By Karl Menger
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Additional info for Calculus: A Modern Approach, Edition: Dover Ed
Journal of Economic Dynamics and Control 18, 119–124. , 1994b. Nonconvexities in stochastic control problems: An analysis. B. ), New Directions in Computational Economics. Advances in Computational Economics, vol. 4. Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 57–94. , 1995. Nonconvexities in stochastic control models. International Economic Review 36, 455–475. , 1997. Active learning: A correction. Journal of Economic Dynamics and Control 21, 1613–1614. , 1999a. Linear-quadratic optimization for models with rational expectations.
First, as within the symmetric IPVP, each individual equation constitutes a first-order differential equation because the highest derivative term in each equation is the first derivative of the function of interest. Unlike within the symmetric IPVP, however, we now have a system of differential equations, one for each bidder. Moreover, note that the functions in this system are the inverse-bid functions ϕn (·), not the bid functions σn (·) themselves. Within the symmetric IPVP, however, we were concerned with an equilibrium in which all (homogeneous) bidders adopted the same bidding strategy σ (v).
The Rational Expectation Hypothesis, Time-varying Parameters and Adaptive Control, Springer, Dordrecht,The Netherlands. , 2010. The parameter set in an adaptive control Monte Carlo experiment: some considerations. Journal of Economic Dynamics and Control 34, 1531–1549. , 2013. Expected optimal feedback with time-varying parameters. Computational Economics 42, 351–371. , 2000a. Learning by doing and the value of optimal experimentation. Journal of Economic Dynamics and Control 24, 501–543. , 2000b.