Feedback in Dynamic Contests: Theory and Experiment

TL;DR

This work analyzes how interim feedback policies affect dynamics in a two-stage all-pay auction with a common-value prize by introducing Cheapest Signal Equilibria to characterize sequential outcomes. The authors prove an irrelevance result: equilibrium payoffs for both players and the auctioneer’s profit are zero regardless of the feedback policy, even though the policy shapes the equilibrium set and can induce sunk costs and head-start effects. They further show explicit equilibrium structures under general feedback and a special Rank feedback case, and derive implications for stage-2 bidding via sunk-cost and discouragement channels. An experimental test across four feedback treatments finds total bids largely invariant to the feedback policy, but reports evidence consistent with sunk-cost and head-start effects in stage 2, albeit weaker than theoretical predictions. The findings contribute to understanding design of dynamic contests and interim information disclosure, with implications for the strategic value of feedback in multi-stage signaling environments.

Abstract

We study the effect of interim feedback policies in a dynamic all-pay auction where two players bid over two stages to win a common-value prize. We show that sequential equilibrium outcomes are characterized by Cheapest Signal Equilibria, wherein stage 1 bids are such that one player bids zero while the other chooses a cheapest bid consistent with some signal. Equilibrium payoffs for both players are always zero, and the sum of expected total bids equals the value of the prize. We conduct an experiment with four natural feedback policy treatments -- full, rank, and two cutoff policies -- and while the bidding behavior deviates from equilibrium, we fail to reject the hypothesis of no treatment effect on total bids. Further, stage 1 bids induce sunk costs and head starts, and we test for the resulting sunk cost and discouragement effects in stage 2 bidding.

Figures (1)

• Figure 1: Bid Distributions

Theorems & Definitions (9)

• Remark 1
• proof
• Definition 1
• Definition 2
• proof
• proof
• proof : Proof of Theorem \ref{['thm:irrelevance']}
• proof
• proof