Studies of Bounded Rationality and Overconfidence in Dynamic Games

Abstract

\\abstract Managers constantly make decisions that depend, at least in part, on what they believe their competitors (or customers, or employees) will do in response. These judgments are susceptible to error. Indeed, behavioral research suggests a widespread bias towards underestimating others. To explore the ramifications of such an intuitively irrational bias, we provide a theoretical model that compares the long-run effects of consistent underestimation bias with those of consistent overestimation bias across different competitive contexts relevant to marketing managers. In the first set of analyses, we derive analytic equations to calculate the relative expected payoffs associated with conditions of overestimation bias, underestimation bias, and no bias and discern trends as a function of environmental features including game complexity and player skill levels. In the second set of analyses, we derive equations for the relative effort costs associated with each of the three bias conditions as a function of the relevant game and player parameters. We then combine the results of the expected payoffs and effort costs to determine the relative net expected payoffs associated with each bias condition as a function of game and player parameters. In the third set of analyses, we relax many of the assumptions present in the first analysis and test the relationships of interest across additional contexts including risk aversion, power imbalance, and opponent arrogance. The results across all analyses are summarized by fifteen propositions which show that, when effort is at all costly, underestimation will provide the best net expected payoff when games are above some critical level of complexity as well as when opponents have above some critical minimum level of skill. The range of underestimation's advantage compared to overestimation can be increased in contexts with high first mover advantage, when payoffs are cumulative over time, when the player is risk averse, when there is an imbalance in power between the players, and when the opponent exhibits arrogance. Furthermore, underestimation can outperform overestimation even when effort is not costly when there is a power imbalance between the players or when the player exhibits certain risk attitudes. The results provide theoretical support for the ecological rationality of underestimation bias by showing it to be advantageous under many conditions, particularly in comparison to overestimation bias. It also provides managers with prescriptive insights regarding when any opponent skill estimation error is more vs. less harmful, and when managers may fare better in the long run if they don't spend too much time trying to think through the competition's eyes..

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