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Dynamic Games and Applications
Erschienen in: Dynamic Games and Applications 1/2014

01.03.2014

Learning and Technological Progress in Dynamic Games

verfasst von: Leonard J. Mirman, Marc Santugini

Erschienen in: Dynamic Games and Applications | Ausgabe 1/2014

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Abstract

We study investment and consumption decisions in a dynamic game under learning. To that end, we present a model in which agents not only extract a resource for consumption but also invest in technology to improve the future stock. At the same time, the agents learn about the stochastic process governing the evolution of public capital, including the effect of investment in technology on future stock. Although the characterization of a dynamic game with Bayesian dynamics (and without the assumption of adaptive learning) is generally intractable, we characterize the unique symmetric Bayesian-learning recursive Cournot–Nash equilibrium for any finite horizon and for general distributions of the random variables. We also show that the limits of the equilibrium outcomes for a finite horizon exist. The addition of learning to a stochastic environment is shown to have a profound effect on the equilibrium.
Vorheriger Artikel Adaptation and the Allocation of Pollution Reduction Costs
Nächster Artikel Do Social Status Seeking Behaviors Worsen the Tragedy of the Commons?

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Fußnoten
1
There is a two-way interaction between decision-making and learning. On the one hand, decision-making may have an effect on learning, which is referred as experimentation. On the other hand, the presence of learning adds risk which affects future payoffs and thus behavior.
 
2
In a different context, Mirman and To [12] have addressed the issue of investing in capital in an overlapping generation model.
 
3
See Bernhardt and Taub [3] for a recent paper on learning in oligopoly when the firms learn from prices.
 
4
There is no experimentation in our model. For the literature on single-agent experimentation with capital accumulation, see Freixas [8], Bertocchi and Spagat [4], Datta et al. [5], El-Gamal and Sundaram [6], Huffman and Kiefer [9], and Beck and Wieland [2].
 
5
There is no adaptive learning. Under adaptive learning, agents are bounded because they assume that beliefs will not change over time, i.e., they do not anticipate learning. See Evans and Honkapohja [7] for a detailed exposition of adaptive learning.
 
6
One popular approach is to rely on the fact that the family of normal distributions with an unknown mean is a conjugate family for samples from a normal distribution.
 
7
A tilde sign is used to distinguish a random variable from its realization.
 
8
Since the investment goods are perfectly substitutable, there exist many equilibrium points in which only total investment can be determined. However, for any equilibrium and for any horizon, total investment remains the same whereas individual investment changes.
 
9
Plugging (31) into (21) (ignoring the constant) and taking limits yields (52).
 
10
Evaluating (52) at the true distribution (i.e., θ ∗ is known) yields (54).
 
Literatur
1.
Antoniadou E, Koulovatianos C, Mirman LJ (2013) Strategic exploitation of a common property resource under uncertainty. J Environ Econ Manag 65(1):28–39 CrossRef
2.
3.
Bernhardt D, Taub B (2011) Oligopoly learning dynamics. Working Paper
4.
Bertocchi G, Spagat M (1998) Growth under uncertainty with experimentation. J Econ Dyn Control 23(2):209–231 CrossRefMATH
5.
Datta M, Mirman LJ, Schlee EE (2002) Optimal experimentation in signal-dependent decision problems. Int Econ Rev 43(2):577–607 CrossRefMathSciNet
6.
El-Gamal MA, Sundaram RK (1993) Bayesian economists… Bayesian agents: an alternative approach to optimal learning. J Econ Dyn Control 17(3):355–383 CrossRefMATHMathSciNet
7.
Evans GW, Honkapohja S (2001) Learning and expectations in macroeconomics. Princeton University Press, Princeton
8.
9.
Huffman GW, Kiefer NM (1994) Optimal learning in a one-sector growth model. Working Papers 90-24, Cornell University, Center for Analytic Economics
10.
11.
Levhari D, Mirman LJ (1980) The great fish war: an example using a dynamic Cournot–Nash solution. Bell J Econ 11(1):322–334 CrossRefMathSciNet
12.
Mirman LJ, To T (2005) Strategic resource extraction, capital accumulation and overlapping generations. J Environ Econ Manag 50(2):378–386 CrossRefMATH
Metadaten
Titel
Learning and Technological Progress in Dynamic Games
verfasst von
Leonard J. Mirman
Marc Santugini
Publikationsdatum
01.03.2014
Verlag
Springer US
Erschienen in
Dynamic Games and Applications / Ausgabe 1/2014
Print ISSN: 2153-0785
Elektronische ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-013-0089-4

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