Jaehan Im

Jaehan Im, Yue Yu, David Fridovich-Keil et al.

Coordination in multiplayer games enables players to avoid the lose-lose outcome that often arises at Nash equilibria. However, designing a coordination mechanism typically requires the consideration of the joint actions of all players, which becomes intractable in large-scale games. We develop a novel coordination mechanism, termed reduced rank correlated equilibria, which reduces the number of joint actions to be considered and thereby mitigates computational complexity. The idea is to approximate the set of all joint actions with the actions used in a set of pre-computed Nash equilibria via a convex hull operation. In a game with n players and each player having m actions, the proposed mechanism reduces the number of joint actions considered from O(m^n) to O(mn). We demonstrate the application of the proposed mechanism to an air traffic queue management problem. Compared with the correlated equilibrium-a popular benchmark coordination mechanism-the proposed approach is capable of solving a problem involving four thousand times more joint actions while yielding similar or better performance in terms of a fairness indicator and showing a maximum optimality gap of 0.066% in terms of the average delay cost. In the meantime, it yields a solution that shows up to 99.5% improvement in a fairness indicator and up to 50.4% reduction in average delay cost compared to the Nash solution, which does not involve coordination.

Jaehan Im

Decentralized air traffic management requires coordination among self-interested stakeholders operating under shared safety and capacity constraints, where conventional centralized or implicitly cooperative models do not adequately capture this setting. We develop a unified perspective on noncooperative coordination, in which system-level outcomes emerge by designing incentives and assigning signals that reshape individual optimality rather than imposing cooperation or enforcement. We advance this framework along three directions: scalable equilibrium engineering via reduced-rank and uncertainty-aware correlated equilibria, decentralized mechanism design for equilibrium selection without enforcement, and structured noncooperative dynamics with convergence guarantees. Beyond these technical contributions, we discuss core design principles that govern incentive-compatible coordination in decentralized systems. Together, these results establish a foundation for scalable, robust coordination in safety-critical air traffic systems.

Jaehan Im, Ufuk Topcu, David Fridovich-Keil

Correlated equilibria enable a coordinator to influence the self-interested agents by recommending actions that no player has an incentive to deviate from. However, the effectiveness of this mechanism relies on accurate knowledge of the agents' cost structures. When cost parameters are uncertain, the recommended actions may no longer be incentive compatible, allowing agents to benefit from deviating from them. We study a chance-constrained correlated equilibrium problem formulation that accounts for uncertainty in agents' costs and guarantees incentive compatibility with a prescribed confidence level. We derive sensitivity results that quantify how uncertainty in individual incentive constraints affects the expected coordination outcome. In particular, the analysis characterizes the value of information by relating the marginal benefit of reducing uncertainty to the dual sensitivities of the incentive constraints, providing guidance on which sources of uncertainty should be prioritized for information acquisition. The results further reveal that increasing the confidence level is not always beneficial and can introduce a tradeoff between robustness and system efficiency. Numerical experiments demonstrate that the proposed framework maintains coordination performance in uncertain environments and are consistent with the theoretical insights developed in the analysis.

Jaehan Im, David Fridovich-Keil, Ufuk Topcu

Correlated equilibria provide a mechanism for coordinating noncooperative agents through incentive-compatible recommendations, but their guarantees degrade under uncertainty in agents' cost structures. Chance-constrained correlated equilibrium addresses this issue by enforcing incentive compatibility with probabilistic guarantees, but computing such equilibria remains intractable in large-scale coordination problems due to the exponential growth of the joint action space. We develop an approximation method for computing chance-constrained correlated equilibria by showing that these equilibria admit a representation as convex combinations of a finite set of chance-constrained pure Nash equilibria, enabling tractable computation without solving the full correlated equilibrium program. Numerical experiments on large-scale multi-airline coordination scenarios demonstrate substantial reductions in computation time while achieving lower system delay costs compared to current operational practice. Under cost uncertainty, the proposed method consistently achieves lower deviation rate compared to the full formulation while achieving comparable coordination performance.

Jaehan Im, Filippos Fotiadis, Ufuk Topcu et al.

Advanced air mobility operations will require reliable coordination mechanisms for managing dense traffic near vertiports. However, sequencing decisions may become vulnerable when they rely on potentially falsified self-reported information such as estimated time of arrival. Self-interested vehicles may misreport their arrival times to obtain favorable landing priority, while malicious actors may spoof information to disrupt sequencing decisions or induce unnecessary congestion. This paper studies secure coordination for vertiport sequencing under sensing uncertainty. We consider a coordinator that combines self-reported Remote-ID information with externally obtained surveillance measurements to check reports and assign separation-feasible arrival schedules. Since surveillance-based estimates are uncertain, falsified reports may remain consistent with the sensing uncertainty region and cannot always be rejected outright. We therefore formulate sequencing as a robust design problem over this uncertainty region. Self-interested misreporting is modeled as a strategic deviation that improves the reporting vehicle's own sequencing outcome, whereas malicious spoofing is modeled as an adversarial disturbance that degrades the system-level objective. The final paper will develop robust sequencing rules over surveillance-consistent uncertainty sets and evaluate their performance in representative vertiport sequencing scenarios.