Optimal strategies for effort investment in sequential contests with failures
Optimal Strategies in a Sequential Contest with Failures
Computer Science and Game Theory
Summary
The paper looks at a situation where two players take turns trying to win a contest by putting in effort, but each can fail to deliver the effort they choose. The chance of failure grows as they try harder, and each player handles failure differently. The authors found the best way for the second player to respond to the first player's effort, the best way for the first player to act knowing the response, and how different skills and failure costs affect who wins and each player's payoff.
What this means in practice
- •For game designers: Design contest rules that account for effort uncertainty and player differences to balance fairness and strategy in sequential competitions.
- •For competitive sports coaches: Develop training strategies that consider players’ likelihood of failing under high effort to optimize performance in tournaments with sequential challenges.
A theory result. No direct application yet.
Authors
Alec Pannunzio, Ashley Shaffer, Gregory Shaver, Shreyas Sundaram
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.