Robustness and Conceptual Analysis in Evolutionary Game Theory


Robustness and Conceptual Analysis in Evolutionary Game Theory
Author(s): Zachary Ernst
Source: Philosophy of Science, Vol. 72, No. 5, Proceedings of the 2004 Biennial Meeting of The
Philosophy of Science Association<break></break>Part I: Contributed
Papers<break></break>Edited by Miriam Solomon (December 2005), pp. 1187-1196
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Philosophy of Science, 72 (December 2005) pp. 1187–1196. 0031-8248/2005/7205-0044$10.00
Copyright 2005 by the Philosophy of Science Association. All rights reserved.

1187

Robustness and Conceptual Analysis in
Evolutionary Game Theory

Zachary Ernst†

A variety of robustness objections have been made against evolutionary game theory.
One of these objections alleges that the games used in the underlying model are too
arbitrary and oversimplified to generate a robust model of interesting prosocial be-
haviors. In this paper, I argue that the robustness objection can be met. However, in
order to do so, we must attend to important conceptual issues regarding the nature of
fairness, justice, and other moral concepts. Specifically, we must better understand the
relationship between moral concepts and formal characterizations of games.

1. Introduction. Evolutionary game theory is primarily understood as a
tool in the descriptive project of explaining the historical origins of certain
behavioral propensities. For example, if we want to know how people
have come to have the propensity to cooperate in certain one-shot Pris-
oner’s Dilemmas, we may try to answer this question by exhibiting an
evolutionary game-theoretic model in which the simulated agents evolve
that behavior under certain initial conditions. If the model is based upon
plausible assumptions, then it is taken as at least a partial explanation of
why people exhibit that behavior in real-world circumstances.

This is understood as a purely descriptive project, and advocates of this
approach—such as Brian Skyrms (1999, 2001, 1994a, 1994b, 1996), Elliott
Sober and David Sloan Wilson (1992, 1994, 1998), and Jason Alexander
(2000, 1999)—tend not to address normative questions or conceptual
questions concerning issues of fairness, justice, and the social contract
generally. Their avoidance of normative and conceptual questions has at
least two motivations. First, they take the descriptive project to be a
philosophically interesting one in and of itself. In particular, Skyrms has
argued at length that the rational choice tradition, in which morality is
supposed to derive from purely rational considerations, has failed to give

†To contact the author, please write to: Department of Philosophy, 438 General Class-
room Bldg., University of Missouri-Columbia, Columbia, MO 65211; e-mail: ernstz@
missouri.edu.



1188 ZACHARY ERNST

an explanation of our moral practices. This leaves a significant gap in the
project, which is to be filled by the descriptive project he has advocated.
Skyrms is not alone in this conviction; philosophically minded economists
such as Ken Binmore (1994, 1989), Larry Samuelson (1994, 1997), and
H. Peyton Young (1994) also take a dim view on the project of rationally
justifying our moral practices. According to them, if we understand ra-
tionality as some kind of informed self-interest, then we have no reason
to expect rational people to behave in a just or fair way, despite the
arguments of rational choice theorists such as Jon Elster (1992, 1989),
David Gauthier (1993, 1986), and John Rawls (1972). Another reason
for avoiding the normative and conceptual questions is out of a fear of
committing the naturalistic fallacy. For if one takes a strong position on
the impossibility of inferring an ought from an is, then any descriptive
project must be carefully distinguished from any normative one.

As a descriptive project, evolutionary game theoretic accounts are sub-
ject to robustness objections. That is, the evolutionary game theoretic
models necessarily contain a large number of simplifications and ideali-
zations, which are crucial for making the models mathematically tractable.
Thus, it is incumbent upon the advocates of evolutionary game theory
to show that these idealizations do not do not render the models so
unrealistic that they are no longer applicable to the real world. The ro-
bustness of these models has been criticized by several authors, and this
is probably the criticism that has attracted the most attention in the
literature (D’Arms et al. 1998; D’Arms 1996; Ernst 2001; Barrett et al.
1999; Kitcher 1999). I believe that these robustness worries may be met
(Ernst 2001). But I shall argue here that the strategy that we employ for
answering the robustness objections bears directly on important concep-
tual issues regarding the nature of fairness, justice, and other prosocial
behaviors. That is, if we cope with the robustness worries in the right
way, then we may simultaneously sharpen our understanding of the ex-
planandum behaviors.

2. Robustness in Evolutionary Game Theory. In this paper, we will not be
concerned with the details of evolutionary game theoretic models.1 For
our purposes it is enough to think of an evolutionary game theoretic
model in very general terms. Such models may be thought of as simulating
the evolution of a large number of individuals who interact by playing a
game, such as the Prisoner’s Dilemma or Divide-the-Cake. The individuals
are paired up, play the game, and are assigned a fitness that is based upon
the payoff that they receive in their interactions. We may then think of

1. A good introduction to a variety of evolutionary game theoretic models may be
found in Weibull 1995, and a quick introduction is in Sober 1993.



EVOLUTIONARY GAME THEORY 1189

the individuals as having a number of offspring that is proportional to
their fitness. The parent generation then dies, and the process is reiterated
with the new generation. In this way, certain strategies may eventually
come to predominate in the population, if their bearers enjoy a higher
than average fitness. If the most successful strategies are the ones that are
intuitively ‘fair’, ‘just’, or ‘altruistic’, then this is supposed to explain why
those behaviors are observed in real world populations.

Robustness worries arise because we must make several different as-
sumptions when we set up the model. We must determine whether the
individuals are paired up at random, or according to some assortative
mechanism based, for instance, on spatial proximity or genetic relatedness.
Similarly, we must determine the functions that relate payoff and fitness;
and we must also decide whether the dynamic is supposed to represent a
social learning function or a biological process of natural selection. And
we must also decide whether we are interested in the long term behavior
of the model, or its behavior in the short run.2

More obviously, we must also choose which game the simulated agents
are supposed to play. Following the work of Robert Axelrod (1984, 1997),
the traditional choice has been to focus on the iterated Prisoner’s Di-
lemma, because that game provides us with a worst case scenario for the
evolution of cooperation. Additionally, Sober and Wilson have argued
that although the Prisoner’s Dilemma has traditionally been used as a
model of cooperation, it also happens to be the best available model of
altruism (1998). But more recently, Skyrms has proposed that we use
Divide-the-Cake, which was introduced by John Nash (1950) as a model
of strategic bargaining. Skyrms has also offered a provocative argument
that the Stag Hunt game, which differs significantly from both the Pris-
oner’s Dilemma and Divide-the-Cake, should be the focus of our inves-
tigations into the evolution of the social contract (2001, 2004). A variety
of other games are commonly discussed in the economics literature (which
is the traditional home of evolutionary game theory), including the so
called Dictator game, the Ultimatum game, and the Centipede game
(Bethwaite and Thompkinson 1996; Camerer and Thaler 1995; Gale et
al. 1993; Güth et al. 1982; Hoffman 1996; McKelvey 1992). Each one has
at least some claim to be a model of fairness, altruism, cooperation, or
other prosocial behavior.

The existence of such a wide variety of games has been taken to com-
prise a robustness objection to the evolutionary game theoretic models.
Clearly, if there are several plausible games that may each serve as a

2. Larry Samuelson has distinguished between what he calls the ‘short run’, the ‘long
run’, and the ‘very long run’ equilibria in evolutionary games (1997), and has argued
that each may be appropriate for different phenomena.



1190 ZACHARY ERNST

model of (say) fairness, and these games behave differently in the evo-
lutionary models, then we will have to justify whichever game we model.
For example, the Prisoner’s Dilemma is notoriously characterized by the
fact that the intuitively fair strategy of cooperation will never be the
rational choice in any one shot game, for defection is guaranteed to have
a higher payoff, regardless of what strategy is played by one’s partner.
But in Divide-the-Cake (which is the focus of Skyrms 1996), the intuitively
‘fair’ strategy will sometimes be the choice of a rational agent, for it yields
the highest payoff when paired up against itself. This single difference is
enough to force radically different behavior in evolutionary models of the
two games. For instance, in the standard replicator dynamics model of
the Prisoner’s Dilemma, cooperation will invariably die out if there are
any defectors in the initial population. But if we model Divide-the-Cake
under identical dynamics, the fair strategy is likely to predominate in the
population. And yet, if each has equal claim as a model of fairness, then
one may object that an evolutionary model of either fails the test of
robustness. Indeed, this objection has been raised by Philip Kitcher (1999).

The favored response to this particular robustness worry has been to
posit some mechanism that favors the evolution of prosocial behavior in
virtually any game. Specifically, the centerpiece of most evolutionary ex-
planations is a mechanism of assortment, by which a player is more likely
to interact with another player who uses the same strategy. It is hard to
overstate how important assortative mechanisms have been in game the-
oretic explanations of prosocial behaviors, both in philosophical, eco-
nomic, and biological work. They are the only plausible mechanisms
capable of sustaining cooperation in the one shot Prisoner’s Dilemma,
and they have an extremely strong positive influence on other games.
However, there are cases—particularly in social settings—where it is un-
realistic to expect correlation. As D’Arms et al. (1998) have argued, if we
are dealing with cognitively sophisticated agents, then we would not expect
the most ‘greedy’ or ‘selfish’ individuals to seek each other out. Rather,
we should expect them to try to establish a strong anticorrelation in the
population.

Other mechanisms that favor the evolution of prosocial behaviors, while
provocative, do not fare as well as assortment. If the population has some
sort of spatial structure, and individuals tend to interact with their neigh-
bors, then the prosocial behaviors may be favored (Skyrms and Alexander
1999; Young 1998). However, this depends crucially upon which game is
played. In Divide-the-Cake, incorporating spatial proximity into the
model has a dramatic and positive effect on the evolution of fairness. But
spatial proximity is largely irrelevant to the evolution of cooperation in
the one shot Prisoner’s Dilemma. In other models, particularly in the
context of biological evolution, we imagine a metapopulation structure



EVOLUTIONARY GAME THEORY 1191

that is divided into relatively isolated subpopulations (Wright 1943, 1945).
If we allow for the right amount of migration between subpopulations,
then the prosocial behavior may be favored in some games like Divide-
the-Cake or the Stag Hunt. But this population structure actually has the
opposite effect in the one shot Prisoner’s Dilemma—if cooperation hap-
pens to evolve in any subpopulation, it is quickly wiped out by even a
single immigrant defector.

3. The Conceptual Question: Game Selection. So on the face of it, it is
difficult to see how a single explanatory strategy can account for the wide
range of observed prosocial behaviors in such a variety of contexts.3 In
the course of gauging how successful an explanatory strategy has been,
we must determine to which class of games it applies. For example, if an
explanation applies only to Divide-the-Cake, but not to the Prisoner’s
Dilemma, then we must be careful to distinguish between situations in
which one or the other game is the most reasonable choice. Of course,
the ideal situation would be to have a mechanism that works in favor of
the prosocial strategy in any game.

At this point, we are led immediately to a prior conceptual question
that has not been adequately addressed in this literature. Some games,
like the Prisoner’s Dilemma, are naturally taken to model prosocial be-
haviors. Other games are not. While many games are of theoretical in-
terest, most are not easily interpreted as representing ‘fairness’, ‘cooper-
ation’, or any related normative concept. The question is this: why are
some games reasonable models of prosocial behaviors, while other games
are not?

Another way to put the same question is to ask how we can determine,
for any given game, what prosocial behavior (if any) the game models.
To see that this conceptual question has not been adequately addressed,
we may examine what social behaviors the standard evolutionary game
theoretic models are taken to explain. Skyrms, for instance, characterizes
Divide-the-Cake as a model of ‘fairness’, ‘justice’, ‘cooperation’, ‘mod-
esty’, and ‘the existing implicit social contract’. Sober and Wilson point
out that the Prisoner’s Dilemma is frequently characterized both as a
model of ‘cooperation’ and ‘altruism’ (1998, 84–85). The famous strategy
of Tit-for-Tat in the iterated Prisoner’s Dilemma is usually called a ‘nice’
or ‘altruistic’ strategy; but someone using Tit-for-Tat will not hesitate to
defect repeatedly against a defector—so this is hard to characterize as an
altruistic strategy. Furthermore, it should be clear that the ‘social contract’
is something much more complex than mere cooperation, while cooper-

3. Thus, we have a prima facie argument against what Alexander (2000) has called
‘explanatory generalism’ in evolutionary game theory.



1192 ZACHARY ERNST

ation is not the same behavior as justice—after all, two people can co-
operate in an unjust behavior. Furthermore, cooperation is clearly not
the same behavior as altruism. For example, we may plausibly cooperate
by agreeing to drive on the right side of the road, but this kind of co-
operation has nothing to do with altruism, either in the psychological or
biological sense.

Thus, there is a considerable level of conceptual unclarity with respect
to the normative concepts that are being explained in the evolutionary
game theory paradigm. Furthermore, as the robustness worry shows us,
we cannot sweep this conceptual issue under the rug and still generate
robust evolutionary explanations. For so long as the different games have
different behaviors in the evolutionary models, we will always be chal-
lenged to justify our choice of game. And it is clear that this challenge
cannot be met if we are unclear as to what normative concept the game
is supposed to model in the first place.

The uncharitable way to interpret this gap in discussions of evolutionary
game theoretic models would be to conclude that this explanatory strategy
is fundamentally flawed. But I favor a charitable interpretation. Instead
of taking a dim view, we could instead note that game theorists do tend
to pick out the same games from a wide array of possibilities, even if they
assign conflicting labels to the corresponding normative concepts. Thus,
we might conclude that, although there is some level of conceptual un-
clarity, we are nonetheless working with some determinate normative
concept. For if game theorists were really as unclear as some of their
language suggests, we might reasonably expect to find a wider range of
games in the evolutionary models; after all, there are infinitely many games
to choose from, and we find only a relatively small number actually being
discussed.

Let us call the class of games that are reasonable models of normative
concepts ‘fairness games’. The conceptual question is to give a reasonable
set of criteria for determining when a game is in the class of fairness
games, and when it is not. If we can answer that question, then we will
have simultaneously made progress on two fronts. First, we will have
clarified the explanandum, and thereby made progress on conceptual ques-
tions regarding the nature of prosocial behaviors like fairness, justice, and
altruism. Second, we will be able to better define a strategy for dealing
with robustness worries. For if we can delimit the set of fairness games,
then we will have a better understanding of what conditions must be met
for an explanation to be robust.

4. Toward a Characterization of Fairness Games. In what follows, I do
not attempt to give a definitive characterization of fairness games, but to
outline some of the considerations that must go into any such charac-



EVOLUTIONARY GAME THEORY 1193

terization. Furthermore, I shall use the word ‘fair’ as a generic term
representing the cluster of related normative concepts that are the subjects
of game theoretic models.

It should be a tautology that fairness games admit of at least two distinct
outcomes, one of which will be fair, and the other of which will be unfair.
If we take seriously the concerns of Skyrms, Binmore, and others who
criticize the rational choice tradition of reducing morality to rationality,
then we must hold that it is possible that rational players could settle on
an unfair outcome. For if it is impossible to give a rational justification
for, e.g., cooperation in the one shot Prisoner’s Dilemma, that is tanta-
mount to saying that rationality might endorse defection. Similar con-
siderations will apply to any fairness game—if rationality does not suffice
to justify the fair choice, then rationality might endorse the unfair one.
And this just means that rational players may converge on the unfair
outcome.

Furthermore, we must follow the lead of economists who define ratio-
nality as a tendency to choose the highest available payoff. For any other
reasonable characterization of rationality defines away the descriptive
problem, by letting rational players be influenced by moral considerations
or other factors that are not represented in the game’s payoff matrix. So
we are led to conclude that in a fairness game, a set of greedy maximizers
might converge on an unfair outcome.

There are several competing theories that each characterize the set of
strategies that a rational player may select. These include rationalizability
(Brandenburger and Dekel 1987), Nash equilibrium (Nash 1950), and
others. For simple games, these concepts will coincide. So let us take a
simple definition as an example. Recall that a strategy is dominated just
in case there is another strategy that yields a higher payoff, at least some
of the time, but never yields a lower payoff. Simple arguments conclude
that rational players will not select dominated strategies; and if it is com-
mon knowledge that all players are rational, then no player will play a
strategy that is justified only on the assumption that someone else might
play a dominated strategy. Thus, we may stipulate that a rational strategy
survives the iteration elimination of dominated strategies.

So when we conclude that in a fairness game, the unfair outcome may
be selected by a rational player, we are saying that:

1. A fairness game will have an unfair outcome g (for greedy) that
survives the iterated deletion of dominated strategies.

Clearly, the unfair outcome cannot be the same as the fair outcome. And
if rationality might not endorse the fair outcome, then it could be elim-
inated by deletion of dominated strategies (although it might not be). So
we have:



1194 ZACHARY ERNST

2. A fairness game will have a fair outcome , which may or mayf ( g
not survive the iteration of dominated strategies.

The concept of efficiency often plays a role in discussions of prosocial
behaviors in games (see, e.g., Skyrms 1994a). A outcome is said to be
efficient just in case it leads to the highest total payoff to all players. So
in the Prisoner’s Dilemma, mutual cooperation is efficient, while mutual
defection is not. In fact, the formal definition of the Prisoner’s Dilemma
guarantees that mutual cooperation is the only efficient outcome. Intui-
tively, it seems that efficiency is a mark of the fair outcome. However, in
other games, efficiency does not correlate with fairness. For example, in
bargaining games, an outcome is efficient just in case all of the available
goods are divided between the players. But the outcome in which one
player gets everything is certainly not fair, even though it is efficient. A
better candidate is Pareto efficiency, where an outcome is Pareto efficient
just in case no player can secure a higher payoff without causing another
player to receive a lower payoff. Clearly, in a bargaining game, the unique
Pareto efficient outcome is one in which the divisible good is evenly split
between the two players; and this coincides with our pre-analytic notion
of fairness. So let us suppose that:

3. In a fairness game, the ‘fair’ outcome f will be Pareto efficient.

Undoubtedly, there is more to the story. But even this simple character-
ization gets quite close, for it corresponds quite closely with the games
that are commonly studied. The Prisoner’s Dilemma, Divide-the-Cake,
the Stag Hunt, as well as the Ultimatum and Dictator games all qualify
under this definition as fairness games. Other games, such as Matching
Pennies, do not. So this conception of a fairness game is at least a rea-
sonable place to begin.

5. Payoff. The payoff of having a characterization of fairness games is
significant. First of all, it saves us from having to adopt an uncharitable
interpretation of evolutionary game theoretic models, which may use dif-
ferent normative labels for the same behavior, or use the same game for
modeling different normative concepts. We can say, instead, that there is
a cluster of related normative concepts that are not equivalent, but center
around a small number of shared characteristics. Our simple definition
of a fairness game provides us with at least a start at characterizing what
is shared by those normative concepts. Specifically, normative concepts
are modeled by strategic situations in which a Pareto efficient outcome
might not be selected by a rational agent, because of the existence of an
alternate outcome yielding a higher payoff, and which survives the iterated
deletion of dominated strategies.



EVOLUTIONARY GAME THEORY 1195

This also gives us a principled way of answering robustness worries.
For if a mechanism or population structure can be shown to increase the
probability of having a Pareto efficient ‘fair’ outcome in the entire class
of fairness games, then we will have addressed an important objection.
Assortative mechanisms may be one such mechanism (as Skyrms (1994b)
suggests), but there may be others. In a biological context, we should be
looking for alternate population structures that favor the fair outcomes
in fairness games. There is every reason to expect that there is a wide
variety of explanatory strategies that will yield interesting results for the
evolutionary game theoretic project. Clarity with respect to the conceptual
issues is a prerequisite for finding these explanations.

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