404 Social Influence and Group Dynamics
of complex systems and are widely used in physics and vari-
ous domains of biology, including neuroscience (Amit, 1989)
and population dynamics (May, 1981). A set of elements is
specified to represent the basic units (e.g., neurons, people)
in the process under consideration. Each element can adopt
a finite number of discrete states (e.g., activated vs. inhibited,
pro- vs. antiabortion). The elements are arranged in a
spatial configuration, the most common of which is a two-
dimensional grid. The state of an element at t+ 1 depends on
the states of the neighboring elements at time t.The exact
form of this dependence is specified by so-called updating
rules. The dynamics of cellular automata depend on the na-
ture of the updating rule and on the format of the grid dictat-
ing the neighborhood structure.
Two classes of cellular automata models are used to char-
acterize social processes. In both, elements represent individ-
uals in a social system. In one, personal characteristics
change as a result of updating rules. This approach explores
changes in attitudes and opinions that occur as a result of
social interaction. In the other class, individuals maintain sta-
ble characteristics but may change their physical location.
This approach has revealed the emergence of spatial patterns
on the basis of stable values and preferences. Shelling (1969,
1971), for instance, developed an updating rule specifying
that an individual who has more dissimilar than similar
neighbors will move to a different random location. Simula-
tions based on this simple rule demonstrated the emergence
of spatial patterns corresponding to social segregation. Both
classes of models reveal the emergence of regularities and
patterns on a global level that were not directly programmed
into the individual elements. These regularities and patterns
typically take the form of spatial configurations, such as co-
herent minority opinion clusters that emerge from an initial
random distribution of opinions. Regularities may also ap-
pear as temporal patterns, including such basic trajectories as
the development of a stable equilibrium (fixed-point attrac-
tor), alternation between different states (periodic attractor),
and apparent randomness (deterministic chaos).
Cellular Automata and Social Processes
Cellular automata models are useful for exploring different
social interaction rules and the generation of societal level
phenomena as a result of such rules (cf. Hegselman, 1998;
Messick & Liebrand, 1995; Nowak, Szamrej, & Latané,
1990). In these applications, the neighborhood structure is
intended to capture the structure of interdependence among
individuals (Thibaut & Kelley, 1959). Indirect interdepen-
dence exists when an individual’s actions have conse-
quences, intended or unintended, for other people. This form
of interdependence is often examined in the context of social
dilemmas, in which an action intended to maximize personal
gain has negative consequences for others (cf. Schulz,
Alberts, & Mueller, 1994). In the tragedy of the commons
(Hardin, 1968), for instance, a farmer is motivated to over-
graze an area of land shared with other farmers. In the short
run, the farmer gains advantage over his neighbors, but in the
long run, everyone—the farmer included—suffers. Direct in-
terdependencereflects what we normally think of as social
influence: One person directly influences the state or behav-
ior of another person. Power, manipulation, and coordination
thus represent direct interdependence. Both indirect and di-
rect forms of interdependence have been examined in cellular
automata models.Interdependence and Social DilemmasHow can altruistic behavior can emerge against the backdrop
of self-interest? Insight into this puzzle derives from cellular
automata models that simulate the short- and long-term
effects of behavior in the Prisoner’s Dilemma Game (PDG).
In pioneering this approach, Axelrod (1984) demonstrated
that cooperation often emerges among individuals trying to
maximize their respective self-interest. Essentially, Axelrod
found that cooperators survived by forming clusters with one
another, so that they could engage in mutual help without
risking exploitation.
In an extension of this approach, Messick and Liebrand
(1995) modeled the consequences of different strategies in
the PDG. Each interactant occupied a fixed position in a two-
dimensional lattice and played a PDG with one of his or
her nearest neighbors. On each trial, the interactant chose
whether to cooperate or defect according to one of several
updating rules, each reflecting a specific social strategy. In a
given simulation, everyone used the same strategy. In the tit-
for-tat strategy, individuals imitated the choice made on the
preceding trial by their neighbor. In the win-cooperate–
lose-defect strategy, the interactant with the greater outcome
cooperated, whereas the interactant with the smaller outcome
defected. In the win-stay–lose-shift strategy, meanwhile, in-
teractants who perceived themselves to be winning behaved
in the same fashion on the next trial, whereas interactants
who perceived themselves as losing changed their behavior
on the next trial. The results of simulations employing these
updating rules reveal different effects depending on the size
of the group. In relatively small groups, an equilibrium tends
to be reached fairly quickly, with all interactants converging
on a particular choice. In larger groups, however, each strat-
egy leads to continuous dynamics characterized by the coex-
istence of different behavioral choices. Eventually, however,
each strategy leads to specific proportions of cooperating in-
dividuals. These proportions tend to be maintained at the