An infinite-horizon maximum principle with bounds on the adjoint variable

Weber, Thomas A.

doi:10.1016/j.jedc.2004.11.006

Cited by 18 publications

(18 citation statements)

References 7 publications

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“…By an extension of Pontryagin's maximum principle, along the lines of ref. 6, we can prove the following: Theorem 2. If the cdf F is strictly convex, then there is a unique optimal stationary policy, α(q), that is the solution of the differential equation…”

Section: The Model With Myopic Consumersmentioning

confidence: 94%

Dynamic pricing of network goods with boundedly rational consumers

Radner

Radunskaya

Sundararajan

2013

Proc. Natl. Acad. Sci. U.S.A.

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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.A good or service is said to display network effects, or more briefly is called a network good, if the value to each consumer of the good or service is influenced by the consumption choices made by some or all other consumers. Economic models of network goods typically assume the following "unboundedly" rational consumer behavior: Consumers immediately react to each observable strategic decision made by a seller, by forming a common expectation of demand and making their consumption choices based on this expectation, which is then realized in equilibrium. This solution is commonly referred to as satisfying "fulfilled expectations" or as a rational expectations equilibrium. In the case of a monopoly, which is the context of the present paper, the seller uses the fulfilled expectations demand function to calculate her initial profit-maximizing price, which is then held constant in time.Some notion of rationality is at the base of most current economic analysis. However, in the specific case of network goods, the requirement of rational expectations equilibrium imposes heavy demands on the cognitive abilities of consumers. Furthermore, the model typically makes predictions that are unrealistic.In this paper we explore how the predictions of models of network effects change under assumptions about consumer rationality that seem more realistic. We do so by presenting a few alternative models of a monopoly market for a service with network effects, in which (i) consumers do not (all) immediately react to every change in the seller's price and, furthermore, (ii) make their consumption choices based on a "boundedly rational" assessment of expected demand. We use these models to study the resulting dynamic pricing problem for the monopolist. The adoption choices of the consumers continuously influence the rate at which demand adjusts over time, and the monopolist therefore chooses a trajectory of prices that maximizes her discounted stream of profits.In our benchmark model, consumers ar...

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Section: The Model With Myopic Consumersmentioning

confidence: 94%

Dynamic pricing of network goods with boundedly rational consumers

Radner

Radunskaya

Sundararajan

2013

Proc. Natl. Acad. Sci. U.S.A.

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“…Moreover in the growth conditions (12) and (13), roughly speaking, the inequalities need not hold for states x that cannot possibly occur, more precisely, the conditions can be modified as follows. Define for each t, …”

Section: The Control Problem Necessary Conditions and Examplesmentioning

confidence: 99%

“…The growth conditions used below, ( (11), (12), (13)) are more demanding than the conditions applied in [9] for the case of no unilateral state constraints and no terminal constraints (problems with a dominant discount). In later work the authors use even more general conditions, see [10] (see also [11], and [12] for problems with a special structure).…”

Section: Introductionmentioning

confidence: 99%

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A Maximum Principle for Smooth Infinite Horizon Optimal Control Problems with State Constraints and with Terminal Constraints at Infinity

Seierstad¹

2015

OJOp

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Necessary conditions for optimality are proved for smooth infinite horizon optimal control problems with unilateral state constraints (pathwise constraints) and with terminal conditions on the states at the infinite horizon. The aim of the paper is to obtain strong necessary conditions including transversality conditions at infinity, which in many cases lead to a set of candidates for optimality containing only a few elements, similar to what is the case in finite horizon problems. However, strong growth conditions are needed for the results to hold.

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“…In the control of heat distribution, one of the main lines of research is concerned with the elimination of the heat source with least control effect, in particular on infinite horizon. It may be noted that the optimal control problems on infinite horizon has attracted several researchers since the last decade [2][3]. The objective of this paper is to develop a computationally efficient methodology to calculate the dynamic temperature profiles by minimizing a given economic-typed performance over the linearly independent square integrable controls on the interval [0,N), say f, gAL 2 [0,N) as described in Section 3.…”

Section: Introductionmentioning

confidence: 99%