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.