arXiv subjects

Christine Konicki

Publications and source records attributed to Christine Konicki.

3 recordsLinked to original sources

arXiv2026

Computing Perfect Bayesian Equilibria, with Application to Empirical Game-Theoretic Analysis

Perfect Bayesian Equilibrium (PBE) is a refinement of the Nash equilibrium for imperfect-information extensive-form games (EFGs) that enforces consistency between the two components of a solution: agents' strategy profile describing their decisions at information sets and the belief system quantifying their uncertainty over histories within an information set. We present a scalable approach for computing a PBE of an arbitrary two-player EFG. We adopt the definition of PBE enunciated by Bonanno in 2011 using a consistency concept based on the theory of belief revision due to Alchourrón, Gärdenfors, and Makinson. Our algorithm for finding a PBE is an adaptation of Counterfactual Regret Minimization (CFR) that minimizes the expected regret at each information set given a belief system, while maintaining the necessary consistency criteria. We prove that our algorithm is correct for two-player zero-sum games and has a reasonable slowdown in time-complexity relative to classical CFR given the additional computation needed for refinement. We also experimentally demonstrate the competent performance of PBE-CFR in terms of equilibrium quality and running time on medium-to-large non-zero-sum EFGs. Finally, we investigate the effectiveness of using PBE for strategy exploration in empirical game-theoretic analysis. Specifically, we compute PBE as a meta-strategy solver (MSS) in a tree-exploiting variant of Policy Space Response Oracles (TE-PSRO). Our experiments show that PBE as an MSS leads to higher-quality empirical EFG models with complex imperfect information structures compared to MSSs based on an unrefined Nash equilibrium.

cs.GT↗

arXiv2025

Policy Abstraction and Nash Refinement in Tree-Exploiting PSRO

Policy Space Response Oracles (PSRO) interleaves empirical game-theoretic analysis with deep reinforcement learning (DRL) to solve games too complex for traditional analytic methods. Tree-exploiting PSRO (TE-PSRO) is a variant of this approach that iteratively builds a coarsened empirical game model in extensive form using data obtained from querying a simulator that represents a detailed description of the game. We make two main methodological advances to TE-PSRO that enhance its applicability to complex games of imperfect information. First, we introduce a scalable representation for the empirical game tree where edges correspond to implicit policies learned through DRL. These policies cover conditions in the underlying game abstracted in the game model, supporting sustainable growth of the tree over epochs. Second, we leverage extensive form in the empirical model by employing refined Nash equilibria to direct strategy exploration. To enable this, we give a modular and scalable algorithm based on generalized backward induction for computing a subgame perfect equilibrium (SPE) in an imperfect-information game. We experimentally evaluate our approach on a suite of games including an alternating-offer bargaining game with outside offers; our results demonstrate that TE-PSRO converges toward equilibrium faster when new strategies are generated based on SPE rather than Nash equilibrium, and with reasonable time/memory requirements for the growing empirical model.

cs.GT↗

arXiv2023

Exploiting Extensive-Form Structure in Empirical Game-Theoretic Analysis

Empirical game-theoretic analysis (EGTA) is a general framework for reasoning about complex games using agent-based simulation. Data from simulating select strategy profiles is employed to estimate a cogent and tractable game model approximating the underlying game. To date, EGTA methodology has focused on game models in normal form; though the simulations play out in sequential observations and decisions over time, the game model abstracts away this temporal structure. Richer models of \textit{extensive-form games} (EFGs) provide a means to capture temporal patterns in action and information, using tree representations. We propose \textit{tree-exploiting EGTA} (TE-EGTA), an approach to incorporate EFG models into EGTA\@. TE-EGTA constructs game models that express observations and temporal organization of activity, albeit at a coarser grain than the underlying agent-based simulation model. The idea is to exploit key structure while maintaining tractability. We establish theoretically and experimentally that exploiting even a little temporal structure can vastly reduce estimation error in strategy-profile payoffs compared to the normal-form model. Further, we explore the implications of EFG models for iterative approaches to EGTA, where strategy spaces are extended incrementally. Our experiments on several game instances demonstrate that TE-EGTA can also improve performance in the iterative setting, as measured by the quality of equilibrium approximation as the strategy spaces are expanded.

cs.GT↗