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NASA NTRS1974

Algebraic Riccati equations in zero-sum differential games

The procedure for finding the closed-loop Nash equilibrium solution of two-player zero-sum linear time-invariant differential games with quadratic performance criteria and classical information pattern may be reduced in most cases to the solution of an algebraic Riccati equation. Based on the results obtained by Willems, necessary and sufficient conditions for existence of solutions to these equations are derived, and explicit conditions for a scalar example are given.

Johnson, T. L.↗

NASA NTRS2002

Time-Extended Payoffs for Collectives of Autonomous Agents

A collective is a set of self-interested agents which try to maximize their own utilities, along with a a well-defined, time-extended world utility function which rates the performance of the entire system. In this paper, we use theory of collectives to design time-extended payoff utilities for agents that are both aligned with the world utility, and are "learnable", i.e., the agents can readily see how their behavior affects their utility. We show that in systems where each agent aims to optimize such payoff functions, coordination arises as a byproduct of the agents selfishly pursuing their own goals. A game theoretic analysis shows that such payoff functions have the net effect of aligning the Nash equilibrium, Pareto optimal solution and world utility optimum, thus eliminating undesirable behavior such as agents working at cross-purposes. We then apply collective-based payoff functions to the token collection in a gridworld problem where agents need to optimize the aggregate value of tokens collected across an episode of finite duration (i.e., an abstracted version of rovers on Mars collecting scientifically interesting rock samples, subject to power limitations). We show that, regardless of the initial token distribution, reinforcement learning agents using collective-based payoff functions significantly outperform both natural extensions of single agent algorithms and global reinforcement learning solutions based on "team games".

Tumer, Kagan↗

NASA NTRS2013

AGATE: Adversarial Game Analysis for Tactical Evaluation

AGATE generates a set of ranked strategies that enables an autonomous vehicle to track/trail another vehicle that is trying to break the contact using evasive tactics. The software is efficient (can be run on a laptop), scales well with environmental complexity, and is suitable for use onboard an autonomous vehicle. The software will run in near-real-time (2 Hz) on most commercial laptops. Existing software is usually run offline in a planning mode, and is not used to control an unmanned vehicle actively. JPL has developed a system for AGATE that uses adversarial game theory (AGT) methods (in particular, leader-follower and pursuit-evasion) to enable an autonomous vehicle (AV) to maintain tracking/ trailing operations on a target that is employing evasive tactics. The AV trailing, tracking, and reacquisition operations are characterized by imperfect information, and are an example of a non-zero sum game (a positive payoff for the AV is not necessarily an equal loss for the target being tracked and, potentially, additional adversarial boats). Previously, JPL successfully applied the Nash equilibrium method for onboard control of an autonomous ground vehicle (AGV) travelling over hazardous terrain.

Huntsberger, Terrance L.↗

DOE OSTI2025

Game Theory in Cybersecurity: A Review of Applications, Models, and Challenges

There are no aspects of society left unchanged by the Internet. From commerce to communication, from entertainment to engineering, every industry and sphere of influence exists in a new state thanks to the advent of the information age. This convenience, rarely controverted, comes with capricious actors, who wish to gain access to these systems for myriad reasons, be it financial, political, or mere intellectual gain. This paper presents information that can help readers to better understand the fundamentals of cybersecurity from a game theory perspective, such as coalitional games, Colonel Blotto systems, or how to find Nash Equilibrium. This paper also reviews how game theory can enhance understanding of cybersecurity through cooperative and non-cooperative methods, such as information sharing, defense modeling, and attacker analysis. The authors use the analysis to serve as a bridge for those in either field who need a way to best comprehend the methodologies of their contrasting fields.

Egan, Matthew↗

DOE OSTI2025

Game Strategies for Entanglement Paths in Quantum Network Infrastructure

Entanglement distribution is a core function of quantum networks, and the paths used for this purpose are composed of quantum and conventional network components and are routed through physical facility sites. A game theoretic model is formulated for the defense of entanglement paths in a quantum network infrastructure by modeling the correlations and probabilities of reinforcement and failure of its components. A sum-form utility function is used to capture the cost-benefit trade-offs in reinforcing the entanglement path components to defend against their failures and attacks. Under Nash Equilibrium criteria, estimates of survival probabilities of entanglement paths are derived using the parameters and correlations of quantum, conventional, hybrid, and facility components. They provide insights into the dependencies of entanglement paths on its components, including cross-boundary effects of conventional, quantum, and facility components.

Rao, Nageswara [ORNL] (ORCID:0000000234085941)↗

DOE OSTI2025

On the Sampling-Based Computation of Nash Equilibria Under Uncertainty via the Nikaido–Isoda Function

We consider the computation of an equilibrium of a stochastic Nash equilibrium problem, where the player objectives are assumed to be L 0 -Lipschitz continuous and convex, given rival decisions with convex and closed player-specific feasibility sets. To address this problem, we consider minimizing a suitably defined value function defined using the Nikaido–Isoda function. Such an avenue does not necessitate either monotonicity properties of the concatenated gradient map or potentiality requirements on the game but does require a suitable regularity requirement under which a stationary point is a Nash equilibrium. We design and analyze a sampling-enabled projected-gradient-response method, reliant on inexact resolution of a player-level best-response subproblem. Here, by deriving suitable Lipschitzian guarantees on the value function, we derive both asymptotic guarantees for the sequence of generated iterates as well as rate and complexity guarantees for computing a stationary point by appropriate choices of the sampling rate and inexactness sequence.

Nikaido-Isoda function↗

DOE OSTI2020

Submodular optimization problems and greedy strategies: A survey

The greedy strategy is an approximation algorithm to solve optimization problems arising in decision making with multiple actions. How effective is the greedy strategy compared to the optimal solution? In this survey, we mainly consider two classes of optimization problems where the objective function is submodular. The first is set submodular optimization, which is to choose a set of actions to optimize a set submodular objective function, and the second is string submodular optimization, which is to choose an ordered set of actions to optimize a string submodular function. Our emphasis here is on performance bounds for the greedy strategy in submodular optimization problems. Specifically, we review performance bounds for the greedy strategy, more general and improved bounds in terms of curvature, performance bounds for the batched greedy strategy, and performance bounds for Nash equilibria.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2003

Theory of Collective Intelligence

In this chapter an analysis of the behavior of an arbitrary (perhaps massive) collective of computational processes in terms of an associated "world" utility function is presented We concentrate on the situation where each process in the collective can be viewed as though it were striving to maximize its own private utility function. For such situations the central design issue is how to initialize/update the collective's structure, and in particular the private utility functions, so as to induce the overall collective to behave in a way that has large values of the world utility. Traditional "team game" approaches to this problem simply set each private utility function equal to the world utility function. The "Collective Intelligence" (COIN) framework is a semi-formal set of heuristics that recently have been used to construct private utility. functions that in many experiments have resulted in world utility values up to orders of magnitude superior to that ensuing from use of the team game utility. In this paper we introduce a formal mathematics for analyzing and designing collectives. We also use this mathematics to suggest new private utilities that should outperform the COIN heuristics in certain kinds of domains. In accompanying work we use that mathematics to explain previous experimental results concerning the superiority of COIN heuristics. In that accompanying work we also use the mathematics to make numerical predictions, some of which we then test. In this way these two papers establish the study of collectives as a proper science, involving theory, explanation of old experiments, prediction concerning new experiments, and engineering insights.

Nash equilibrium↗

DOE OSTI2021

Multi-objective Eco-Routing Model Development and Evaluation for Battery Electric Vehicles

This paper develops a multi-objective eco-routing algorithm (eco- and travel time-optimum routing) for battery electric vehicles (BEVs) and internal combustion engine vehicles (ICEVs) and investigates the network-wide impacts of the proposed multi-objective Nash optimum (user equilibrium) traffic assignment on a large-scale network. Unlike ICEVs, BEVs are more energy efficient on low-speed arterial trips compared with highway trips. Different energy consumption patterns require different eco-routing strategies for ICEVs and BEVs. This study found that single-objective eco-routing could significantly reduce the energy consumption of BEVs but also significantly increase their average travel time. Consequently, the study developed a multi-objective routing model (eco- and travel time-routing) to improve both energy and travel time measures. The model introduced a link cost function that uses the specification of the value of time and the cost of fuel/energy. The simulation study found that multi-objective routing could reduce BEV energy consumption by 13.5%, 14.2%, 12.9%, and 10.7%, as well as ICEV fuel consumption by 0.1%, 4.3%, 3.4%, and 10.6% for “not congested, “slightly congested,”“moderately congested,” and “highly congested” conditions, respectively. The study also found that multi-objective user equilibrium routing reduced the average vehicle travel time by up to 10.1% compared with the standard user equilibrium traffic assignment for highly congested conditions, producing a solution closer to the system optimum traffic assignment. The results indicate that the proposed multi-objective eco-routing strategy can reduce vehicle fuel/energy consumption effectively with minimum impacts on travel times for both BEVs and ICEVs.

Engineering↗

DOE OSTI2021

Multi-objective Eco-Routing Model Development and Evaluation for Battery Electric Vehicles.

This paper develops a multi-objective eco-routing algorithm (combined eco- and travel time-optimum routing) for battery electric vehicles (BEVs) and internal combustion engine vehicles (ICEVs) and investigates the network-wide impacts of the proposed multi-objective Nash optimum (user equilibrium) traffic assignment on a large-scale network. Eco-routing is a technique that finds the most energy efficient route. ICEV and BEV energy consumption patterns are significantly different with regard to their sensitivity to driving cycles. Unlike ICEVs, BEVs are more energy efficient on low-speed arterial trips compared to highway trips. Different energy consumption patterns require different eco-routing strategies for ICEVs and BEVs. This study found that single objective eco-routing could significantly reduce the energy consumption of BEVs but also significantly increase their average travel time. Consequently, the study developed a multi-objective routing model (eco- and travel time-routing) to improve both energy and travel time measures. The model introduced a link cost function that uses the specification of the value of time and the cost of fuel/energy. The simulation study found that multi-objective routing could reduce the BEV energy consumption by 13.5%, 14.2%, 12.9%, and 10.7%, as well as ICEV fuel consumption by 0.1%, 4.3%, 3.4%, and 10.6% for “not congested, “slightly congested,” “moderately congested,” and “highly congested” conditions, respectively. The study also found that multi-objective user equilibrium routing reduced the average vehicle travel time by up to 10.1% compared to the standard user equilibrium traffic assignment for highly congested conditions, producing a solution closer to the system optimum traffic assignment. The results indicate that the proposed multi-objective eco-routing strategy can reduce vehicle fuel/energy consumption effectively with minimum impacts on travel times for both BEVs and ICEVs.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Unmasking the Conformational Stability and Inhibitor Binding to SARS-CoV-2 Main Protease Active Site Mutants and Miniprecursor

We recently demonstrated that inhibitor binding reorganizes the oxyanion loop of a monomeric catalytic domain of SARS CoV-2 main protease (MPro) from an unwound (E) to a wound (active, E*) conformation, independent of dimerization. Here we assess the effect of the flanking N-terminal residues, to imitate the MPro precursor prior to its autoprocessing, on conformational equilibria rendering stability and inhibitor binding. Thermal denaturation (T m ) of C145A mutant, unlike H41A, increases by 6.8 °C, relative to wild-type mature dimer. An inactivating H41A mutation to maintain a miniprecursor containing TSAVL[Q or E] of the flanking nsp4 sequence in an intact form [ (-6) MPro H41A and (-6*) MPro H41A , respectively], and its corresponding mature MPro H41A were systematically examined. While the H41A mutation exerts negligible effect on T m and dimer dissociation constant (K dimer ) of MPro H41A , relative to the wild type MPro, both miniprecursors show a 4–5 °C decrease in T m and > 85-fold increase in K dimer as compared to MPro H41A . The K d for the binding of the covalent inhibitor GC373 to (-6*) MPro H41A increases ~12-fold, relative to MPro H41A , concomitant with its dimerization. While the inhibitor-free dimer exhibits a state in transit from E to E* with a conformational asymmetry of the protomers’ oxyanion loops and helical domains, inhibitor binding restores the asymmetry to mature-like oxyanion loop conformations (E*) but not of the helical domains. Finally, disorder of the terminal residues 1–2 and 302–306 observed in both structures suggest that N-terminal autoprocessing is tightly coupled to the E-E* equilibrium and stable dimer formation.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Cesium Removal Performance Comparisons of Crystalline Silicotitanate Media Batches with Savannah River Site Waste Simulant

The Tank Closure Cesium Removal (TCCR) system uses ion exchange columns filled with Crystalline Silicotitanate (CST) media to process radioactive waste solutions for the removal of Cs137. TCCR currently focuses on dissolving Savannah River Site (SRS) Tank 10H waste (primarily sodium salt cake solids) within the tank followed by at-tank ion exchange column treatment. Plans are underway to prepare and install a second TCCR unit at SRS. Capacity and particle size differences exist between archived (IE-911) and more recently-prepared CST media batches (9120- B and 9140-B). Side-by-side comparison testing was performed to evaluate the cesium removal performance of each batch to aid in selecting the preferred CST batch and media characteristics to load into the second TCCR unit. Batch contact equilibrium and flow-through column tests have been conducted with three CST batches using an SRS Average Simulant. Simulant batch contact equilibrium cesium loading results for the three CST batches (including two lots of one batch) are provided in Table ES-1. The 35 °C data indicates that the archived IE-911 batch has a higher cesium capacity than recently-prepared CST media and that the minor TCCR CST 9120-B media lot (2099000035) has similar cesium removal performance to the major TCCR lot (2099000034). Tests conducted at 25 ºC for the archived IE-911 CST batch indicated lower cesium removal performance with this simulant batch than was observed recently with a different SRS Average Simulant batch. A dilution factor (DF) is typically utilized when modeling engineered CST media cesium loading performance to account for mass contributions from the binder material. In cases where CST performance is lower than expected, this factor includes corrections for the binder and for low performance. The ZAM (Zheng, Anthony, and Miller) Isotherm Model DF values are provided in Table ES-1 for each simulant batch contact result. DF values near 0.5 were determined for the 9120-B and 9140-B CST batch contact tests while DF values near 0.6 (20% higher) were determined for the tests with IE-911. These dilution factors are lower than recently observed with a different SRS Average Simulant batch (9140-B DF = 0.68; IE-911 DF = 1.0). Based on these results, it appears that some component in the simulant solution used for equilibrium testing may have resulted in reduced cesium loading on the CST media.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

Autoprocessing and oxyanion loop reorganization upon GC373 and nirmatrelvir binding of monomeric SARS-CoV-2 main protease catalytic domain

The monomeric catalytic domain (residues 1–199) of SARS-CoV-2 main protease (MPro 1-199 ) fused to 25 amino acids of its flanking nsp4 region mediates its autoprocessing at the nsp4-MPro 1-199 junction. We report the catalytic activity and the dissociation constants of MPro 1-199 and its analogs with the covalent inhibitors GC373 and nirmatrelvir (NMV), and the estimated monomer-dimer equilibrium constants of these complexes. Mass spectrometry indicates the presence of the accumulated adduct of NMV bound to MPro WT and MPro 1-199 and not of GC373. A room temperature crystal structure reveals a native-like fold of the catalytic domain with an unwound oxyanion loop (E state). In contrast, the structure of a covalent complex of the catalytic domain-GC373 or NMV shows an oxyanion loop conformation (E* state) resembling the full-length mature dimer. These results suggest that the E-E* equilibrium modulates autoprocessing of the main protease when converting from a monomeric polyprotein precursor to the mature dimer.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Visualizing the Active Site Oxyanion Loop Transition Upon Ensitrelvir Binding and Transient Dimerization of SARS-CoV-2 Main Protease

N-terminal autoprocessing from its polyprotein precursor enables creating the mature-like stable dimer interface of SARS-CoV-2 main protease (MPro), concomitant with the active site oxyanion loop equilibrium transitioning to the active conformation (E*) and onset of catalytic activity. Here, through mutagenesis of critical interface residues and evaluating noncovalent inhibitor (ensitrelvir, ESV) facilitated dimerization through its binding to MPro, we demonstrate that residues extending from Ser1 through Glu14 are critical for dimerization. Combined mutations G11A, E290A and R298A (MPro™) restrict dimerization even upon binding of ESV to monomeric MPro™ with an inhibitor dissociation constant of 7.4 ± 1.6 µM. Contrasting the covalent inhibitor NMV or GC373 binding to monomeric MPro, ESV binding enabled capturing the transition of the oxyanion loop conformations in the absence of a reactive warhead and independent of dimerization. Characterization of complexes by room-temperature X-ray crystallography reveals ESV bound to the E* state of monomeric MPro as well as an intermediate approaching the inactive state (E). It appears that the E* to E equilibrium shift occurs initially from G138-F140 residues, leading to the unwinding of the loop and formation of the 3 10 -helix. Finally, we describe a transient dimer structure of the MPro precursor held together through interactions of residues A5-G11 with distinct states of the active sites, E and E*, likely representing an intermediate in the autoprocessing pathway.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS2011

Deep Metastable Eutectic Nanometer-Scale Particles in the MgO-Al2O3-SiO2 System

Laboratory vapor phase condensation experiments systematically yield amorphous, homogeneous, nanoparticles with unique deep metastable eutectic compositions. They formed during the nucleation stage in rapidly cooling vapor systems. These nanoparticles evidence the complexity of the nucleation stage. Similar complex behavior may occur during the nucleation stage in quenched-melt laboratory experiments. Because of the bulk size of the quenched system many of such deep metastable eutectic nanodomains will anneal and adjust to local equilibrium but some will persist metastably depending on the time-temperature regime and melt/glass transformation.

Reitmeijer, Frans J. M.↗

DOE OSTI2020

Cesium Removal Performance Comparisons of Crystalline Silicotitanate Media Batches with Savannah River Site Waste Simulant

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

NASA NTRS1983

Io's atmosphere - Pressure control by regolith cold trapping and surface venting

A new model for the basal pressure of Io's atmosphere is developed. This model takes into account the previously ignored fact that much of Io's surface has very high porosity, typically about 90 pct. Such porosity allows efficient subsurface cold trapping of atmospheric gases which tends to keep ambient surface pressures very low. SO2 is the only gas identified on Io, and the basal pressures for atmospheric models are usually pegged to local surface temperature via the SO2 vapor pressure equilibrium curve. Near Io's subsolar point the pressure in equilibrium with a surface SO2 frost deposit is about 1/10,000,000th bar. Porous surface models of the type developed invoke equilibrium with the colder, subsurface permafrost (at about 3-cm depth) and yield pressures of about 1/10 to the 12th bar. The subsurface cold trapping model explains many but not all observations relevant to Io's atmosphere. The new subsurface cold trapping model and the earlier surface frost equilibrium model, when taken together, provide lower and upper limits, respectively, on the basal SO2 pressure of Io's atmosphere.

Matson, D. L.↗

DOE OSTI2024

Characterization of alternate encounter assemblies of SARS-CoV-2 main protease

The assembly of two monomeric constructs spanning segments 1-199 (MPro 1-199 ) and 10-306 (MPro 10-306 ) of SARS-CoV-2 main protease (MPro) was examined to assess the existence of a transient heterodimer intermediate in the N-terminal autoprocessing pathway of MPro model precursor. Together, they form a heterodimer population accompanied by a 13-fold increase in catalytic activity. Addition of inhibitor GC373 to the proteins increases the activity further by ~7-fold with a 1:1 complex and higher order assemblies approaching 1:2 and 2:2 molecules of MPro 1-199 and MPro 10-306 detectable by analytical ultracentrifugation and native mass estimation by light scattering. Assemblies larger than a heterodimer (1:1) are discussed in terms of alternate pathways of domain III association, either through switching the location of helix 201 to 214 onto a second helical domain of MPro 10-306 and vice versa or direct interdomain III contacts like that of the native dimer, based on known structures and AlphaFold 3 prediction, respectively. At a constant concentration of MPro 1-199 with molar excess of GC373, the rate of substrate hydrolysis displays first order dependency on the MPro 10-306 concentration and vice versa. An equimolar composition of the two proteins with excess GC373 exhibits half-maximal activity at ~6 μM MPro 1-199 . Catalytic activity arises primarily from MPro 1-199 and is dependent on the interface interactions involving the N-finger residues 1 to 9 of MPro 1-199 and E290 of MPro 10-306 . Importantly, our results confirm that a single N-finger region with its associated intersubunit contacts is sufficient to form a heterodimeric MPro intermediate with enhanced catalytic activity.

60 APPLIED LIFE SCIENCES↗