Evolution of ethnocentrism in the Hammond and Axelrod model

Ethnocentrism is the tendency to favor one’s own group at the expense of others; a bias towards those similar to us. Many social scientists believe that ethnocentrism derives from cultural learning and depends on considerable social and cognitive abilities (Hewstone, Rubin, & Willis, 2002). However, the only fundamental requirement for implementing ethnocentrism is categorical perception. This minimal cognition already merits a rich analysis (Beer, 2003) but is only one step above always cooperating or defecting. Thus, considering strategies that can discriminate in-groups and out-groups is one of the first steps in following the biogenic approach (Lyon, 2006) to game theoretic cognition. In other words, by studying ethnocentrism from an evolutionary game theory perspective, we are trying to follow the bottom-up approach to rationality. Do you know other uses of evolutionary game theory in the cognitive sciences?

The model I am most familiar with for looking at ethnocentrism (in biology circles, usually called the green-beard effect) is Hammond & Axelrod (2006) agent-based model. I present and outline of the model (with my slight modifications) and some basic results.

Model

The world is a square toroidal lattice. Each cell has four neighbors: east, west, north, south. A cell can be inhabited or uninhabited by an agent. The agent (say Alice) is defined by 3 traits: the cell she inhabits; her strategy; and her tag. The tag is an arbitrary quality, and Alice can only perceive if she has the same tag as Bob (the agent she is interacting with) or that their tags differ. When I present this, I usually say that Alice thinks she is a circle and perceives others with the same tag as circles, but those with a different tag as squares. This allows her to have 4 strategies:

The blue Alice cooperates with everybody, regardless of tag; she is a humanitarian. The green Alice cooperates with those of the same tag, but defects from those with a different; she is ethnocentric. The other two tags follow a similar pattern and are traitorous (yellow) and selfish (red). The strategies are deterministic, but we saw earlier that a mixed-strategy approach doesn’t change much.

The simulations follow 3 stages (as summarized in the picture below):

  1. Interaction – agents in adjacent cells play the game between each other (usually a prisoner’s dilemma). Choosing to cooperate or defect for each pair-wise interaction. The payoffs of the games are added to their base probability to reproduce (ptr) to arrive at each agents actual probability to reproduce.
  2. Reproduction – each agent rolls a die in accordance to their probability to reproduce. If they succeed then they produce an offspring which is placed in a list of children-to-be-placed
  3. Death and Placement – each agent on the lattice has a constant probability of dying and vacating their cell. The children-to-be-placed list is randomly permuted and we try to place each child in a cell adjacent to (or in place of) their parent if one is empty. If no empty cell is found, then the child dies

Simulation cycle of the Hammond & Axelrod model

The usual tracked parameters is the distribution of strategies (how many agents follow each strategy) and the proportion of cooperative interactions (the fraction of interactions where both parties chose to cooperate). The world starts with a few agents of each strategy-tag combination and fills up over time.

Results

The early results on the evolution of ethnocentrism are summarized in the following plot.

Early results in the H&A model

Number of agents grouped by strategy versus evolutionary cycle. Humanitarians are blue, ethnocentrics are green, traitorous are yellow, and selfish are red. The results are an average of 30 runs of the H&A model (default ptr = 0.1; death = 0.1; b = 0.025; c = 0.01) with line thickness representing the standard error. The boxes highlight the nature of early results on the H&A model.

Hammond and Axelrod (2006) showed that, after a transient period, ethnocentric agents dominate the population; humanitarians are the second most common, and traitorous and selfish agents are both extremely uncommon. Shultz, Hartshorn, and Hammond (2008) examined the transient period to uncover evidence for early competition between ethnocentric and humanitarian strategies. Shultz, Hartshorn, and Kaznatcheev (2009) focused on explaining the mechanism behind ethnocentric dominance over humanitarians, and observed the co-occurrence of world saturation and humanitarian decline. Kaznatcheev and Shultz (2011) concluded that it is the spatial aspect of the model that creates cooperation; being able to discriminate tags helps maintain cooperation and extend the range of parameters under which it can occur.

As you might have noticed from the simple DFAs drawn in the strategies figure, ethnocentrism and traitorous agents are more complicated than humanitarians or selfish; they are more cognitively complex. Kaznatcheev (2010a) showed that ethnocentrism is not robust to increases in the cost of cognition. Thus, in humans (or simpler organisms) the mechanism allowing discrimination has to have been in place already (and not co-evolved) or be very inexpensive. Kaznatcheev (2010a) also observed that ethnocentrics maintain higher levels of cooperation than humanitarians. Thus, although ethnocentrism seems unfair due to its discriminatory nature, it is not clear that it produces a less friendly world.

The above examples dealt with the prisoner’s dilemma (PD) which is a typical model of a competitive environment. In the PD cooperation is irrational, so ethnocentrism allowed the agents to cooperate irrationally (thus moving over to the better social payoff), while still treating those of a different culture rationally and defecting from them.
Unfortunately, Kaznatcheev (2010b) demonstrated that ethnocentric behavior is robust across a variety of games, even when out-group hostility is classically irrational (the harmony game). In the H&A model, ethnocentrism is a two-edged sword: it can cause unexpected cooperative behavior, but also irrational hostility.

References

Beer, R. D. (2003). The dynamics of active categoricalperception in an evolved model agent. Adaptive
Behavior
, 11, 209-243.

Hammond, R., & Axelrod, R. (2006). The Evolution of Ethnocentrism Journal of Conflict Resolution, 50 (6), 926-936 DOI: 10.1177/0022002706293470

Hewstone, M., Rubin, M., & Willis, H. (2002). Intergroup bias. Annual Review of Psychology, 53, 575-604.

Kaznatcheev, A. (2010a). The cognitive cost of ethnocentrism. In S. Ohlsson & R. Catrambone (Eds.), Proceedings of the 32nd annual conference of the cognitive science society. (pdf)

Kaznatcheev, A. (2010b). Robustness of ethnocentrism to changes in inter-personal interactions. Complex Adaptive Systems – AAAI Fall Symposium. (pdf)

Kaznatcheev, A., & Shultz, T.R. (2011). Ethnocentrism Maintains Cooperation, but Keeping One’s Children Close Fuels It. In L. Carlson, C, Hoelscher, & T.F. Shipley (Eds), Proceedings of the 33rd annual conference of the cognitive science society. (pdf)

Lyon, P. (2006). The biogenic approach to cognition. Cognitive Processing, 7, 11-29.

Shultz, T. R., Hartshorn, M., & Hammond, R. A. (2008). Stages in the evolution of ethnocentrism. In B. Love, K. McRae, & V. Sloutsky (Eds.), Proceedings of the 30th annual conference of the cognitive science society.

Shultz, T. R., Hartshorn, M., & Kaznatcheev, A. (2009). Why is ethnocentrism more common than humanitarianism? In N. Taatgen & H. van Rijn (Eds.), Proceedings of the 31st annual conference of the cognitive science society.

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About Artem Kaznatcheev
From the ivory tower of the School of Computer Science and Department of Psychology at McGill University, I marvel at the world through algorithmic lenses. My specific interests are in quantum computing, evolutionary game theory, modern evolutionary synthesis, and theoretical cognitive science. Previously I was at the Institute for Quantum Computing and Department of Combinatorics & Optimization at the University of Waterloo and a visitor to the Centre for Quantum Technologies at the National University of Singapore.

35 Responses to Evolution of ethnocentrism in the Hammond and Axelrod model

  1. Luke Knoche says:

    I have currently been studying over human communication and interactions in my psychology class and i agree that there are a lot of groups who display ethnocentrism to others. I have learned in my class that people’s reactions or views towards others are determined by their perceptions of them and not by who they really are. It’s like the famous saying “judging a book by its cover”. There has be reasons for why certain groups gather together and stay away from one another through social categorizations.

  2. Stephane says:

    I don’t understand how ethnocentric agents do better than selfish agents. In the prisoner’s dilemma, it is always more advantageous to defect. If agents know how agents have been behaving in the past, that’s a different story, as well as if the tag provides information about their strategy. But that’s not the case here, right?

    Oh, actually, lower in the article, tags seem to be linked to strategies. You may want to change these sentences:
    “The agent (say Alice) is defined by 3 traits: the cell she inhabits; her strategy; and her tag. The tag is an arbitrary quality, and Alice can only perceive if she has the same tag as Bob (the agent she is interacting with) or that their tags differ.”
    Reading them, I thought the tags and the strategies are unrelated. Something like “The agent is defined by 2 traits: the cell she inhabits and her strategy. Her tag is a bijective function of her strategy” would have been clearer to me.

    Then, thinking about it, in real life, tags are not immutably linked to strategies. How does the model react to, for example, occasional mutations that change the association between the tag and the strategy?

    • That’s the whole point, Stephane! The tags and strategies are independent, and on first thought it seems like selfish agents should do better. The point of the research in evolution of cooperation is to show how this can be overcome.

      Think about it this way: sure a selfish agent does better if they get to interact with the same agents as a non-selfish. But is this obviously the case? Well, let’s look, what does doing ‘better’ mean in an evolutionary setting? It means the agents gets to produce more children, where do these children get placed? Next to the agent (since this is a spatial model). So the agent then has to interact with its own off-spring, getting a very poor payoff. Thus, selfish agents (and traitorous ones) are extremely self-limiting because small clusters of them can’t grow larger.

      Of course, if the world was inviscid (if we didn’t place children next to their parents) then indeed your intuition would be correct. In an inviscid environment selfish agents would be the dominant strategy.

      • Stephane says:

        Aha! Thanks for clarifying. Indeed, my reasoning failed to take locality into account. I was imagining mobile agents, for some reason.

  3. Yan says:

    The paper I have in mind is bit different from the original model. But it might be be an explanation why children should be placed around their parents.
    As you pointed out, the reason that etho agents does better is because selfish people can not grow very large. In Schelling’s segregation model, agents are allowed to move. and if they perceive their own type fall below certain percentage, even a very low one, then they move. in equilibrium, you would observe racial segregation, meaning different types of people would live together.

    • Can you provide a more detailed summary of Schelling’s model or a reference? The details of these models matter a lot, especially since a lot of modelers hide very important things in their assumptions.

      For instance, a lot of the early models of ethnocentrism (for instance Riolo, Cohen, Axelrod 2001) did not allow selfish, and traitorous agents because they assumed the agent HAD to cooperate with those like it and could only adjust its level of tolerance (but even at zero tollarance it cooperated with those of exactly same tag). Thus, these early models could not show the evolution of ethnocentrism, since they pre-supposed it in their constraints.

      If Schelling’s model has the “if they perceive their own type fall below certain percentage … then they move” feature coded into the agent’s strategy then showing segregation is not an interesting result. If they assumed that agents want to move away from those not-similar-to-them and then showed that the equilibrium is agents not near those not-similar-to-them; that would not be a very exciting result. So you really need to be much more precise about how you describe the model. However, if you write a blog post (on our blog or yours) summarizing Schelling’s model and results then I would be very eager to read it!

  4. Yan says:

    I guess the whole point of that is even with low intolerance level, 33% in the example you give, it would still lead to segregation. But I agree in general it is feeding the model what people expect to see in their assumptions

    • “Low” is not a precise term. How is 1/3rd low? It is a rather arbitrary judgement. In general, you would expect that parameter to only effect the noise level and time to equilibrium (since it is the only real timescale in the model, apart from the discretization). But we can discuss the model in more detail after you blog about it. It unfortunately doesn’t have much to do with our game-theoretic approach in the H&A model.

  5. Bethany says:

    This is a really good example of social categorization and its effects. I found it interesting that the blue icon player really did better. It seems that there is a common belief that most ethnocentric people accomplish more for their group, whatever group that is. Good work!

    • The green icon player (ethnocentrics) you mean ;)

      I was also surprised to see that ethnocentric agents maintain higher levels of cooperation than humanitarians in the prisoner’s dilemma. However, it is unfortunate that ethnocentrics in the harmony game go out of their way to hurt other groups, as opposed to simply helping there own. I would expect higher levels of cooperation without tags in the harmony game, but we have not tested it closely.

      One of the questions that remains from the point of view of mechanism design is to ask ourselves: what kind of constraints can be placed on the system to allow humanitarian agents to be more common that ethnocentrics without sacrificing general level of cooperation. I do not have an answer for this, but I am definitely working on it!

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  7. Equinox Zephyr says:

    Reblogged this on Mediocre Blog.

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