing, whose complexity is growing because of the trend towards licensing software on a subscription or usage basis. However, unlike electricity and gas, the usage of software or server products is not measurable. As a consequence, software vendors are experimenting with di¤erent proxy variables for pricing. The present study develops a model tailored to the metrics selection problem. Our model is related to the menu cost literature (Hanson and Martin, 1990) but the formulation is di¤erent. In practice, the pricing metrics of enterprise software are di¤erent across vendors for similar products, or even for the same product in di¤erent generations. For example, in 2003, Sun Microsystems changed radically to o¤er the Java Enterprise System at a …xed annual cost of $100 per employee. Microsoft introduced per-processor licensing terms for eight server products in 2003. IBM mainframe and complementary products have long been priced based on the horsepower (MIPS) of the hardware. Oracle was …rst priced based on the number of CPUs of the server. They once experimented for two years with licensing based on the speed of the CPU, but abandoned it after Oracle 9i. In 2005, Oracle adjusted its per-CPU licensing to accommodate newly invented multicore chips. Interestingly, di¤erent vendors also treat modern multicore chips di¤erently. Some vendors (e.g. Microsoft SQL Server) price one chip as one CPU whereas the others (e.g. IBM DB2 and Oracle before 2005) price it as multiple CPUs. At the same time, HP, IBM, and Sun are independently developing new usage metrics for on-demand computing (utility computing), and have proposed di¤erent metrics. This phenomenon motivates our research questions: (1) How does the design of an optimal pricing schedule vary with the number and combination of metrics on which pricing is based? (2) How should a seller choose the optimal combination of pricing metrics?

Global warming (GW) is now recognized as a significant threat to sustainable development on an international scale. After providing some introductory background material, we introduce a benchmark dynamic game within which to study the GW problem. The model allows for population growth and is subsequently generalized to allow for changes in technology. In each case, a benchmark “Business as Usual” (BAU) equilibrium is analyzed and contrasted with the efficient solution. Furthermore, a complete characterization is provided in the benchmark model of the entire subgame perfect equilibrium value correspondence.

A modern firm often employs multiple production technologies based on distinct engineering principles, causing non-convexities in the firm's unit cost as a function of product quality. Extending the model of Mussa and Rosen (1978), this paper investigates how a monopolist's product line design may crucially depend on the non-convexities in the unit cost function. We show that the firm does not offer those qualities where the unit cost exceeds its convex envelope. Consequently, there are gaps in its optimal quality choice. When the firm is only permitted to offer a limited number of quality levels (due to possible fixed costs associated with offering each quality), the optimal location of quality levels still lies within those regions of the quality domain where the unit cost function coincides with its convex envelope. We further show that the firm's profit is a supermodular function of its quality levels, and characterize a necessary condition for the optimal quality location

We revisit the issue of product line design by a monopolist and extend the model of Mussa and Rosen (1978) in two ways. First, we consider the case in which the unit cost is a nonconvex function of product quality. We show that the firm does not offer those qualities where the unit cost is linear or exceeds its lower convex envelope. Consequently, there are gaps in its optimal quality choice. Second, when the firm can offer only a limited number of quality levels (due to possible fixed costs), we characterize the optimal location of these finitely many quality levels. This characterization again has the property that none of these qualities will lie within an interval where the unit cost is linear or exceeds its lower convex envelope. Several implications of the above results are discussed.

In the absence of world government, an effective treaty to control the emissions of greenhouse gases should be self-enforcing. A self-enforcing treaty has the property that, if a country expects other countries to abide by the treaty, it will be in the self-interest of that country to abide by the treaty too. (A difficulty with the Kyoto Protocol is that it does not appear to lay the groundwork for a self-enforcing treaty). A self-enforcing treaty can be modeled as a Nash equilibrium of a suitably defined dynamic game among a large number of sovereign countries of diverse sizes and economic capabilities. We study such a game and characterize its equilibria (typically there are many) and the global-Pareto-optimal solutions. We identify one of the equilibria, which we call "business as usual," with the current situation. The multiplicity of equilibria provides an opportunity to move from the inefficient business-as-usual equilibrium to one or more equilibria that are Pareto-superior. Using a calibrated model with 184 countries, we give numerical illustrations of business-as-usual and global-Pareto-optimal trajectories and estimate the potential welfare gains from a self-enforcing treaty.

In many markets, demand adjusts slowly to changes in prices, i.e., demand is "viscous". This viscosity gives each firm some monopoly power, since it can raise its price above that of its competitors without immediately losing all of its customers. The resulting equilibrium pricing behavior and market outcomes can differ significantly from what one would predict in the absence of demand viscosity. In particular, the model explains the importance of market share as an investment, as well as "kinked demand curves". It also explains how apparently "competitive" pricing behavior can lead to outcomes that mimic those of collusion.

Call a perfect information (PI) game simple if each player moves just once. Call a player rational if he never takes an action while believing, with probability 1, that a different action would yield him a higher payoff. Using syntactic logic, we show that an outcome of a simple PI game is consistent with common strong belief of rationality iff it is a backward induction outcome. The result also applies to general PI games in which a player's agents act independently, rendering forward inferences invalid.