Asymmetric Power Among Agents in Evolutionary
Games
Stephen J. Majeski
majeski@u.washington.edu
A set of artificial worlds based upon a group of repeated
(2X2) games is constructed and analyzed. Chicken, Stag, Assurance,
and Deadlock games are selected for this analysis because of their substantive
importance for international relations and because they provide a range of
structural settings where cooperation is both more and less likely to occur
than in the much-studied PD. In addition, asymmetric power among agents
is introduced into these worlds and its consequences for cooperation analyzed.
Such asymmetries are an enduring feature of international systems and indeed
most social setting involving collective action. Asymmetric power is
introduced in two ways. First, agents are differentially rewarded for
the joint outcomes of the various games. Those agents having asymmetric
power receive uniformly higher payoffs across all joint outcomes of the relevant
game. Second, asymmetric power is introduced by giving some agents the ability
to selectively interact with other agents while making interaction mandatory
for all other agents.
The artificial worlds have the following general features.
An explicit spatial dimension is introduced by constructing a set of toroidal
worlds (a 20 X 20 grid of cells) consisting initially of 60 agents randomly
assigned locations on the grid. Agents interact with their von Neumann
neighbors. Each agent is represented by a strategy specifying how the
agent behaves as it interacts with other agents. Agent strategies are
restricted to those employing just the previous interaction with the other
agent(s) to determine current choices. An environmental carrying capacity
is incorporated into the artificial worlds by introducing a cost of survival
for agents. Because all individuals die and all social units eventually
fall apart, disband, go bankrupt, are taken over, or overrun, agents are
assumed to have a limited existence or life span. Agents reproduce
or replicate themselves asexually. Finally, to give the artificial
world some dynamic, strategy mutation is introduced probabilistically at
the time of replication.
Simulation results indicate that anticipated variations
in evolutionary outcomes regarding the likelihood of cooperation across these
different game structures holds. Also, the introduction of asymmetric
power substantially increases the chances that both cooperative agents survive
and cooperative worlds evolve. This is particularly the case when agents
are endowed with the ability to selectively interact with other agents in
their world. In addition, simulation results suggest that exploitative
agents do not benefit from asymmetric power.