Benchmarking the Process

Agent-Patch Simulation time series: BENIGN ENVIRONMENT/MIXED INITIAL POPULATION Defector: Yellow Cooperator: Light Blue			Back to Start EAME Home e-mail Programmer

Frame 1: Cycle 0; Cooperators: 40 Defectors: 40	Frame 2: Cycle 1025 Cooperators: 1925 Defectors: 1429	Frame 3: Cycle 1770 Cooperators: 3695 Defectors: 3516	Frame 4: Cycle 2675 Cooperators: 195 Defectors: 3168

The way that the evolution of cooperation is usually studied is via a game called the "prisoner's dilemma".

It is simplest to interpret the game as follows: Agents pair up at random and each has the opportunity to confer a benefit on the other at a small cost to themselves. There are two strategies. Cooperate both confers and accepts. Defect accepts but does not confer. If the benefit is worth 4 and the cost 1, you get the payoffs in the table. In in the simplest cases, whether it is rational agents or populations with inherited strategies, or even imitation on the basis of success, Defect always wins. In order for cooperate to win, you need something a little bit complicated. A segregation mechanism, or some way that players can condition what they do on some information about the opponent. In Step one, we just let them play.

Just to make sure the simulator does what you would expect, we run it initially without mortality risk, with the same initial configuration as will be used in Step 2. As expected, the cooperators are all driven out by the defectors. What is interesting is the way cooperators form a wavefront that moves out ahead of the defector migration. Note that the movement rate for all agents is the same, and the probability of movement is the same in all directions (except at the edges. The grid is not wrapped.) So it is not individual movement rate that accounts for this phenomenon. Rather, cooperators produce resource which results in increased reproduction. Instead of cooperator populations stabilizing at the patch resource carrying capacity (5 agents per patch) as defector populations do, they climb to the level at which crowding costs kick in, which is 20 agents. If 20 agents have four times the chance of moving to a given patch that 5 agents do, then cooperator populations can move up to four times as fast. But the defectors nibbling at the rear of the cooperator wave are getting this resource as well, which is why they are able to keep up at all. If open space were unlimited, perhaps coopertors could outrun the defectors indefinitely.

The other thing to realize is that sometimes the wavefront phenomenon does not emerge because not enough cooperators get out in front. The typical time to cooperator extinction when the wavefront forms is about 3000 cycles, as shown in the bar graph of exintion times for 50 of these trials. But sometimes they are driven extinct much more quickly than that, in between 700 and 1400 cycles. This happened in 16% of the trials run. This explains why the pattern demonstrated in the next step does not always emerge.