Equilibria In Complex Multi-Agent Games: Implications For Platform Economy And Cybersecurity

Abstract

As individuals increasingly engage with platform economies such as rideshares through algorithmic interfaces, questions of strategic behavior and fairness become critically important, especially for the labor side of the market (drivers). Leveraging recent advances in game theory, particularly Mathematical Program Networks (MPNs), we investigate hierarchical interactions within these platform duopolies using a parsimonious theoretical model that encompasses all observed network effects, helping us derive analytical insights that uncover structurally disadvantageous equilibria for specific market segments. Comparisons with real-world data indicate that our model has a high fit and can explain observed platform behaviors and metrics. To overcome the computational challenges inherent in solving such models, we develop a Monte Carlo-based approximation method and further extend the analysis to dynamic environments using multi-agent reinforcement learning. We are able to demonstrate that algorithmic collusion can arise in complex multi-agent platform economies not solely from algorithmic properties but also from intrinsic market characteristics like inertia, i.e., the willingness of participants to adjust their strategies in response to the latest pricing decisions. Our experiments in a dynamic platform game with information asymmetry indicate that information advantage can implicitly give rise to market collusion, where specific market segments can coordinate together to induce a collusive outcome that can impact general welfare. In discrete strategic domains such as cyber infrastructure defense, we introduce the concept of local equilibria, enabling scalable computation while preserving the obtained quality of solutions. We also introduce efficient SAT encodings to further scale these games with respect to higher-order solutions. Collectively, these contributions advance both theoretical and computational understanding of platform duopolies, algorithmic collusion, information asymmetry, regulatory risk, and emergent strategic phenomena in algorithmically mediated systems.