The paper describes at a high-level the network-form game framework (based on Bayes net and game theory), which can be used to model and analyze safety issues in large, distributed, mixed human-automation systems such as NextGen

Brat, Guillaume

NASA Technical Reports Server

Position Paper: Modeling Multiple Human-Automation Dis-
tributed Systems using Network-form Games 
Guillaume Brat  
NASA 
Ames Research Center - USA 
guillaume.p.brat@nasa.gov  
ORIGIN AND UNDERLYING PRINCIPLES 
The focus of the modeling framework is on interactions 
between human and automation agents in large, distributed 
agent networks/systems. This model combines Bayes nets 
with Game Theoretic methods to model human behavior 
and predict the behavior of a composite system involving 
humans and automation. In general, some of the nodes of 
the Bayes net will be set by the humans in the system, some 
will be set with known conditional distributions (e.g., noise 
models of sensors), and some might be “black boxes” pro-
vided by the proposer that simulate behavior of automated 
devices. Novel algorithms are required for sampling and 
prediction with this model. 
Bayes nets have been widely studied to describe stochastic 
systems [1-3]. A Bayes net is a directed acyclic graph in 
which nodes represent random variables and edges repre-
sent conditional dependencies between these variables. The 
variables can be observable quantities or unknown quanti-
ties (or hypotheses). An edge between two nodes indicates 
that the random variables represented by the nodes are con-
ditionally independent of each other. Each node is assigned 
a probability function that takes as inputs the random varia-
bles of the parent node and that gives the probability as-
signed by to the random variable associated with the node. 
There exist many algorithms to calculate the interference 
and learning in Bayesian networks. 
Game Theory is also a well-know technique, which has 
been used to describe the behavior of interacting humans [4, 
5]. It has been widely studied in economics contexts to rep-
resent human behaviors and study how decisions are made 
in auctions and negotiations for examples. The field first 
addressed zero sum games (so that gains and losses be-
tween participants are perfectly balanced), but it has 
evolved beyond that and can now study different models of 
equilibrium (Nash equilibrium, Quantal Response equilibri-
um, Quantal Level-K and Cognitive Hierarchy). 
Wolpert has combined Bayes nets and Game Theory in a 
novel framework, called semi network-form games, to 
model systems in which humans interact with other humans 
and with automation. The semi network-form game is a 
specialization of the complete framework “network-form 
games” formally defined in [6, 7] by Wolpert. Currently it 
is relying on level-K equilibrium. 
In a semi network-form game, a Bayes net is used to de-
scribe probabilistic interactions between agents (humans or 
automation) in a system using random variables. Automa-
tion (and physical sub-systems) is represented by a 
“chance” node while a human is represented by a “deci-
sion” node. The conditional probability distributions asso-
ciated with “chance” nodes are pre-specified. The “deci-
sion” nodes also differ in the sense that they are associated 
with a utility function, which maps an instantiation of the 
net to a real number quantifying the player’s utility. Utility 
functions are used to encode the goals of a player. In other 
words, it represents what a human tries to optimize during 
the game. A semi network-form game allows a player to 
control only one decision node while a complete network-
form game make no such restriction allowing a player to 
control multiple decision nodes in the net. Network-form 
games bear a resemblance to Multi-Agent Influence dia-
grams [8], except that network-form games consider 
bounded rational agents and uses utility functions rather 
than utility nodes. 
We illustrate the use of network-form games with the ex-
ample of a 2-aircraft mid-air encounter (similar to the infa-
mous Überlingen accident). The corresponding Bayes net is 
shown in Figure 2. At time t, the system is represented by a 
layer of observation (of the world state) nodes (for both 
pilots and TCAS boxes), a layer of TCAS nodes, a layer of 
pilot nodes, the world state as an input node and an out-
come node. The state of the pilot node is influenced by both 
the pilot’s observations and the TCAS outcome. The final 
outcome state is calculated by simulating the aircraft states 
forward in time using a model of the aircraft kinematics. 
The social welfare of the system is then calculated from the 
outcome state. The observational layer is necessary to mod-
el observational noise and incomplete information resulting 
from pilots and TCAS imperfectly observing the world 
state. 
MODELED RELATIONSHIPS 
The relationships modeled with network-form games are 
different from traditional techniques in human factors and 
user interaction perspectives. The modeling framework is 
best suited to capture the following types of relationships:  
(1). The model strength resides in its ability to capture non-
deterministic pilot behavior. For example, TCAS assumes 
that a pilot receiving an RA will delay for 5 seconds and 
accelerate at ¼ g to execute the RA maneuver. Despite their 
https://ntrs.nasa.gov/search.jsp?R=20120011860 2019-08-30T21:01:09+00:00Z
training, pilots actually have different reactions to TCAS 
RAs. A recent study [9] in the Boston area has found that  
• 13% of RAs are obeyed in compliance 
• 64% of RAs are obeyed in partial compliance, i.e., 
the aircraft is moved in the right direction but with 
an improper timing, and, 
• 23% of RAs are ignored and the aircraft is moved 
in the opposite direction. 
Clearly, pilots are not always responding in the same way 
to TCAS RAs. In fact, pilots make up their mind using 
more than just the TCAS information, taking into accounts 
other sources of information, including their own visual 
clues. The network-form game framework is able to capture 
this non-determinism by using probability distributions.  
(2). The included game theory framework is also very use-
ful to model the “gamesmanship”, or guessing game, that 
may happening when humans interact with other humans. 
In a mid-air collision possibility, it is important to model 
the fact that a pilot is always wondering if the other pilot is 
going to react according to the training he received. Will 
the other person/pilot make the right move? What if he 
doesn’t? What is my back-up strategy? When do I need to 
decide which strategy to follow? These types of questions 
are best answered in a game theory framework. 
PROBLEMS ADDRESSED 
The idea is to describe human and machine interactions 
within a large multi-agent system, e.g., airplane crew inter-
acting with air traffic controllers and automation such as 
TCAS or ADS-B. From a safety point of view, problems 
can occur because of misunderstanding between  
• humans, e.g., a pilot misunderstanding the orders 
issued by a controller, or, the pilots of two planes 
encroaching on their respective runways in order 
to optimize their on-time gate arrival time, or, 
• humans and automation, e.g., a pilot doubting, or 
misunderstanding, the outputs of an automated 
box, or, a pilot following a TCAS advise when the 
controller is actually issuing a contradictory com-
mand. 
Figure 2. Example of a 2-aircraft mid-air encounter. 
Figure 1. A Bayes net for a 2-aircraft mid-air collision example. 
The framework can be used at different level of granularity. 
It works for modeling human/machine interaction problems 
as well as new air traffic concepts of operation. 
APPLICATIONS 
This approach is also being used to discover and correct 
problems in cyber-security (cyber physical attack on smart 
power grid, denial of service). 
LIMITATIONS AND DEVELOPMENT OPPORTUNITIES 
The presented framework focuses on human factors issues 
such as decision making and (in some ways) perception. 
Issues such a cognition, and, physical limitations are hard to 
model. At this stage, the biggest limitation is that the analy-
sis relies on having valid probability distributions for hu-
man behavior. The best solution would be to get access to 
results of high-fidelity, human-in-the-loop studies done by 
the FAA. However, getting access is difficult, and, the 
number of simulations in those studies does not lend to es-
timating statistically-valid probability distributions. This 
problem is being currently addressed by studying the possi-
bility of using multi-fidelity simulations. 
 
REFERENCES 
1. Bishop, C.M., “Pattern recognition and machine learn-
ing,” Springer 2006.  
2. Darwiche, A., “Modeling and reasoning with Bayesian 
networks,” Cambridge University Press, 2009. 
3. Russel, S., Norvig, P., “Artificial intelligence a modern 
approach,” 2nd ed. Pearson Education, 2003. 
4. Crawford, V.P., “Introduction to experimental game 
theory, “ Journal of Economic Theory, 104, pp. 1-15, 
2002. 
5. Crawford, V.P., “Modeling behavior in novel strategic 
situations via level-k thinking,” In Third World Con-
gress of Game Theory Society (GAMES), 2008. 
6. Lee, R., Wolpert, D., “Game theoretic modeling of 
pilot behavior during mid-air encounters,” Chapter 4 in 
Decision Making with Imperfect Decision Makers, ed. 
By T.V. Guy, M. Karny, and D. Wolpert, Springer, 
2012. 
7. Wolpert, D., Lee, R., “Network-form games: using 
Bayesian networks to represent non-cooperative 
games,” NASA Ames Research Center working paper, 
Moffett Field, California. 
8. Koller, D., Milch, B., “Multi-agent influence diagrams 
for representing and solving games,” Games and Eco-
nomic Behavior, 45(1), pp. 181-221, 2003. 
9. Kushar, J.K., Drumm, A.C., “The Traffic and Collision 
Avoidance System,” Lincoln Laboratory Journal, 
16(2), 2007. 
 


Modeling Multiple Human-Automation Distributed Systems using Network-form Games

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