Targeted Position Games: A Framework for Strategic Rank Optimization in Competitive Environments

In contemporary competitive landscapes, such as digital marketplaces and online auctions, agents often prioritize achieving specific ranks over outright victory, challenging conventional game-theoretic paradigms focused on payoff maximization. This paper introduces Targeted Position Games (TPGs), a novel framework where players strategically aim for designated ranks, incorporating positional constraints inspired by exclusivity principles like the Pauli Exclusion Principle in quantum mechanics. We formalize TPGs, prove the existence of Nash equilibria under general conditions, and extend the model to accommodate avoidance strategies and overlapping target ranks— allowing multiple players to compete for the same position. Through rigorous mathematical analysis, including pure and mixed strategy equilibria, we demonstrate the framework’s robustness. Empirical insights from position auction data and computational simulations validate the model’s predictions. Applications span online advertising , e-commerce, AI decision-making, and interdisci-plinary analogies to quantum systems. By bridging theoretical game theory with practical and empirical domains, TPGs provide a versatile tool for modeling rank-centric competition, with implications for mechanism design and strategic optimization.