arXiv subjects

Mel Krusniak

Publications and source records attributed to Mel Krusniak.

3 recordsLinked to original sources

arXiv2025

Mixed Strategy Constraints in Continuous Games

When modeling robot interactions as Nash equilibrium problems, it is desirable to place coupled constraints which restrict these interactions to be safe and acceptable (for instance, to avoid collisions). Such games are continuous with potential mixed strategy equilibria, and this combination of characteristics means special care must be given to setting coupled constraints in a way that respects mixed strategies while remaining compatible with continuous game solution methods. Here, we investigate the problem of constraint-setting in this context, primarily focusing on a chance-based method. We first motivate these chance constraints in a discrete setting, placing them on n-player matrix games as a justifiable approach to handling the probabilistic nature of mixing. Then, we describe a numerical solution method for these chance constrained, continuous games with simultaneous pure strategy optimization. Finally, using a modified pursuit-evasion game as a motivating example, we demonstrate the actual behavior of this solution method in terms of its fidelity, parameter sensitivity, and efficiency

cs.GT↗

arXiv2025

Online Competitive Information Gathering for Partially Observable Trajectory Games

Game-theoretic agents must make plans that optimally gather information about their opponents. These problems are modeled by partially observable stochastic games (POSGs), but planning in fully continuous POSGs is intractable without heavy offline computation or assumptions on the order of belief maintained by each player. We formulate a finite history/horizon refinement of POSGs which admits competitive information gathering behavior in trajectory space, and through a series of approximations, we present an online method for computing rational trajectory plans in these games which leverages particle-based estimations of the joint state space and performs stochastic gradient play. We also provide the necessary adjustments required to deploy this method on individual agents. The method is tested in continuous pursuit-evasion and warehouse-pickup scenarios (alongside extensions to $N > 2$ players and to more complex environments with visual and physical obstacles), demonstrating evidence of active information gathering and outperforming passive competitors.

cs.GT↗

arXiv2025

Locally Optimal Solutions for Integer Programming Games

Integer programming games (IPGs) are n-person games with integer strategy spaces. These games are used to model non-cooperative combinatorial decision-making and are used in domains such as cybersecurity and transportation. The prevalent solution concept for IPGs, Nash equilibrium, is difficult to compute and even showing whether such an equilibrium exists is known to be Sp2-complete. In this work, we introduce a class of relaxed solution concepts for IPGs called locally optimal integer solutions (LOIS) that are simpler to obtain than pure Nash equilibria. We demonstrate that LOIS are not only faster and more readily scalable in large-scale games but also support desirable features such as equilibrium enumeration and selection. We also show that these solutions can model a broader class of problems including Stackelberg, Stackelberg-Nash, and generalized IPGs. Finally, we provide initial comparative results in a cybersecurity game called the Critical Node game, showing the performance gains of LOIS in comparison to the existing Nash equilibrium solution concept.

cs.GT↗