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remove the caption in exercise for latex build error
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lectures/_static/quant-econ.bib

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@@ -5307,14 +5307,15 @@ @article{BergemannValimaki1997
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year = {1997}
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}
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@article{BergemannValimaki1996,
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@article{BergemannValimaki2000,
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author = {Bergemann, Dirk and V{\"a}lim{\"a}ki, Juuso},
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title = {Learning and Strategic Pricing},
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journal = {Econometrica},
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volume = {64},
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number = {5},
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pages = {1125--1149},
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year = {1996}
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title = {Experimentation in Markets},
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journal = {Review of Economic Studies},
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volume = {67},
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number = {2},
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pages = {213--234},
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year = {2000},
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doi = {10.1111/1467-937X.00128}
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}
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@article{BoltonHarris1999,

lectures/market_diffusion.md

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@@ -731,7 +731,7 @@ undiscounted limit to keep the Bellman equations tractable, comes from
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{cite:t}`BoltonHarris1999`, who were the first to study strategic experimentation in
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continuous time.
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A companion paper, {cite:t}`BergemannValimaki1996`, studies the same duopoly with a
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A companion paper, {cite:t}`BergemannValimaki2000`, studies the same duopoly with a
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continuum of *identical* consumers.
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Homogeneity there rules out market sharing, so the horizontal differentiation that
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Here is one solution:
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```{code-cell} ipython3
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---
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mystnb:
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figure:
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caption: The value of information to each firm
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name: fig-md-voi
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---
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Ai = np.linspace(0.005, 0.995, 2001)
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voi_1 = v1(mkt, Ai) - (1 - n_eq(mkt, Ai)) * p1(mkt, Ai)
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voi_2 = v2(mkt, Ai) - n_eq(mkt, Ai) * p2(mkt, Ai)
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axes[1].set(xlabel=r'$\alpha$', yscale='log',
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title='second derivatives of the value functions')
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axes[1].legend(fontsize=9)
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fig.suptitle('The value of information to each firm')
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fig.tight_layout()
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plt.show()
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