Computational evolution of decision-making strategies
Peter Kvam (kvampete@msu.edu)
Center for Adaptive Rationality, Max Planck Institute for Human Development
Lentzeallee 94, 14195 Berlin, Germany

Joseph Cesario (cesario@msu.edu)
Department of Psychology, Michigan State University
316 Physics Rd, East Lansing, MI 48824, USA

arXiv:1509.05646v1 [] 18 Sep 2015

Jory Schossau (jory@msu.edu)
Department of Computer Science and Engineering, Michigan State University
428 South Shaw Rd, East Lansing, MI 48824, USA

Heather Eisthen (eisthen@msu.edu), Arend Hintze (hintze@msu.edu)
Department of Integrative Biology, BEACON Center for the Study of Evolution in Action, Michigan State University
288 Farm Ln, East Lansing, MI 48824, USA
Abstract
Most research on adaptive decision-making takes a strategyfirst approach, proposing a method of solving a problem and
then examining whether it can be implemented in the brain
and in what environments it succeeds. We present a method for
studying strategy development based on computational evolution that takes the opposite approach, allowing strategies to
develop in response to the decision-making environment via
Darwinian evolution. We apply this approach to a dynamic
decision-making problem where artificial agents make decisions about the source of incoming information. In doing so,
we show that the complexity of the brains and strategies of
evolved agents are a function of the environment in which they
develop. More difficult environments lead to larger brains and
more information use, resulting in strategies resembling a sequential sampling approach. Less difficult environments drive
evolution toward smaller brains and less information use, resulting in simpler heuristic-like strategies.
Keywords: computational evolution, decision-making, sequential sampling, heuristics

Introduction
Theories of decision-making often posit that humans
and other animals follow decision-making procedures that
achieve maximum accuracy given a particular set of constraints. Some theories claim that decision-making is optimal
relative to the information given, involving a process of maximizing expected utility or performing Bayesian inference
(Bogacz, Brown, Moehlis, Holmes, & Cohen, 2006; Griffiths
& Tenenbaum, 2006; Von Neumann & Morgenstern, 1944).
Others assume that behavior makes trade-offs based on the
environment, tailoring information processing to achieve sufficient performance by restricting priors (Briscoe & Feldman,
2011), ignoring information (Gigerenzer & Todd, 1999), or
sampling just enough to satisfy a particular criterion (Link
& Heath, 1975; Ratcliff, 1978). In most cases, mechanisms
underlying the initial development of these strategies are assumed – either explicitly or implicitly – to be the result of
natural and artificial selection pressures.
In cognitive science research, however, the evolution of a
strategy often takes a back seat to its performance and co-

herence. The clarity and intuitiveness of a theory undoubtedly play an immense role, as does its ability to explain and
predict behavior, but whether or not a strategy is a plausible result of selection pressures is rarely considered. To be
fair, this is largely because the process of evolution is slow,
messy, and often impossible to observe in organisms in the
lab. Fortunately, recent innovations in computing have enabled us to model this process with artificial agents. In this
paper, we propose a method of studying the evolution of dynamic binary decision-making using artificial Markov brains
(Edlund et al., 2011; Marstaller, Hintze, & Adami, 2013; Olson, Hintze, Dyer, Knoester, & Adami, 2013) and investigate
the evolutionary trajectories and ultimate behavior of these
brains resulting from different environmental conditions.
In order to demonstrate the method and investigate an interesting problem, we focus on the simple choice situation
where a decision-maker has to choose whether the source of
a stimulus is ’signal’ S or ’noise’ N (for preferential decisions, nonspecific choices A or B can be substituted). A similar decision structure underlies a vast array of choices that
people and other animals make, including edible/inedible,
healthy/sick, safe/dangerous, and so on. The task requires a
decision-maker to take in and process information over time
and make a decision about which source yielded that information. However, the decision maker is free to vary the amount
of information it uses and processing it applies, and different
theories make diverging predictions about how each of these
should vary. On one hand, it may be more advantageous to
use every piece of information received, feeding it through a
complex processing system in order to obtain maximum accuracy. On the other, a simpler processing architecture that
ignores information may be sufficient in terms of accuracy
and more robust to random mutations, errors, or over-fitting.

More complex models
Many of the most prominent complex decision-making models fall under the sequential sampling framework (Bogacz et

al., 2006; Link & Heath, 1975; Ratcliff, 1978). These models
assume that a decision-making agent takes or receives samples one by one from a distribution of evidence, with each
sample pointing toward the signal or noise distribution. They
posit that agent combines samples to process information, for
example by adding up the number favoring S and subtracting
the number favoring N. When the magnitude of this difference exceeds a criterion value θ (e.g. larger than 4 / smaller
than -4), a decision is triggered in favor of the corresponding
choice option (+θ ⇒ S, −θ ⇒ N). This strategy implements
a particular form of Bayesian inference, allowing a decisionmaker to achieve a desired accuracy by guaranteeing that the
log odds of one hypothesis (S or N) over the other is at least
equal to the criterion value.
In these models, each piece of information collected is used
to make a decision. Although organisms may not literally add
and subtract pieces of information, we should expect to observe two characteristics in organisms that implement these
or similar strategies. First, they should be relatively complex, storing the cumulative history of information to make
their decisions. Second, they should give each piece of information they receive relatively equal weight, spreading out the
weights assigned to information across a long series of inputs.

more detail.

Less complex models

Decision task

Toward the other end of the spectrum of model complexity
are heuristics which deliberately ignore information in order to obtain better performance in particular environments
(Brandstätter, Gigerenzer, & Hertwig, 2006; Gigerenzer &
Brighton, 2009; Gigerenzer & Todd, 1999). Many of these
strategies are non-compensatory, meaning that they terminate the use of information as soon as one piece of evidence
clearly favors either S or N. Accordingly, a decision maker
can have a relatively simple information processing architecture, as it can just copy incoming information to its output
indicators to give an answer. Some of these require ordinal information about different sources of information and their validity, resulting in increased complexity (Dougherty, FrancoWatkins, & Thomas, 2008), but for the current problem we
assume that all information comes from a single source.
As a result of the relatively simple architecture and onepiece decision rules, we can expect to observe two characteristics in organisms that implement strategies similar to these
heuristics. First, they should have relatively simple information processing architectures, favoring short and robust pathways that do little integration. Second, they should appear to
give the most weight to the last piece(s) of information they
receive before making their decision, yielding a relationship
between the final decision and the sequence of inputs that is
heavily skewed to the most recently received inputs.
Of course, the real behavior of artificially evolved organisms will probably lie somewhere along the spectrum between these two poles. However, we can compare the relative
leanings of different populations of organisms by varying the
characteristics of the environments in which they evolve. We
next describe the decision-making task and manipulations in

The task that the agents had to solve was a binary decision
problem, where they received information from one source S
or another N. The information coming from either source included two binary numbers, and therefore could yield any of
the inputs [00], [01], [10], or [11]. Source S would yield primarily 0s on the left and 1s on the right, and source N would
yield primarily 1s on the left and 0s on the right. The exact
proportion of these inputs was varied in order to alter the difficulty of the task. For example, an easy S stimulus would
give 90% 0s (10% 1s) on the left, and 90% 1s (10% 0s) on
the right. The two inputs were independent, so this would
ultimately give 81% [01] inputs, 9% [11], 9% [00], and 1%
[10]. In a more difficult environment, an S stimulus might
have 60% 0s on the left and 60% 1s on the right, yielding
36% [01], 24% [11], 24% [00], and 16% [10]. For an N stimulus, the possible inputs would be the same, but the frequency
of [01] and [10] inputs would be flipped (i.e. more 1s on the
left and 0s on the right). These frequencies were not shown to
the agents at the start of each trial. Instead, each trial started
with a random frequency of 50%, increasing each consecutive
step by 1% until the target frequency was reached. This was
done in part to emulate how agents encounter stimuli in real
situations (i.e. stimuli progressively come into sensory range,
increasing in strength over time rather than simply appearing), but also to avoid ’sticking’ at a local maximum where
agents simply copy their first input to outputs.
The target frequency of 1s and 0s was manipulated to be
60 − 90% (in 5% increments), resulting in 7 difficulty levels
for different populations of agents.
For each decision, the agents received up to 100 inputs.
Each new input constituted one time step during which the

Methods
We were interested in examining the strategies and evolutionary trajectories that digital agents took to solve a simple dynamic decision-making problem. To do so, we developed a
binary decision-making task for the agents to solve. The fitness of an agent was defined as the number of correct decisions it made over 100 trials of the task, and the probability
that it would reproduce was determined by this fitness value.
Note that fitness was determined by the number of correct answers, reflecting agents’ propensity to respond together with
their accuracy when they did respond - there was no fitness
penalty or cost for agent complexity. Formally, the probability that it generated each child of the next generation was
given by its fitness divided by the total fitness across the total
population (roulette wheel selection). An agent reproduced to
the next generation by creating a copy of itself with random
mutations. Over the course of 10,000 generations, this selection and mutation process led to evolution of agents that could
successfully perform the task, and enabled us to analyze the
strategies that the evolved agents ultimately developed.

agent could process that information. If an agent gave an answer by signaling [01] to indicate S or [10] to indicate N (see
below), then the decision process would come to a halt, where
no new inputs would be given and the agent would be graded
on its final answer. An agent received 1 point toward its fitness if it gave the correct answer or 0 points if it was incorrect
or if it failed to answer before 100 inputs were given.
In addition to the difficulty manipulation, we included a
“non-decision time” manipulation, where an agent was not
permitted to answer until t time steps had elapsed (i.e. the
agent had received t inputs). This number t was varied
from 10 to 50 in 5-step increments, yielding 9 levels of nondecision time across different environments. Increasing t
tended to make agents evolve faster, as longer non-decision
time tended to allow agents to more easily implement strategies regardless of difficulty level.

pings in the gate tables (e.g. it could change between any of
the gates shown in Figure 1). This code consisted of 2000200,000 ’nucleotides’ and included mutation rates of 0.005%
point mutations, 0.2% duplication mutations, and 0.1% deletion mutations, consistent with previous work (Edlund et al.,
2011; Marstaller et al., 2013; Olson et al., 2013). More precisely, logic gates are specified by ’genes’ within this genetic
code. Each gene consists of a sequence of nucleotides, numbered 1-4 to reflect the four base nucleotides present in DNA,
and starts with the number sequence ’42’ followed by ’213’
(start codon), beginning at an arbitrary location within the
genome. Genes are typically about 300 nucleotides long and
can have ’junk’ sequences of non-coding nucleotides between
them, resulting in the large size of the genomes.
The first generation of Markov brain agents in each population was generated from a random seed genome. The first
100 agents were created as random variants of this seed brain
using the mutation rates described above, resulting in approximately 20 − 30 random connections per agent. These 100
agents each made 100 decisions, and were selected to reproduce based on their accuracy. This process was repeated for
each population for 10,000 generations, yielding 100 agents
per population that could perform the decision task.

Data

Figure 1: Diagram of the structure of a sample Markov brain
with input, processing, and output nodes (circles) with connecting logic gates (rectangles). Each gate contains a corresponding table mapping its input values (left) to output values
(right). Note that our actual agents had twice the number of
nodes shown here available to them.

Markov brain agents
The Markov brain agents (Edlund et al., 2011; Marstaller et
al., 2013; Olson et al., 2013) consisted of 16 binary nodes and
of directed logic gates that moved and/or combined information from one set of nodes to another (see Figure 1). Two of
these nodes (1 and 2) were reserved for inputs from the environment, described above. Another two (15 and 16) were
used as output nodes. These output nodes could show any
combination of two binary values. When they did not read
[01] (indicating S), or [10] (indicating N), the agents were
permitted to continue updating their nodes with inputs until
time step 100. To update their nodes at each time step, the
agents used logic gates (represented as squares in Figure 1,
which took x node values and mapped them onto y nodes using an x × y table.
The input nodes, table, and output nodes for these gates
were all specified by an underlying genetic code that each
Markov brain possessed. Point, insertion, or deletion mutations in the genetic code would cause them add / subtract
inputs to a gate, add / subtract outputs, or change the map-

For each of the 63 conditions (7 difficulty levels × 9 nondecision times), we ran 10,000 generations of evolution for
100 different sub-populations of Markov brains, giving 6300
total populations. From each of these populations, a random
organism was chosen and its line of ancestors was tracked
back to the first generation. This set of agents from the last
to the first generation is called the line of decent (LOD). For
each of the 100 replicates per experimental conditions, all parameters (such as fitness) of agents on the LOD were averaged for each generation.
In each of these LODs, we tracked the average number of
connections between nodes (see Figure 1) that agents had in
each condition and each generation. We refer to this property
of the agents as “brain size” — the analogous properties in an
organism are the number and connectivity of neurons — and
we show its evolutionary trajectory in Figure 2.
Finally, we took a close look at the behavior of generation
9970 – this is near the end to ensure that the generation we examined could solve the task, but slightly and somewhat arbitrarily removed from generation 10,000 to ensure that agents
in this generation weren’t approaching one of the random dips
in performance (i.e. random mutations from this generation
were less likely to be deleterious than more recent ones). For
these agents, we examined each trial to see what information
they received at each time step, which step they made their
decision, and which decision they made (coded as correct or
incorrect). This allowed us to examine the relationship between the inputs they received and the final answer they gave,
giving an estimate of the weight they assigned to each new
piece of information.

Materials
The agents, tasks, and evolution were implemented in C++
using Visual Studio Desktop and Xcode, and the full evolution simulations were run at Michigan State University’s High
Performance Computing Center.

Results
With the exception of high difficulty, low non-decision time
conditions, most populations and conditions of agents were
able to achieve essentially perfect accuracy on the decision
task after 10,000 generations. However, the strategies implemented by each population varied heavily by condition.
It is perhaps worth noting at this point the tremendous
amount of data that our approach yields. Each condition consisted of 100 populations of 100 agents that made 100 decisions each generation, yielding 10,000 agents and 1 million
decisions per generation per condition. This tremendous sample size renders statistical comparisons based on standard error, for example, essentially moot. For this reason, we present
mostly examples that illustrate important findings rather than
exhaustive statistical comparisons.

Brain size
Final brain size (number of connections among nodes) varied as a function of both stimulus difficulty and non-decision
time. We focus primarily on high non-decision time conditions, as many of the low non-decision time populations —
particularly in the difficult stimuli conditions — were unable
to achieve the high performance of other groups. As Figure
2 shows, agents faced with the easiest conditions (10-15%)
tended to have the smallest final brain size, with means of
around 15 − 20 connections. Agents faced with medium difficulty environments evolved approximately 25 − 30 connections, and agent brain size in the most difficult conditions approached 35 connections and appeared to still be climbing
with further generations.
Perhaps more interesting, though, is the evolutionary trajectory that each of the populations in these conditions took.
As shown, each group started with 25-30 connections in the
initial generation, and in all of them the number of connections initially dropped for the first 200-400 generations. After that, however, the conditions appear to diverge, with the
agents in the easy conditions losing even more connections,
agents in the medium conditions staying approximately level,
and agents in the difficult conditions adding more and more
connections.

Strategy use
In order to examine the pattern of information use in the
agents, we additionally examined the relationship between
each piece of information received and the final answer
given. We did so by taking the series of inputs (e.g.
[00],[11],[01],[01],[11]) and assigning each one a value - information favoring S ([01] inputs) was assigned a value of +1,
information favoring N ([10] inputs) was assigned a value of

Figure 2: Mean number of connections in agent brains across
generations for three levels of task difficulty. For the sake of
comparison, the trajectories shown are all from populations
with a non-decision time of 40 steps
−1, and others ([00] and [11]) were assigned a value of 0. Answers favoring S were also given a value of +1 and answers
favoring N a value of −1. Doing so allowed us to track the
sequence of −1, 0, +1 — which we refer to as the trajectory
— leading to the decision and to correlate this with the final
+1 or −1 answer. The result of this analysis for the example
conditions is shown in Figure 3.
As shown, the trajectory correlations in the more difficult
conditions tend to be flatter than those in the easy conditions,
and final answers tend to correlate with a longer history of
inputs. This indicates that these agents were assigning more
similar weight to each piece of information they use, utilizing
the full history of inputs they had received rather than just the
final piece. Note that all agents appeared to use the most recent pieces of information more heavily. This will be the case
for almost any model that generates the data, as the last pieces
of information tend to be those that trigger the decision rule
– for example, in sequential sampling this will be the piece
of information that moves the evidence across the threshold
– and as such will always be highly correlated with the final
answer. 1
Information use also varied somewhat across levels of nondecision time, but its effect was not particularly pronounced
except in the more difficult conditions (e.g. 60-70%). However, this effect is largely a consequence of agent populations’
failure to evolve to perform the task as well when stimulus
1 However,

since it can sometimes take several updates / time
steps to move a ’trigger’ input through the brain to the output nodes,
the final piece of information will not always be perfectly correlated
with the output.

Figure 3: Example correlations between inputs and final decision for easy (blue), medium (purple) and difficult (red) conditions. The trajectories are time-locked on the final answer
on the right side, so the last piece of information an agent received is the rightmost value, and to the left is moving backward through the trajectory.
discriminability and non-decision time were low. For example, agents in the difficult, short non-decision time condition
(red in left panel of Figure 3) attained accuracy of only 82%,
compared to 95+% in other conditions. Higher difficulty still
led to larger brains and a longer history of processing in these
conditions, but its effect was less pronounced. Therefore,
high values of non-decision time apparently made it easier
to evolve complex strategies, likely because agents were exposed to more information before making their decisions.

Discussion
While agents’ strategies spanned a range of complexity, more
difficult environments pushed them toward more complex
strategies resembling sequential sampling while easier environments led to strategies more similar to non-compensatory
heuristics. Therefore, both sequential sampling and heuristics
seem to be strategies that could plausibly result from different
environmental demands. However, our results run counter to
the idea that heuristics are invoked when decisions are particularly difficult or choice alternatives are not easily distinguished (Brandstätter et al., 2006).
The final strategies may not support the claim that organisms are primarily heuristic decision-makers (Gigerenzer &
Brighton, 2009), but it still lends credence to the premise of
ecological rationality on which many heuristics are based.
This approach suggests that different environments (choice
ecologies) lead to different decision-making strategies rather
than a one-size-fits-all process. It is certainly plausible that
agents in environments with mixed or changing difficulty levels converge on a single strategy, but for the moment it seems
that multiple strategies can be implemented across multiple

choice environments.
While difficult conditions led to larger brains and more information processing, perhaps a more critical finding is that
simpler choice environments led to simpler decision strategies and architectures. While this may initially seem like the
other side of the same coin, this result is particularly interesting because we did not impose any penalties for larger brains.
Although other researchers have suggested that metabolic
costs limit the evolution of large brains (Isler & Van Schaik,
2006; Laughlin, van Steveninck, & Anderson, 1998) and can
be substantial in real brains (Kuzawa et al., 2014), they were
not necessary to drive evolution toward smaller brains.
Instead, we suspect that the drop in brain size is a result of
the agents’ response to mutations, or the mutation load imposed by the size of its genome. For example, a random mutation in the genome that connects, disconnects, or re-maps
a gate is more likely to affect downstream choice-critical elements of a brain that uses more nodes and connections to
process information (has a higher mutation load), particularly
if it has a larger ratio of coding to non-coding nucleotides. In
this case, a smaller brain would be a tool for avoiding deleterious mutations to the information processing stream. Alternatively, the minimum number of nodes and connections
required to perform the task is likely lower in the easier conditions than in the more difficult ones, so mutations that reduce brain size and function might be able to persist in the
easier but not the more difficult conditions. In either case,
it is clear that a larger brain does not offer sufficient benefits in the easier conditions to overcome the mutation load it
imposes.
Another potential risk of having a larger brain is the chance
of a random mutation preventing information from reaching
the output nodes – with a longer chain of processing nodes
being easier to interrupt or confuse than a shorter one. While
the agents in more difficult conditions were evidently able to
overcome such a possibility (usually answering within 20
steps of the end of non-decision time), it may be a barrier that
required substantial fitness rewards to cross, which were not
present in the easier conditions.
We hesitate to make claims that are too broad given the
scope of our study, but the finding that brain size can be limited by mutation load is provoking. This may explain why
systems that are subject to mutations and selection pressures
– including neurons and muscle cells – are reduced when they
are unused, even when the energetic costs of maintaining the
structure appear to be low. It seems a promising direction for
future research to examine in-depth how mutation rate and
robustness contribute to organisms’ fitness above and beyond
the costs associated with metabolism.

Approach
We hope to have presented a method for examining questions regarding adaptation and evolution that often arise in
cognitive science and psychology. Whereas previous studies have worked from a particular strategy and examined the
choice environments in which it succeeds, we present a way

of answering questions about how the environment can shape
the evolution of a strategy. The strategies resulting from this
computational evolution approach are adaptive, easily implemented in the brain, and the result of realistic natural selection pressures. Additionally, we have shown that this approach is capable of addressing important questions about existing models of simple dynamic decisions, though it could
undoubtedly shed light on an array of related problems.
Of course, there are limitations to this approach, many of
which are computational. The agents we used had only 16
nodes, 4 of which were reserved for inputs and outputs, meaning that only 12 could be used for storing (memory) and processing information. Although more nodes could be added –
and certainly an accurate model of even very simple nervous
systems would have many times more – this would severely
slow down the steps required for evolution. It might also lead
to problems that are analogous to the over-fitting that occurs
when more parameters are added to a model, though this is
itself a question worth exploring.

Conclusions
In this paper, we presented a computational evolution framework that could be used to examine how environments lead to
different behaviors. This framework allowed us to examine
the strategies that might have arisen in organisms to address
the problem of dynamic decision-making, where agents receive information over time and must somehow use this input
to make decisions that affect their fitness.
We found that both the evolutionary trajectory and the
strategies ultimately implemented by the agents are heavily
influenced by the characteristics of the choice environment,
with the difficulty of the task being a particularly notable
influence. More difficult environments tended to encourage
the evolution of complex information integration strategies,
while simple environments actually caused agents to decrease
in complexity, perhaps in order to maintain simpler and more
robust decision architectures. They did so despite no explicit
costs for complexity, indicating that mutation load may be
sufficient to limit brain size.
Finally, we discussed these results in the context of existing models of human decision-making, suggesting that both
non-compensatory strategies such as fast and frugal heuristics (Gigerenzer & Todd, 1999) and complex ones such
as sequential sampling (Link & Heath, 1975) may provide
valid descriptions – or at least serve as useful landmarks –
of the strategies implemented by evolved agents. In doing
so, we provided evidence that strategy use is environmentdependent, as different decision environments led to different patterns of information use. More generally, we have
shown that a computational evolution approach integrating
computer science, evolutionary biology, and psychology is
able to provide insights into how, why, and when different
decision-making strategies evolve.

Acknowledgments
This work was supported by Michigan State University’s
High Performance Computing Facility and the National Science Foundation under Cooperative Agreement No. DBI0939454 and Grant No. DGE-1424871.

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