Strategic experimentation with asymmetric players

Abstract

We examine a two-player game with two-armed exponential bandits à la (Keller et al. in Econometrica 73:39-68, 2005), where players operate different technologies for exploring the risky option. We characterise the set of Markov perfect equilibria and show that there always exists an equilibrium in which the player with the inferior technology uses a cutoff strategy. All Markov perfect equilibria imply the same amount of experimentation but differ with respect to the expected speed of the resolution of uncertainty. If and only if the degree of asymmetry between the players is high enough, there exists a Markov perfect equilibrium in which both players use cutoff strategies. Whenever this equilibrium exists, it welfare dominates all other equilibria. This contrasts with the case of symmetric players, where there never exists a Markov perfect equilibrium in cutoff strategies. Keywords Two-armed bandit • Heterogeneous agents • Free riding • Learning JEL Classification C73 • D83 • O31 The second author gratefully acknowledges support from the Social Sciences and Humanities Research Council of Canada. Part of the results presented in this paper was already contained in the third author's undergraduate thesis, entitled "Strategisches Experimentieren mit asymmetrischen Spielern", which she submitted at the University of Munich in 2009 under her maiden name Tönjes.

Do Stronger Patents Lead to Faster Innovation? The Effect of Clustered Search

“…Our model builds on the literature on strategic experimentation with bandits, started by Bolton and Harris (1999). In particular, we use a variant of the exponential model of Keller et al (2005), into which Das et al (2020) has introduced asymmetric players. Besanko and Wu (2013) has introduced payoff externalities into the model, applying it to an R&D race.…”

“…(2005), into which Das et al. (2020) has introduced asymmetric players. Besanko and Wu (2013) has introduced payoff externalities into the model, applying it to an R&D race.…”

“…This insight also applies in a setting without payoff externalities, seeDas et al (2020).20 Boyarchenko (2019) analyzes a game of strategic experimentation with irreversible action choice in which the hazard rate of a breakthrough is increasing in the time spent pursuing it.…”

Special Issue: Supermodularity and Monotonicity in Economics

“…Unlike standard experimentation models with Poisson bandits (e.g. Das et al 2020), the news arrival rate is hump or inverse U-shaped over time. In contrast to Poisson bandits, "humped" bandits are suitable for studying long-term negative effects of experimentation such as, e.g., harmful pollutants or drugs that have a potential for accumulation and long term storage in a human body; or positive effects, such as accumulated effort of economic agents or resources.…”

Strategic investment evaluation

“…Our paper is most closely connected to models of collective experimentation, in particular Bonatti and Hörner (2011, 2017), Bolton and Harris (1999), Keller, Rady, and Cripps (2005), Keller and Rady (2010, 2015), and Dong (2021). 3 These papers study environments in which effort simultaneously dictates both the production and the aggregation of information.…”