Optimal Experimentation in a Changing Environment

Abstract

This paper studies optimal experimentation by a monopolist who faces an unknown demand curve subject to random changes, and who maximizes profits over an infinite horizon in continuous time. We show that there are two qualitatively very different regimes, determined by the discount rate and the intensities of demand curve switching, and the dependence of the optimal policy on these parameters is discontinuous. One regime is characterized by extreme experimentation and good tracking of the prevailing demand curve, the other by moderate experimentation and poor tracking. Moreover, in the latter regime the agent eventually becomes ''trapped'' into taking actions in a strict subset of the feasible set.

Location-then-price competition with uncertain consumer tastes

“…For work that considers learning about demand through experimentation given exogenous product characteristics see[1,17], and[22] 9. It is easy, but very tedious, to check that all equilibria satisfy the condition that the support of the uncertainty is contained in the area where firms share the market.…”

Costly switching and investment volatility

“…9 The fact that the optimal switching rule is fully characterized by the profit difference is in contrast with the results from learning models (Rothschild, 1974;McLennan, 1984;Easley and Kiefer, 1988;Rustichini and Wolinsky, 1995;Keller and Rady, 1999) where profitabilities of investments are unknown a priori. In learning models, there is a trade-off between the informational benefits and the short-run profits.…”

“…10 The threshold rule itself is not new in the literature. See, for example, Balvers and Cosimano (1993) and Keller and Rady (1999).…”

“…Curves are, from top to bottom, for β equal to 0.8, 0.5 and 0.2.17 Consult pp. 190-191 in Rothschild (1974) for an heuristic argument on the possibility of ending up with one choice forever in the Bandit problem.18 See, for example,Banks and Sundaram (1992) andKeller and Rady (1999) for such results in the learning model context.…”

Output adjusting cartels facing dynamic, convex demand under uncertainty: The case of OPEC

“…Only few papers address these or at least a subset of these characteristics. Keller and Rady (1999) consider output experimentation by a monopolist facing uncertain but static demand. Hyndman (2008) focuses on quantity setting cartels and the application to OPEC finds that bargaining is more likely to succeed in 'good times'.…”