Optimal Strategies in a Sequential Contest with Failures
Abstract
We study a Stackelberg model where two players compete in a sequential contest, and the player that successfully invests the most effort wins. Our formulation considers a probability that each player fails to invest their chosen level of effort, as captured by a failure function that increases with the amount of effort. The players each have their own cost of failure, as well as a maximum level of effort (capturing different abilities of the players). We prove three key results. First, we provide the optimal strategy for Player 1 (the follower), to maximize their utility given an observed effort exerted by Player 2 (the leader). Next, we characterize the optimal strategy to maximize the expected utility of Player 2, anticipating the optimal response by Player 1. Finally, we analyze the expected utilities of each player when both play their optimal strategy, and provide key insights into how heterogeneous player abilities and failure costs affect the outcomes of the game.
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BibTeX
@misc{pannunzio2026optimal,
title = {{Optimal Strategies in a Sequential Contest with Failures}},
author = {Alec Pannunzio and Ashley Shaffer and Gregory Shaver and Shreyas Sundaram},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19706},
eprint = {2609.19706},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19706},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Optimal Strategies in a Sequential Contest with Failures
AU - Alec Pannunzio
AU - Ashley Shaffer
AU - Gregory Shaver
AU - Shreyas Sundaram
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19706
UR - https://arxiv.org/abs/2609.19706
AB - We study a Stackelberg model where two players compete in a sequential contest, and the player that successfully invests the most effort wins. Our formulation considers a probability that each player fails to invest their chosen level of effort, as captured by a failure function that increases with the amount of effort. The players each have their own cost of failure, as well as a maximum level of effort (capturing different abilities of the players). We prove three key results. First, we provide the optimal strategy for Player 1 (the follower), to maximize their utility given an observed effort exerted by Player 2 (the leader). Next, we characterize the optimal strategy to maximize the expected utility of Player 2, anticipating the optimal response by Player 1. Finally, we analyze the expected utilities of each player when both play their optimal strategy, and provide key insights into how heterogeneous player abilities and failure costs affect the outcomes of the game.
ER -