"La Emergencia de classes en un model multiagent"

Robert L. Axtell, Joshua M. Epstein and H. Peyton Young
CSED Working Paper No. 9
February 2000

 

Figure 2: Convergence to the Equity Norm
Suppose for example that N = 100, m = 10 and e = 0.2, and the initial state is random about the point of indifference between the three strategies. After 80 periods, all agents have encountered frequent demands of M in the past, and thus they expect their opponents to play M in the next period. Given this expectation, M is the best response. Hence most agents play M next period, which reinforces the expectation of M. However, by a process we do not model explicitly, agents occasionally deviate from best reply and play either H or L. This may occur due to random errors, conscious experimentation, simple imitation or for any number of other reasons. This is analogous to mutation in biological models and serves to create variety in the population. If the process is allowed to continue, the probability is high that most agents will remain in the light gray region for quite a long period of time. This is because the equity norm has a large basin of attraction, and even substantial deviations caused by random 'mutations' in individual behavior may not be enough to tip society into a fundamentally different regime. Nevertheless such tipping events will eventually occur, and they can lead to regimes that have a fundamentally different character.
Figure 3: Emergence of a fractious state
In this fractious state, people at each instant are either aggressive or passive; they have not learned to compromise. But while this is an inefficient state, it does not exhibit classes, because agents frequently migrate between zones.
Figure 6: Equity between and within types Intra-type (left); Inter-type (right)
At this point the process has reached a state where something close to the equity norm prevails both between and within groups. In particular, the process is in the basin of attraction of the equity norm for dark against dark, light against light, and light against dark. Average payoffs in this regime are high, because most agents succeed in dividing the pie rather than fighting over it.
Figure 7: Equity between, but not within, types Intra-type (left); Inter-type (right) This model begins from a different random initial conditions. Internally, the darks (black dots) come close to the equity norm while the lights (gray dots) are still in a fractious state. However, something close to the equity norm prevails between the lights and the darks.
Figure 8: Equity within, but not between, types Intra-type (left); Inter-type (right) In this case the process evolves fairly rapidly (after 225 periods) to a state in which the equity norm holds within each group, whereas a discriminatory norm governs relations between the two groups. When agents meet others of their own type, most of them expect to divide the pie in half. But when a dark agent meets a light agent, the darks act aggressively and the lights act passively. The result is that, on average, the payoff to dark agents (70) is over twice as high as it is to light agents (30). In other words, class distinctions have emerged endogenously.
Figure 9: Equity above, division below Intra-type (left); Inter-type (right)   The final case is to us the most interesting. Starting from a different random initial state, society evolves after 260 periods to the state shown in Figure 9. As evident in the right (inter-type) simplex, the darks dominate the lights. However, from the left simplex, it is clear that the equity norm prevails within the dominant darks while the lights are a fractious society. This, then, is the picture of a divided underclass oppressed by a unified elite. This result seems particularly disturbing in that every individual is behaving rationally -- playing the best reply strategy -- and yet the social outcome is far from optimal.