Swarmfest 2013- will be held in Orlando, Florida at the University of Central Florida from Monday, July 8 to Tuesday, July 9, 2013. Please visit home page for more information for more information.

Location: Saint Paul, Minnesota, USA

Workshop Website: Click here

Description: The workshop will consist of researchers from the Multiagent Systems community (MAS) of engineering and the social/economic/organizational sciences. This workshop is extensively recognized for its role in cross-fertilization and has been an important source of inspiration for the body of knowledge that has been produced in the area of MAS. Multi-Agent Based Simulation (MABS) is a vibrant inter-disciplinary area which brings together researchers within the agent-based social simulation community (ABSS) and MAS.

The focus of ABSS is on simulating and organization social behaviours in order to understand real social systems via the development and testing of new concepts. The focus of MAS is on the solution of hard engineering problems related to the construction, deployment and efficient operation of multiagent systems. The range of technical issues that MABS has dealt with, and continues to deal with, is quite diverse and extensive.

This is where the similarity in their methods ends. Nate Silver’s model may be the most complex and theoretical, integrating economic data, state polls, and national polls into a predictive model.  Sam Wang’s model, on the other hand, relies only on meta-analysis of recent state polls.  But, even though each model is very different, they all converged on similar predictions because they relied on state polls.

Was the complexity of these models necessary? The answer appears to be “No.”  Just pooling polls within states is as effective as more complex models. Imagine you are a super pollster who has different polling groups providing you with polling data on percentages for candidates, sample sizes, and the span of time the data were collected.  You pool these polls over some larger window of time.  By pooling the polls, the super-state polls have much larger sample sizes and potential biases of individual polling groups may tend to cancel out. I generated super-state polls, which yielded 100% correct predictions for all the states and the District of Columbia.  These super-state polls were generated from state polls taken from approximately the beginning of September until November 5th.   In addition to predicting the electoral vote exactly (332 vs. 206), the differences predicted between Obama and Romney for each state were highly correlated (r = 98%) as illustrated in Figure 1.

Figure 1. Plot of the predicted differences between Obama and Romney for each polled state (x-axis) and the outcome as of 11-9-12.

This raises an interesting problem.  Since pooled polls were as predictive as any other statistical approach to aggregating polls and produced a near perfect correlation with the actual voting results (Figure 1), how could we determine whether a new statistical approach for aggregating polls is better than pooling?  It doesn’t appear possible since there is very little room for meaningful improvement (see Figure 1).  In future elections, however, events may occur that significantly alter voter preferences and these events might be best detected by Sam Wang’s meta-analytic approach or by pooling polls with smaller windows (i.e., creating super tracking polls with windows of a month, two weeks, or even a week) for highly polled swing states.

Figure 1. Percentage difference between Obama and Romney for Florida with 99% confidence intervals. The dashed line is .25%. Sample size was 57,001 likely voters.

The popular vote is predicted to favor Obama by 2.67%, which is down from 3% in previous posts for several reasons.  First, the difference favoring Obama in California dropped a couple of points, which brings down the national average about .2%.  Second, several small states were never polled and I originally used 2008 voting estimates for them, but to be more conservative, I used 2000 voting estimates for those states due to the closeness of that election. Third, the percentage difference favoring Romney in Texas increased a couple of percentage points, which decreased the predicted difference between Obama and Romney.

If we assume 1% of the vote goes to other candidates, then the popular vote should be Obama 50.87% and Romney 48.17%.

MEDIAN

One way to reduce the influence of outliers (e.g., large biases in particular polls or fluctuations in enthusiasm), is to calculate the median for each state for the polls taken over the approximately 2-month period pooled for each state.  Means-Medians sorts the states into those for Obama, Romney and Tossup with corresponding means and medians.  As can be seen, the means and medians are in strong agreement and the predicted popular vote based on the medians should favor Obama by 2.61%.

POOLING ASSUMPTION

For each state, the pooled poll can be viewed as one large poll conducted over approximately two months by a number of polling groups.  The main assumption is that most voters had stable preference for Obama or Romney by the beginning of September.   People can switch candidates, but this assumption requires that switching occurs at low rates and is essentially random.  This suggests we should see the polls for states converge on percentage differences rather than continuing to gradually increase or decrease over the sampled period.  This appears to be true for Ohio (Figure 2), North Carolina (Figure 3), Virginia (Figure 4) and Colorado (Figure 5).

Figure 1. Percentage difference between Obama and Romney for Ohio with 99% confidence intervals. The dashed line is 3%. Sample size was 73,077 likely voters.

Figure 2. Percentage difference between Romney and Obama for North Carolina with 99% confidence intervals. The dashed line is 2%. Sample size was 29,914 likely voters.

Figure 3. Percentage difference between Obama and Romney for Virgina with 99% confidence intervals. The dashed line is 1.5%. Sample size was 51,323 likely voters.

Figure 4. Percentage difference between Obama and Romney for Colorado with 99% confidence intervals. The dashed line is 1.5%. Sample size was 34,303 likely voters.

Figure 1. Percentage difference between Obama and Romney for Colorado with 99% confidence intervals. The 99% confidence interval for 11/3 just crosses the x-axis. Most of the time, Colorado has been on the border of statistical significance.

State Polls 11-3-12

As of today, the predicted electoral vote outcome is 294 for Obama and 206 for Romney with 38 electoral votes to be decided.

Nate Silver has an interesting discussion today on the problem of calculating the probability of Obama winning.  If the sampling error in polls is random error and if over a given period of time, there is no systematic change in voter decisions, then pooling polls yields a near certain decision.  If there are different biases among polling groups, these biases may tend to cancel out, but whether these biases cancel out also depends on the frequency of polls from different polling groups.  This adds some uncertainty but probably not much.  I have tested removing Rasmussen polls, which have a Romney lean, but the electoral vote outcome is not meaningfully changed except that Colorado is significantly for Obama.  Thus, these types of biases are likely of little concern.

The fundamental problem, as Nate Silver points out, is systematic bias.  Due to some commonly used methods or problems in polling (such as low response rate of people polled).  This could mean systematic differences between actual voting percentages from polled percentages by up to several points.  If this is the case, then Romney may well win or if the bias is in the other direction, Obama may win in a landslide.  As Nate Silver points out, the current state polling data indicates near certainty of an Obama win, but his 85.1% Obama win vs. 14.9% Romney win (11/3/2012 calculations) is intended to capture the systematic bias uncertainty in the prediction.  That is the 14.9% probability of a Romney win is solely based on the uncertainty of systematic bias. This estimated uncertainty is based on an analysis of previous systematic biases in polling in previous elections.

I’m not convinced, however, that this uncertainty can be estimated.  The hidden assumption is that methods or problems that cause systematic biases in the past are the same or similar in relevant respects to possible systematic biases that may be occurring in polling now.  Since we have no theory of systematic biases and their sources that can project into the future, it seems dubious that we can generalize from the past.  The best that we can say is that if there are no systematic biases, then given the relevant polling data, the probability of Obama winning is very high or near certainty.

At the alpha = 0.01 level of significance, only Florida is undecided (Table 1).  Figure 1 illustrates the gradual convergence of the percentile difference between Obama and Romney in Florida.  The next two closest states are Colorado and North Carolina (Figures 2 and 3).  Both are statistically significant for Obama and Romney respectively, but one or a few polls could make them insignificant.

State Polls 11-2-12

Figure 1. Percentage difference between Obama and Romney for Florida with 99% confidence intervals.

Figure 2. Percentage difference between Obama and Romney for Colorado with 99% confidence intervals.

Figure 3. Percentage difference between Obama and Romney for North Carolina with 99% confidence intervals.

Ohio has been holding steady at about 3% for the last couple of weeks with numerous polls (Figure 4).  Ohio also looks the closest to a bellwether state for this election since the predicted difference as of today is 3% for Obama.  The predicted national vote difference stands at 3.1%.

Figure 4. Percentage difference between Obama and Romney for Ohio with 99% confidence intervals.

As of today, the predicted electoral vote outcome is 303 for Obama and 206 for Romney with 29 electoral votes to be decided.

The re-weighting had little affect on the predicted national vote difference, which stands at 3.1%. This is still considerably higher than the national polls as of this date. Sam Wang at the Princeton Election Consortium, is also seeing the same discrepancy between his state-based poll meta-analysis and the national polls. I wouldn’t be surprised to see the national polls move closer to the state-based estimate by election day.

A number of polls have come out since my first post and Colorado is now statistically significantly polling for Obama.  Only Florida remains undecided (see Table 1).

State Polls 10-31-12 (Table 1)

Thus, based on the polling results as of today, Obama would win 303 electoral votes and Romney 206 with 29 yet to be decided.  The difference between Obama and Romney for Florida is not statistically significant for alpha = 0.01, and it appears doubtful that there will be enough polls of Florida before election day to decide the Florida one way or the other.  In Nebraska, there have been two additional polls reporting Romney leading the 2nd district.  No numbers were given, but it appears that all 5 Nebraska electoral votes are solidly for Romney.

The logical place to look for a reduction in uncertainty is poll aggregators.  Poll aggregators take available polls and reduce uncertainty by applying different complex statistical models for combining polls.  One of the more complex poll aggregation models is Nate Silver’s at FiveThirtyEight.  His model aggregates state polls, national polls, and economic data to generate the probability that a candidate will win the election.  The details of his model, to my knowledge, are not publically available.  So, although I admire his efforts at integrating empirical and theoretical information, lack of knowledge about the underlying model does little to reduce uncertainty for me.

At the opposite extreme is Real Clear Politics.   Their methodology is very simple: average state and national polls for about the previous 10 days.  I like the simplicity but mere averaging is problematic.  Polls with different sample sizes should be weighted differently.  Another problem is that they do not consider all the polls.  They attempt to exclude partisan polls.  In principle, this appears reasonable, but how do we know that partisan polls are really biased?  Which ones are and which are not?

My favorite poll aggregator is the Princeton Election Consortium run by Sam Wang.  Professor Wang aggregates only state polls, which provide the most information about the outcome of the presidential election for two reasons.  First, a US president is elected by an Electoral College majority.  Thus, the popular vote does not necessarily correspond to the electoral college vote.  Second, state polls have relatively large sample sizes for small populations (when compared to national polls), so they provide more information about a given state and how the electoral college vote will go.  Wang uses meta-analysis on state polls and unlike other poll aggregators, his methods are publically available.  For these reasons, if I had to rely on any poll aggregator, it would be Princeton Election Consortium.  Nevertheless, I still have some nagging uncertainty.

One reason for my continued uncertainty is the fluctuations in Wang’s Median EV estimator.  As you can see, changes in the meta-margin correspond very closely to key events during the 2012 presidential campaign. Two changes are especially salient: The selection of Paul Ryan as Romney’s vice presidential running mate and the first presidential debate.  Both involved fairly large changes in the meta-margin, but did they involve large changes in voter preferences?  The Rand tracking poll indicates that changes in preferences between candidates is rather small and very noisy.  A less scientific poll of the Xbox/YouGov panel also suggests that changes in voter’s preferences are small and noisy.  Doug Rothschild and Doug Rivers suggest that relatively large changes seen in the polls may be driven by voter enthusiasm rather than changes in voter preferences.  If this is the case, then the fluctuations we see in Wang’s meta-margin are driven largely by voter enthusiasm.  If the vast majority of voters already know the two candidates and have a preference for one of them, then events such as picking a vice presidential running mate or presidential debates may affect voter enthusiasm much more than voter preferences.

Another concern about poll aggregation is bias in individual polls.  For example, Alan Abramowitz has recently argued that Rasmussen is biased towards republican candidates.  His points are good, but they only show that Rasmussen polls tend to be outliers for republican candidates.  How do we know that they are outliers for this election cycle?

At one point, I thought it would be great to have an agent-based model of the voting population in the United States.  I could model voter enthusiasm, the likelihood of answering phones for polls etc.  Then I could test various assumptions made by polling groups to assess bias.  I quickly realized that this was a fantasy.  There were too many possible factors affecting voter preferences and enthusiasm and there is almost no theory to base such a model on.

What if almost all people already have a preference one way or another even a weak one?  If so, then fluctuations in voter enthusiasm may allow us to detect weak voting preferences.  During periods of high republican enthusiasm we may be able to detect weak republican preferences and during periods of democratic enthusiasm, we may be able to detect weak democratic preferences.  If this hypothesis is correct, polls should be aggregated over longer periods of time, so that enough fluctuations in enthusiasm occur to detect weak presences one way or the other.  With this in mind, I made two assumptions:

(1) The vast majority of the voting population had at least weak preferences for Romney or Obama by the time of the republican and democratic conventions.  Aggregation of polls should therefore start around the 1st of September.

(2) By aggregating polls, especially over a long-period of time, biases in individual polls will tend to cancel out.

Based on these two assumptions, I decided to aggregate all state polls from approximately September 1, 2012 till the last polls before the election on November 6, 2012.  The method of aggregation is described in the next section and in the subsequent section I report the results up to today.

METHODS

The state polls used in this analysis come from Pollster.com and Statewide opinion polling for the United States presidential election, 2012 from Wikipedia.  For each state the sample sizes are combined as they become available.  For some smaller states that traditionally lean strongly republican or democratic, there are few if any polls available.  In those cases, a poll as old as June, 2012 may be used.  In cases where there are no polls either Pollster.com’s estimate is used or the voting percentages from the last election.

From the aggregated polls for each state, new percentages are calculated for Obama and Romney.  The aim is to calculate a P-value for the difference in the percentage favoring one candidate over the other.  In other words, if a difference is observed in the polling data, how probable is it assuming that there is no difference at all?

To calculate a P-value for each state from the polling data, we must calculate the standard error of the differences in percentage, which is given by the following equation:

where p and q are the observed frequencies for the two candidates and N is the aggregate sample size.  A P-value can then be calculated using a cumulative Gaussian distribution with parameters SE and the difference between p and q.  A state is decided for one candidate or the other if the calculated P-value is less than alpha = 0.01 or if there is no polling data available and the state is traditionally a strong lean to either republican or democratic candidates.

RESULTS

The link to the Table 1 provides the aggregate sample sizes, the calculated percentages for Obama and Romney, the difference in percentages, and where possible, whether the difference is statistically significant.

State Polls 10-28-12 (Table 1)

Figure 1 is a graph of the difference between Obama and Romney in Ohio and Figure 2 is the same for Florida.  For Ohio, the difference is about 3% in favor of Obama and it is statistically significant.  For Florida, there is about a .5% difference in favor of Obama, but it is not statistically significant.

Figure 1. Percentage difference between Obama and Romney for Ohio with 99% confidence intervals.

Figure 2. Percentage difference between Obama and Romney for Florida with 99% confidence intervals..

DISCUSSION

One of the surprising results is that there are only two tossups states: Florida and Colorado.  For all other states, the percentage differences between Obama and Romney are statistically significant.  Thus, based on the polling results as of today, Obama would win 294 electoral votes and Romney 206.  The differences between Obama and Romney for Florida and Colorado are not statistically significant for alpha = 0.01, but they are both in the direction of Obama, so my best guess as of today is 332 electoral votes for Obama and 206 for Romney.  There are currently only two polls for Nebraska.  One reports a tie between Obama and Romney in the 2nd district and the other reports a 3% lead for Obama. Based on this scant evidence, the electoral vote distribution might end up 333 electoral votes for Obama and 205 for Romney as of today.

It is also possible to use the state data to estimate the popular vote.  I weighted each state by its 2008 turnout, which yielded as state-based estimate for Obama of 48.3% and for Romney of 45% with a 3.3% difference.  This is in striking contrast to the current average of the national polls.  It will be interesting to see whether the national polls begin to converge on the state-based poll estimate as we approach the election.

There are many ways that this analysis could go wrong.  It could be that changes in poll numbers are primarily driven by changes in preferences for Obama or Romney rather than changes in enthusiasm.  There could also be systematic biases in the polls due to systemic sampling problems, bad assumptions, or over representation of polls from some polling groups.  However, if assumptions (1) and (2) are correct, then this approach to poll aggregation should provide an accurate estimation of the presidential election results.

Welcome to Agent-Based Models. The goal of agents-based-models.com is to facilitate the use of agent-based modeling as a general theoretical and methodological tool for investigating behavior, and more generally, investigating agents as realized in software or hardware (e.g., robots).

This site, as it develops, will become an information hub for agent-based modeling. Researchers using agent and multi agent models in a variety of fields are listed here. Various tools and organizations using agent models are also listed here. Finally, it will also promote discussion of the methodological and philosophical foundations of agent-based modeling.

Agent-based modeling (ABM) is a style of modeling that focuses on modeling individuals, components of individuals, or heterogeneous parts of a complex system. Agent-based models are often intended to model real systems, but this is not a necessary feature of ABM (e.g., intelligent agents, Software agent, autonomous robots).   ABM as a style of computational modeling, requires both mathematical and experimental approaches for its development and application.  There are many resources available for those interested in developing or using ABM.  Good places to start are Scholarpedia and Wikipedia.

Recently, OpenABM Consortium is emerging as an organization of ABM researchers aiming to improve the way ABMs are developed, shared, and utilized in the socioecological sciences and is funded by the National Science foundation.  The Swarm Development Group has similar aims as does this site.  There are also a number on Internet sites that focus on specific applications of ABM (e.g.,  Leigh Tesfatsion’s site on Agent-Based Computational Modeling).  Other organizations, centers and institutes can be found here.  The community of people across disciplines who develop or are using ABM is rapidly growing.  Many of these can be found on this website under ABM Researchers. Eventually, researchers will be categorized by field and more sophisticated search engine facilities will be available.

For those interested in applying ABM in their research, there are tutorials that can be found on  Swarm Development Group, Agent-Based Computational Modeling, and on this website.  There are a number of simulation environments available, which can be found on Swarm Development Group, Agent-Based Computational Modeling, and on this website.  For those interested in watching videos on ABM, this site maintains a list.  An evolving list of journals that publish research involving ABM can be found on this site and this site has a list of conferences and workshops related to ABM. OpenABM Consortium also has a Jobs and Appointments page.  There are a number of ABM related blog listed herehere.

There are a growing number of fields of research with researchers using ABM and these fields are rapidly expanding.  ABM is finding increasing application in Animal Behavior, Biology/Ecology, and the Social Sciences.  The emerging diversity of uses of ABM, however, can only truly be described by browsing the vast diversity of interests of Researchers using and developing ABMs.

If you know of researchers, resources, conferences, centers, or other information related to agent-based modeling broadly conceived, please email Jeff Schank.

In its ordinary sense, a scaffold is a temporary structure used to support people and material in the construction or repair of a building or physical structure.  This ordinary sense of scaffold has been metaphorically applied to educational settings in which instructional scaffolding is a temporary educational support structure that provides resources, tasks, guidelines, and guidance in learning.  As students learn, the educational scaffolding supporting learning is gradually removed as students develop their own learning strategies.  In this article, I will explore some of the ways in which the idea of how the notion of scaffolding explicates how agent-based modeling builds insight and understanding into complex systems.

All Models are False

When we build models in science, we may have one or more aims in mind.  We may build a model to help explain a phenomenon.  For example, if we believe that a phenomenon (e.g., flocking in birds) is caused by some causal mechanism that involves the interactions of birds, then a model of the mechanism may reveal whether the proposed mechanism could cause the phenomenon in question and thus explain it.  Flocking in birds is a good example because a few simple rules characterizing the local causal interactions in birds can explain flocking (see boids simulation).  Such models, however, while possibly explanatory are also false in many respects (i.e., they make assumptions that are false and unrealistic).  So, if a model is false in different respects, how can it explain anything?  That is, how can unrealistic models explain real phenomena?  How can unrealistic models build insight and understanding into complex systems?

It could be argued that in the context of prediction, the truth or falsity of a model does not matter.  The only thing that matters is whether a model generates good predictions.  This is an instrumentalist view of models: models are good in so far as they generate true predictions about the system in question.  It does not matter whether the model is realistic or makes true assumptions about the causal mechanism operating in the system.  All that matters are the predictions that can be cranked out of it.  The problem is that most scientific modelers are not instrumentalists.  They attempt to represent at least some important aspects of the systems they model (e.g., see Grim, et al., 2005).  This is especially true for agent-based modeling with its focus on modeling individuals (at one or more levels) and their interactions (e.g., see Schank, 2000; Grim, et al., 2005).  It is hard, if not impossible, to use agent-based models and not be a scientific realist in some sense.  If agent-based modelers are realists in the sense of Grim, et al. (2005), then we do have to be concerned about all the false assumptions we make.

A starting point for resolving the problem of inescapably false models is the recognition that our use of models, especially ABMs, is to gain insight and understanding into phenomena.  It is in the context of understanding, insight, and context of discovery that the idea of scaffolding can help explicate how agent-based modeling can provide insight and understanding into phenomena and ultimately explanation and prediction even though the models we build are false in many respects.

False Models at Means to Truer Theories

This heading was the title of a paper written by William Wimsatt (1986), which tackled the problem of how false models could lead to truer models, theories, and explanations of phenomena. His examples illustrate that models have to be viewed in a broader context of a model building process in which models are analyzed, tested, compared, discussed, revised, discarded, and rebuilt.  By truer Wimsatt meant that the model building process discovers (1) models better supported by data, (2) properties of causal mechanisms operating in the system, (3) which false assumptions have small effects, and (4) which models are robust to different false assumptions.

Wimsatt’s view of template matching is especially important for agent-based modeling and the idea that ABMs are scaffolds to insight and understanding.  We are often in situations where we lack data on a system (especially at multiple levels) and have at best an incomplete understanding of the causal mechanisms operating in the system. In such cases, a good strategy is to build a simple model with some of the mechanisms and properties of the system, analyze the model, and compare it to what data we have or our expectations about how the system should behave.  The model will likely fail to match the behavior of the system in, at least, some important respects, nevertheless it can serve as a template for either building new models or revising the model itself.

Building or revising models can happen in at least two ways. First, by examining the original model, its behavior may help us localize assumptions that should be changed. Second, the original model provides a template against which to compare new or revised models.  New or revised models may not match the data well, but by comparing a new model to a previous model, we may see whether the model behaves better than the original model in one or more respects, indicating that we are making progress in our model building and therefore gaining insight and understanding of a system.

Model-Building as Scaffolds to Understanding and Insight

Understanding is an interesting term in ordinary language.  To have an understanding of a phenomenon can mean having an explanation for how and/or why it occurs.  It can also mean that understanding may lead to better prediction or manipulation of phenomena.  Understanding also comes in degrees.  We can have partial understanding of a phenomenon.  That is, we may have evidence for some factors playing a causal role in the generation of the phenomenon in question, but we do not know how the factors dynamically interact with others to produce the phenomenon.  For example, there is growing evidence that the hormone oxytocin plays a role in pair bonding in some species of mammals (Carter, et al.,1995) and generosity in humans (Zak, Stanton, and Ahmadi, 2007).  We even have growing knowledge of oxytocin receptors and their distribution in brains, but we are far from having a dynamic and detailed understanding of how the system works to facilitate pair bonding or generosity.  Indeed, if we look at the history of oxytocin research in these areas, we first find research reporting a relationship between oxytocin and pair bonding in prairie voles (Carter, et al. 1995), which provided the initial scaffolding for further studies examining other species, the neurophysiology, and neuroanatomy of the oxytocin system (Bales and Carter, 2007). This is analogous to the way that modeling, and especially agent-based modeling, provides a scaffolding to understanding complex phenomena.

Consider cooperative or altruistic behavior.  Such behavior is especially interesting when cooperation or altruism has direct costs to the cooperator or altruist.  Social insects are paradigms of cooperative and altruistic behavior, where workers perform specific tasks that benefit the colony but at the cost of forgoing individual reproduction.   How could altruistic behavior evolve if individuals that are altruistic forgo reproduction?  Surely, individual worker bees that cheat and reproduce their own young would do well against cooperators since they are directly reproducing at least a few offspring while cooperative workers produce none.  This is an example of the problem of understanding how and why cooperation evolves; why cheaters do not always succeed.

There have been several models proposed for understanding the evolution of cooperation.  For example, Hamilton (1966) proposed kin selection as an explanation cooperation in social insects and other animal social systems in which animals forgo some or all of their reproductive fitness.  His key insight  was that forgoing reproduction does not mean a total loss of fitness.  Individuals share genes and phenotypic characters in common with their relatives.  Thus, by helping relatives, indirect fitness effects of promoting the survival and reproduction of relatives can out weigh the direct effects of reproduction.  The problem is that kin selection may not be a good explanation for the evolution of cooperation in all social systems where individuals forgo some or all reproduction. For example, there are a number of social insect species in which colonies consist of number of unrelated queens and workers (Keller, 1995).  Unrelated workers feed offspring of unrelated queens and forgo reproduction.  How does cooperation evolve when kin selection does not appear to apply?

The evolution of cooperative behaviors are a class of phenomena for which we lack any thing close to complete understanding.  Nevertheless, modeling approaches are proving invaluable in providing insight and understanding into the evolution of cooperation.  Kin selection models have provided insight and understanding but not without problems (Keller, 1995) and game theory is providing another source of insight.  Game theory has provided a small set of initially simple models to investigate how and why cooperation occurs in many social contexts (e.g., Maynard Smith and Price, 1973; Axelrod, 1984). One paradigm for investigating cooperative behavior is the prisoner’s dilemma (also see SEP). In this game, there are two players and each player has two strategies:  cooperate or defect.   Thus, there are four possible outcomes to the game.  If both decide to cooperate, then each receives the cooperative reward payoff, R. If, however, the first player cooperates and the second player defects, then the first player receives the sucker’s payoff, S, the second player receives the temptation to defect payoff, T.  The same holds if the first player defects and the second player cooperates.  If both players defect, then they both receive the mutual punishment payoff, P. It is assumed that T > R > P > S.

The matrix above illustrates the normal form of the prisoner’s dilemma game.  If we assume that players seek to maximize their expected payoff and play only once, then if we substitute any values into the normal form of the game above that conform to the assumed constraints on the payoff, there is only one equilibrium solution and that is for both players to defect.  This is, however, Pareto-suboptimal solution.  That is, both players could do better if they both cooperated.

The prisoner’s dilemma game as just described does not explain cooperation.  In this sense, it is clearly a false model of cooperation.  It does, however, provide insight into understanding cooperation and that understanding cooperation is not going to be easy.  It also formalizes and makes precise a context in which individuals can engage in cooperative and non-cooperative strategies.  Perhaps most importantly, it provides a template against which to evaluate new and revised models of cooperative and non-cooperative behavior.

One way to extend the prisoner’s dilemma game is make it more realistic by allowing players to play each other repeatedly. Robert Axelrod (1984) introduced simple agents in the prisoner’s dilemma game.  In his simulated tournament, all agents played n rounds and agents could have memory of previous encounters and use their memory of previous encounters to choose to either cooperate or defect.  In the first tournament, Axelrod invited colleagues to submit strategies.  He found that nice strategies (i.e., they do not defect until an opponent defects), which retaliate (i.e., at some point, they defect in response to opponent defections) but are forgiving (i.e., they will at some point return to cooperation after an opponent defects) did best.  In particular, the strategy tit for tat (TFT) did the best.  TFT always cooperates on the first round with an opponent and then copies its opponent’s strategy on all subsequent rounds.

The introduction of agents with minimal properties of memory and the ability to play repeatedly, reveals that prisoner’s dilemma situations may provide insight and understanding into the evolution of cooperation.  In this sense, performing simulations of agents with memory and using different strategies based on an agent’s memory, is the erection of new scaffolding for building insight and understanding into the evolution of cooperation.  Of course, the scaffolding may be faulty and our apparent understanding and insight may collapse or the scaffolding may allow us to only build insight and understanding in only a limited respect.  Nevertheless, it is a starting point from which other work can be compared.

References

Axelrod, R. (1984). The Evolution of Cooperation. New York: Basic Books.

Bales, K. L. , Carter, C. S. (2007). Neuropeptides and the Development of Social Behaviors Implications for Adolescent Psychopathology. Adolescent psychopathology and the developing brain: integrating brain and prevention science. Oxford University Press, pp. 173-195.

Carter, C. S. et al. (1995). Physiological substrates of mammalian monogamy: the prairie vole model. Neurosci. Biobehav. Rev. 19: 303–314.

Grimm, V., Revilla, E., Berger, U., Jeltsch, F., Mooij, W. M., Railsback, S. F., Thulke, H., Weiner, J., W. Thorsten, DeAngelis, D. L. (2005). Pattern-Oriented Modeling of Agent-Based Complex Systems: Lessons from Ecology. Science, 310: 987-991.

Keller, L. (1995). Social life: the paradox of multiple-queen colonies. Trends in Ecology & Evolution, 10: 355-360.

Maynard Smith, J. & Price, G. R. (1973). The logic of animal conflict. Nature, 246: 15-18.

Nowak, M. A. & May, R. M. (1992). Evolutionary games and spatial chaos. Nature, 359: 826-829.

Zak P. J., Stanton, A. A. & Ahmadi, S. (2007). Oxytocin Increases Generosity in Humans. PLoS ONE, 2: e1128.

A chapter on this topic will be appearing in the Vienna Series in Theoretical Biology, MIT Press.