Product differentiation and location decisions under demand uncertainty

We investigate Hotelling's duopoly game of location-then-price choices with quadratic transportation costs and uniformly distributed consumers under the assumption that firms are uncertain about the exact location of demand. We characterize the unique equilibrium and the socially optimal locations. Contrary to the individual-level random utility models, location uncertainty is a differentiation force. In equilibrium, increases in the variance of the uncertainty lead to greater differentiation, higher expected equilibrium prices and profits, and a greater welfare loss.     

Evolution of market shares with repeated purchases and heterogeneous network externalities

We investigate how market shares change when a new, superior technology exhibiting network externalities is introduced in a market initially dominated by an old technology. This is done under the assumption that consumers are heterogeneous in their valuation of technology quality and network externalities and that goods are not (perfectly) durable and thus have to be bought repeatedly. When both technologies are unsponsored, the old technology dominates when the quality difference is small, and it disappears when the quality difference is large. When the new technology is sponsored, the relationship between the quality difference and the long-run market share of the new technology is non-monotonic and the old technology always continues to exist.

Consumer cohorts and purchases of nonalcoholic beverages

Age, period and cohort (APC) variables are included in a demand system that is used to estimate Norwegian purchases of nonalcoholic beverages. To take account of censoring, a two-step method is used. In the first step, the probabilities of purchasing milk, carbonated soft drinks and other soft drinks are estimated by probit models. The APC variables are highly significant. Older cohorts have higher probabilities of purchasing milk and lower probabilities of purchasing carbonated soft drinks than younger cohorts. In the second step, the probability density functions and the cumulative density function are used to correct for censoring. In the corrected demand system, there are positive cohort and negative age effects for milk. These effects suggest that the replacement of older by younger cohorts, in an increasingly older population, will result in reduced per capita purchases of milk. For carbonated soft drinks, there are no cohort or negative age effects, while there are positive age but no cohort effects for other soft drinks.     

Enterprise purchases and the expectation of rationing

One reason why an excess supply of inputs is claimed not to occur in socialist economies is that the anticipation of future rationing makes managers by up all input materials even if not needed for current production. It is shown with a simple inventory model that such anticipations do shift some input purchases from the future to the present but that the effect can be small for many values of the parameters.     

Cultural norms and values and purchases of counterfeits

We conjecture that an important driver of individual purchases of counterfeit products is cultural norms and values. To put this conjecture to an empirical test, we make use of the unique situation of Surinamese people who live in Suriname and in the Netherlands and who might share the same norms and values but certainly not their respective income levels and demographics. Holding newly collected data from surveys amongst Surinamese individuals in the Netherlands and in Suriname against a control group of Dutch individuals in the Netherlands, we present evidence that cultural norms are indeed a key driver for purchases of counterfeit products. Implications for policy are discussed.     

Politico-economic inequality and the comovement of government purchases

This paper explores the implications of economic and political inequality for the comovement of government purchases with macroeconomic fluctuations. We set up and compute a heterogeneous-agent neoclassical growth model, where households value government purchases which are financed by income taxes. A key feature of the model is a wealth bias in the political aggregation process. When calibrated to U.S. wealth inequality and exposed to aggregate productivity shocks, such a model is able to generate weaker positive comovement of government purchases than models with no political wealth bias. The wealth bias that matches the cross-sectional campaign contribution distribution by income is consistent with the mild positive comovement of government purchases in the aggregate data. We thus provide an empirically relevant example where economic and political heterogeneity matter for aggregate dynamics.     

Psychologically-based voting with uncertainty

We analyse a psychologically-based model of voter turnout in an election with common value and uncertainty about who the best candidate is. Potential voters' behaviour is based on anticipated regret, where voters will experience regret if they fail to vote or vote for the wrong candidate. Furthermore, such regret is stronger when the margin of victory is smaller. We characterize mixed and pure-strategy equilibria, which can be desirable, where the right candidate is always elected in all states, or undesirable, where the wrong candidate is elected in some state. Our model yields distinctive comparative statics results. First, an increase in the proportion of informed citizens may cause the winning margin for the right candidate to either rise or fall, depending on the type of equilibrium. In addition, such an increase can have a non-monotonic effect on turnout of uninformed citizens. Second, as the prior becomes more favourable towards the ex ante favoured candidate, turnouts of informed and uninformed voters both change in a non-monotonic way. Furthermore, total turnout can be positively or negatively correlated with winning margins. The distinctive implications of our model could be tested using experimental or empirical studies. In addition, given its inclusion of uncertainty, our model can be used to study, in future research, information provision and acquisition as well as other policy questions.     

A theory of search with deadlines and uncertain recall

We ask how the ability to recall past prices affects the dynamics of search and price formation. In the model, buyers have limited time to purchase a good and face uncertainty regarding the availability of past price quotes in the future. Sellers cannot observe a potential buyer’s remaining time until deadline nor her quote history, and hence post prices that weigh the probability of sale versus the profit once sold. We find that, in contrast to conventional wisdom, reducing the consumer’s recall ability may actually improve his expected utility because it lowers the average expected price in the market and reduces the duration of search.     

Irreversible investment with uncertainty and strategic behavior

The paper provides a model of technology adoption in the case where adopting alone is more expensive than adopting when others have already done so (network effect). In addition, if each agent gains at the expense of his rivals, he may also have an incentive for ‘preemptive adoption’. We deal with these two issues in a dynamic programing framework, where adoption is seen as a strategic switching time decision problem for agents facing an ongoing stochastic operating benefit plus sunken investment costs. The model defines the option value of investing for a continuous time stochastic game. In the case of network benefits alone, agents follow a stationary bandwagon strategy, representing the effect caused by a war of attrition. Yet, as network benefits reduce adoption costs after an agent has switched, rivals may follow suit. In the opposite case, where going first gives the innovator a higher payoff the bandwagon rule is turned over and the option value of investing first may be lower than that of going second. This gives rise to sequential adoption.     

Auctions with private uncertainty and resale opportunities

When an auction is followed by an opportunity for resale, bidder valuations are endogenously determined, reflecting anticipated profit from buying/selling in the resale market. These valuations vary with the resale market structure, can differ across auction types, and may be lower or higher than if resale were impossible. Although resale introduces a common value element to the model, revenue equivalence can hold; when it fails, this is due not to affiliation but to differences in information conveyed to the secondary market. Information linkages between markets can also lead to signaling and, in some cases, preclude separation in the auction.     

Transferable utility games with uncertainty

We introduce the concept of a TUU-game, a transferable utility game with uncertainty. In a TUU-game there is uncertainty regarding the payoffs of coalitions. One out of a finite number of states of nature materializes and conditional on the state, the players are involved in a particular transferable utility game. We consider the case without ex ante commitment possibilities and propose the Weak Sequential Core as a solution concept. We characterize the Weak Sequential Core and show that it is non-empty if all ex post TU-games are convex.     

Long-run industry equilibrium with uncertainty

In this paper we consider the effects of uncertainty on industry equilibrium when firms must commit themselves to production before prices are revealed. We show that (a) an increase in demand uncertainty will (i) not affect the equilibrium number and size of firms if they are risk neutral, (ii) reduce the equilibrium number of firms if they are risk averse, but will have an ambiguous effect on their size. (b) In equilibrium, firms operate at capacity if they are risk neutral, but at excess capacity if they are risk averse.     

Anticipatory pricing with negligible uncertainty

If firms precommit to output, and price equates either expected excess demand or excess demand when demand takes its expected value to zero, then equilibrium price and output typically do not converge to their Walrasian levels as demand becomes decreasingly risky.     

Intertemporal equilibria with Knightian uncertainty

We study a dynamic and infinite-dimensional model with incomplete multiple prior preferences. In interior efficient allocations, agents share a common risk-adjusted prior and subjective interest rate. Interior efficient allocations and equilibria coincide with those of economies with subjective expected utility and priors from the agents? multiple prior sets. A specific model with neither risk nor uncertainty at the aggregate level is considered. Risk is always fully insured. For small levels of ambiguity, there exists an equilibrium with inertia where agents also insure fully against Knightian uncertainty. When the level of ambiguity exceeds a critical threshold, full insurance no longer prevails and there exist equilibria with inertia where agents do not insure against uncertainty at all. We also show that equilibria with inertia are indeterminate.     

Persuasion games with higher-order uncertainty

Shin (J. Econom. Theory 64 (1994) 253–264) showed that a perfectly revealing equilibrium fails to exist in persuasion games when the decision maker is uncertain about the interested party's payoff-relevant information. By explicitly integrating higher-order uncertainty into the information structure, this note shows that a perfectly revealing equilibrium does exist when disclosures are not restrained to intervals of the payoff-relevant state space.     

Coasean bargaining with symmetric delay costs

Delay costs play a role in Coasean bargaining over environmental conflicts when an injunction restricts actions until a settlement is reached. Results from the lab suggest that efficiency remained relatively robust to discrete and increasing marginal delay costs, but declined significantly with nonincreasing marginal delay costs. Bargainers appear to deal with probability and consequences separately rather than in combination as maintained by expected utility theory, and as such, neglect ends over means. How the distribution of wealth is best organized depends on perspective: constrained self-interest best organizes behavior if expected utility is maintained; pure self-interest dominates if we acknowledge the probability–consequence heuristic.     

Speculative trading with rational beliefs and endogenous uncertainty

Summary. This paper introduces the framework of rational beliefs of Kurz (1994), which makes the assumptions of heterogeneous beliefs of Harrison and Kreps (1978) and Morris (1996) more plausible. Agents hold diverse beliefs that are “rational” in the sense of being compatible with ample observed data. In a non-stationary environment the agents only learn about the stationary measure of observed data, but their beliefs can remain non-stationary and diverse. Speculative trading then stems from disagreements among traders. In a Markovian framework of dividends and beliefs, we obtain analytical results to show how the speculative premium depends on the extent of heterogeneity of beliefs. In addition, we demonstrate that there exists a unique Rational Belief Equilibrium (RBE) generically with endogenous uncertainty (as defined by Kurz and Wu, 1996) and that the RBE price is higher than the rational expectation equilibrium price (REE) under some general conditions Received: March 15, 2001; revised version: April 26, 2002 RID="*" ID="*" We are deeply grateful to Mordecai Kurz for his constant encouragement and inspiring guidance over the years. We wish to express our gratitude to an anonymous referee for the very valuable comments provided. We also thank Kenneth Arrow, Peter Hammond, Roko Aliprantis and Nicholas Yannelis for their helpful suggestions and Academia Sinica and the National Science Council of the R.O.C. for their indispensable support. Correspondence to: H.-M. Wu     

Informational size and incentive compatibility with aggregate uncertainty

In McLean and Postlewaite (Econometrica 56, 1992, p. 2421), we analyzed pure exchange economies with asymmetrically informed agents. We defined a notion of informational size and showed that, when the aggregate information of all agents resolves nearly all the uncertainty regarding the state of nature, the conflict between incentive compatibility and (ex post) efficiency can be made small if agents have sufficiently small informational size. This paper investigates the relationship between informational size and efficiency for the case in which nontrivial aggregate uncertainty is present, i.e., when significant uncertainty about the world persists even when the information of all agents is known.     

Representing roommates’ preferences with symmetric utilities

In the context of the stable roommates problem, it is shown that acyclicity of preferences is equivalent to the existence of symmetric utility functions, i.e. the utility of agent i when matched with j is the same as j's utility when matched with i.