Feedback in Dynamic Contests: Theory and Experiment

2025-10-27

AI Summary

This study examines the impact of mid-stage feedback policies on two-player, two-stage common-value all-pay auctions. Theoretically, we construct a sequential equilibrium model and characterize a “cheapest-signaling equilibrium,” revealing how first-stage bids influence second-stage irrational behavior via sunk costs and lead advantages; we prove that expected payoffs are zero in equilibrium and total bids equal the prize value. Experimentally, we conduct a controlled laboratory study comparing four feedback policies—full information, rank-only, dual-threshold, and no feedback. Results show systematic behavioral deviations from theory, yet feedback type does not significantly affect aggregate bidding levels. This work is the first to integrate stage-specific information feedback mechanisms with sunk-cost effects into the analytical framework of dynamic all-pay auctions, offering novel theoretical insights and empirical evidence on irrational strategic interactions in auction settings.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

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.

Problem

• Analyzing interim feedback effects in dynamic all-pay auctions
• Characterizing sequential equilibrium outcomes via Cheapest Signal Equilibria
• Testing sunk cost and discouragement effects in bidding behavior

Innovation

• Dynamic all-pay auction with two-stage bidding
• Cheapest Signal Equilibria characterize sequential outcomes
• Four feedback policies tested for treatment effects