Sequential game dynamics produce subgame perfect equilibria in sports networks through bounded rationality
TL;DR
Bounded rationality is extended from simultaneous to sequential decision structures on scale-free networks, showing how modified backward induction yields approximate subgame perfect equilibria that converge to their exact counterparts as the rationality parameter increases, forming bounded-rationality refinements of Nash equilibria.
Abstract
Strategic decision-making in networked systems unfolds sequentially, with each agent’s choice shaped by the observable actions of those who decide earlier. We extend bounded rationality from simultaneous to sequential decision structures on scale-free networks, showing how modified backward induction yields approximate subgame perfect equilibria that converge to their exact counterparts as the rationality parameter increases, forming bounded-rationality refinements of Nash equilibria. Agents ordered by network centrality condition on their predecessors’ actions through a centrality-weighted observation term, with social learning and strategic exploration jointly defining a behavioral regime that ranges from winner-takes-all configurations concentrated among hub agents to broader participation with flattened centrality gradients. In the four equilibrium scenarios examined, the sequential protection distribution stochastically dominates the simultaneous baseline, and centrality-based ordering outperforms random and inverse alternatives. Cross-domain calibration against banking, epidemiological, and sports network data shows that introducing the observation term strengthens the centrality–protection correlation in all three domains, consistent with a common mechanism operating across distinct behavioral systems.