Modifying Variability and Correlations in Winner-Take-All Contests

Abstract

We consider contests with a fixed proportion of winners based on relative performance. Special attention is paid to winnertake-all contests, which we define as contests with relatively few winners receiving relatively large awards, but we consider the full range of values of the proportion of winners. If a contestant has the opportunity to modify the distribution of her performance, what strategy is advantageous? When the proportion of winners is less than one-half, a riskier performance distribution is preferred; when this proportion is greater than one-half, it is better to choose a less risky distribution. Using a multinormal model, we consider modifications in the variability of the distribution and in correlations with the performance of other contestants. Increasing variability and decreasing correlations lead to improved chances of winning when the proportion of winners is less than one-half, and the opposite directions should be taken for proportions greater than one-half. Thus, it is better to take chances and to attempt to distance oneself from the other contestants (i.e., to break away from the herd) when there are few winners; a more conservative, herding strategy makes sense when there are many winners. Our analytical and numerical results indicate that the probability of winning can change substantially as variability and/or correlations are modified. Furthermore, in a game-theoretic setting in which all contestants can make modifications, choosing a riskier (less risky) performance distribution when the proportion of winners is low (high) is the dominant best-response strategy. We briefly consider some practical issues related to the recommended strategies and some possible extensions. Subject classifications: decision analysis: strategies in contests, modifying variability, modifying correlations. Area of review: Decision Analysis.

The attraction of uncertainty: Interactions between skill and levels of uncertainty in market-entry games

“…The paradigm of Gaba et al (2004), however, differs from ours in two ways. First, their agents choose between actions implying different levels of uncertainty as opposed to between a safe option (not entering the market) and an outcome subject to uncertainty (with no control over the level experienced).…”

“…First, their agents choose between actions implying different levels of uncertainty as opposed to between a safe option (not entering the market) and an outcome subject to uncertainty (with no control over the level experienced). Second, Gaba et al (2004) do not differentiate between low-and high-skill individuals. Similarly, in the experiments reported in Gaba and Kalra (1999), performance does not depend on skill, but only on a value drawn from the distribution that each participant chooses.…”

“…Thus, it could be rational for agents to choose higher levels of uncertainty. For example, Gaba et al (2004) showed analytically that when the proportion of winners is less (greater) than 50%, by choosing a riskier (safer) performance distribution an agent improves her probability of winning the tournament. Indeed, Gaba and Kalra (1999) provide evidence supporting this conclusion in experiments simulating how sales representatives react to incentives in the form of a competition (e.g., bonuses are only paid to the best 3 of 10 representatives).…”

Sourcing Innovation: Public and Private Feedback in Contests

“…This stream was originated by Taylor (1995) in the context of R&D contests and later generalized by Fullerton and McAfee (1999). An extreme is presented by Gaba et al (2004) and in-contest feedback. Several studies highlight the motivation effect of feedback.…”

Managerial Motivation Dynamics and Incentives

“…Optimal response to risk, under various compensation schemes, is investigated from an agent's perspective by Gaba and Kalra (1999) and Gaba et al (2004), and, in a principal-agent model, by Godes (2004). The financial literature has extensively investigated the influence of nonlinear contracts (typically convex options) on the agent's risk-taking behavior.…”