Strategic Effort and Bandwagon Effects in Finite Multi-Stage Games with Non-Linear Externalities: Evidence from Triathlon

TL;DR

This study investigates how strategic effort and positioning in multi-stage triathlon races are influenced by externalities like drafting, revealing nonlinear effects and costs associated with leading positions through causal analysis.

Contribution

It introduces a structural contest framework with endogenous effort and drafting position, using exogenous variation from COVID-19 bans to identify causal effects in triathlon.

Findings

Small group drafting yields over 30% improvement in rank per position

Diminishing returns in larger groups for drafting benefits

Leading positions are more costly than optimal, consistent with energy expenditure theories

Abstract

This paper examines strategic effort and positioning choices resulting in bandwagon effects under externalities in finite multi-stage games using causal evidence from triathlon (Reichel, 2025). Focusing on open-water swim drafting where athletes reduce drag most effectively by swimming directly behind peerswe estimate its performance effects through a structural contest framework with endogenous, deterministic effort and drafting position. Leveraging exogenous variation from COVID-19 drafting bans in Austrian triathlons, we apply a panel leave-one-out (LOO/LOTO) peer ability instrumental variables (IV) strategy to isolate the causal non-linear effect of drafting. Results from restricted sample analysis and pooled estimated bandwagon IV effects show substantial and nonlinear gains: in small (group size below 10) drafting swim groups/clusters, each deeper position improves finishing rank on average by over 30%, with rapidly diminishing returns in larger groups. Leading however is consistently more costly than optimal positioning, aligning with theoretical predictions of energy expenditure (metabolic costs).