We are in a golden age of grift. Where adventurers once flocked to California or the Yukon because “there was gold in them thar hills,” the fastest way to get rich today is by fleecing suckers. We’ve got crypto rug pulls, meme stocks, nutritional supplements, MLMs—anything to make a quick buck.

Fraud is hardly a new phenomenon. The Great Depression brought with it a wave of con artists, mythologized in movies such as Paper Moon or The Sting. A century earlier, Mark Twain wrote about the innumerable swindlers and card sharps operating along the Mississippi River; indeed, Twain himself lost most of his fortune in fraudulent investment schemes. Medievalist Umberto Eco wrote several novels exploring frauds, liars, and magical thinkers in the Middle Ages. Such men thrived thanks to superstition and poor record keeping.

Is the current boom the new normal? The start of a slide into a new post-truth dark age? Or are we simply experiencing yet another high watermark in a cycle as old as civilization? If it is cyclic, is it driven by external circumstances such as war or poverty, or does it arise naturally from the dynamics of the system?

The answer, I’d argue, lies in a moderately obscure mathematical theory from the 1980s.

Evolutionary Game Theory

The version of game theory most people have seen is the rational-agent sort: perfectly informed players maximize utility, best responses snap into place, and equilibria have the clean finality of a solved puzzle. Evolutionary Game Theory (EGT) is different. It assumes that all strategies exist in the population and that success in games slowly increases the relative proportion of that strategy in the population over time. Strategies that earn higher payoffs become more common. Strategies that earn lower payoffs decline.

This is the framework John Maynard Smith popularized in Evolution and the Theory of Games. The book is now mostly read by specialists, but it contains a small number of ideas that are so widely applicable that once you know about them, you start seeing them everywhere.

I’d like to tackle the problem of understanding the cycle of grift by proposing a novel EGT model. The model is similar to the classic Hawks, Doves, & Retaliator model (which I’ll come back to later) but has a different payoff matrix that leads to very different dynamics.

The GSM Model

To define our model, we’ll choose three strategies, specify the payoff matrix which describes what happens when two strategies interact, then use the mathematical tools of EGT to study that model. The three strategies are:

• Grifter: attempts exploitation when possible.
• Skeptic: pays an ongoing cost to avoid being exploited.
• Mark: trusts by default; cooperates cheaply, but is vulnerable.

We can formalize these strategies within EGT by defining a payoff matrix:

When a Grifter meets another Grifter or a Skeptic, the scam fails. The Grifter wastes time and effort and incurs a loss. Only when a Grifter meets a Mark does the strategy pay off: the Grifter successfully exploits the Mark and gains a sizable reward.

A Skeptic can avoid getting scammed, but pays a constant price for vigilance, which represents the cost of investing in education and doing due diligence. When interacting with honest players (Skeptics or Marks), they still achieve mutual cooperation, but still have to pay the cost for their caution. However, when interacting with a Grifter, they’re able to walk away from the deal early, losing only the constant cost of skepticism.

In contrast, a Mark is trusting and unguarded. When a Mark meets another Mark, everything goes smoothly: they cooperate without hesitation and both receive maximal payoffs. Things go almost as well when they meet a Skeptic; after the Skeptic has done their homework the two are able to cooperate without issue, and the Mark still receives a maximal payoff.

It’s only when a Mark encounters a Grifter that things go south. When that happens, the Mark gets exploited and incurs a large loss.

The specific parameters don’t affect the qualitative outcome much, but here are some reasonable parameter values for concreteness:

With those parameters, the concrete payoff matrix is:

Replicator Dynamics

To turn payoffs into population dynamics, we use replicator equations: each strategy grows (or shrinks) in proportion to how well it is doing relative to the population average.

Here is the simple, discrete-time simulator I used:

def replicator(populations, A, delta=0.05, N=2000):
    """
    Given an initial vector of `populations`, a payoff matrix `A`, a step size
    `delta`, and a number of iterations `N`, return the trajectory as a 2D
    numpy matrix and the final population as a 1D numpy array the same shape as
    the population.
    """
    # ensure populations is a normalized numpy vector
    populations = np.asarray(populations, float)
    populations = populations / populations.sum()

    # initialize the trajectory with the initial conditions
    trajectory = [populations.copy()]
    
    for _ in range(N):
        # payoff for this iteration
        fitness = A @ populations 

        # update population in direction of the most successful strategy
        average = populations @ fitness
        populations = populations + delta * (populations * (fitness - average))

        # avoid extinction and normalize
        populations = np.clip(populations, 1e-6, 1 + delta) 
        populations = populations / populations.sum()
        
        # track the full history of population trajectories
        trajectory.append(populations.copy())

    return np.array(trajectory), populations

The full source code is available as a Jupyter notebook. It even has a cell with interactive widgets so you can play around with the parameters in real time.

Results

The state of a three-strategy population fits naturally on a simplex: a triangle where each corner is a pure population (100% Grifter, 100% Skeptic, 100% Mark), and each interior point is a mixture. Several different trajectories are shown as colored fields, each with different random initial conditions, and a vector field showing the evolutionary pressure at each point is overlaid.

It’s immediately obvious that each trajectory spirals outward until it is following a roughly triangular orbit which visits each corner in turn, almost reaching it before it starts to curve dramatically towards the next.

It’s also instructive to look at the longitudinal view, plotting the three populations as a time series:

Taking these two visualizations together, we can see the system does not settle down to a single equilibrium point but instead falls into quasi-periodic cycles. Each strategy takes a turn dominating, but inevitably falls to the strategy which it is weak to. This is a signature of “non-transitive” games such as rock-paper-scissors; in such games trajectories orbit rather than converge.

Our game is “non-transitive” because success is a function of the current population mix, and that very success always leads to a different mix:

• Marks prosper when grifters are rare, because trust is efficient.
• Grifters prosper when marks are common, because exploitation is easy.
• Skeptics prosper when grifters are common, because vigilance pays for itself.

In models like this, a few different long-run patterns are possible: the system might converge to one stable balance (a fixed-point attractor), it might circle around in a stable loop (a limit cycle), or it might swing closer and closer to each corner in turn, spending long stretches dominated by one strategy before shifting again (a heteroclinic cycle). The qualitative behavior is roughly the same, though: periodic cycles, not a steady state.

Hawks, Doves, and Retaliators

A useful contrast is the classic Hawks, Doves, & Retaliators model, which is often used as a first EGT example because it tends to settle to a stable equilibrium point. Here is the same simulation run using the HDR payoff matrix:

No orbits here: instead, all trajectories converge to a single point at a 60-40 split between Hawks and Doves, with Retaliators going extinct. Such a stable equilibrium point is called an evolutionarily stable strategy (ESS).

Why does HDR converge to an ESS while GSM does not? The Retaliator strategy goes extinct and stays extinct because it bears the full cost of policing Hawks itself. In contrast, the Skeptic in GSM is not concerned with punishing Grifters but simply avoiding them.

Conclusion

If you believe the assumptions of the model, the implications are clear. Grift is cyclical, and any period of high grift will soon give way to a period of high skepticism, which will last until enough time has passed for people to once again forget the lessons they’ve learned. In concrete terms, the current generation of grifters is putting on a masterclass in spotting con artists and it won’t be long before their tricks are well known, at which point they’ll stop working. Consider NFTs, which crashed pretty hard once people saw through them.

OK then, should you believe the model? On one hand, obviously not. It’s a ridiculously simplified caricature of human behavior and every aspect of the model can be legitimately challenged. In some ways we can say it is definitely wrong: for example, it has the various populations crashing to near zero with each period, whereas in the real world the change is more a matter of degree. On the other hand, sometimes very simple toy models do somehow capture the essence of a phenomenon. “All models are wrong, but some are useful,” to quote George Box. If nothing else, I think this model shows that a certain fluctuation in the number of con artists arises naturally from the dynamics of the system without the need for any external drivers as the general populace gradually forgets and then is forced to relearn how to protect themselves from various scams.

In terms of concrete predictions, that depends on whether or not you think we’ve reached “peak grift” or not. I think we have, and that we should therefore anticipate more skepticism in the near future with a corresponding lack of success from grifters. Perhaps that’s naïve.

Exercise caution in your business affairs; for the world is full of trickery. But let this not blind you to what virtue there is; many persons strive for high ideals; and everywhere life is full of heroism.
—Max Ehrmann, Desiderata