Cognitive psychologist Steven Pinker argues that while the Enlightenment ideals of using knowledge to enhance human well-being are not inherently natural to us, they are vital for societal progress.
But one obstacle standing in front of greater progress centers on game theory, particularly situations involving the tragedy of the commons. The tragedy of the commons describes a predicament in which individuals independently pursue their own interests, leading to the overexploitation and eventual depletion of a shared resource, ultimately harming everyone’s well-being.
According to Pinker, one example of a tragedy of the commons lies within what we choose to believe in public. An individual might be incentivized to believe in something because it will make them look good to people in their circle. But if enough people behave in this way, the likely consequence is that fewer people will be incentivized to earnestly search for truth.
Still, Pinker maintains a hopeful outlook. He cites advancements in science and morality as evidence of progress, and he argues that humanistic values hold an inherent advantage, as they appeal to universal human desires and shared experiences.
Game theory is a useful tool for decision-making in situations where the outcome depends on multiple parties. It provides a systematic way to analyze the interdependence of individuals or organizations and their potential strategies.
Not only does game theory help you identify the optimal strategy for achieving your goals, it can also help you avoid the sunk-cost fallacy — the tendency to persist in an endeavor because of the resources you’ve already invested.
By taking into account the potential actions and responses of other players, game theory allows you to minimize your losses and make informed choices that lead to better outcomes. Whether you’re negotiating a business deal or making investment decisions, game theory can be a valuable asset in helping you make smarter choices and achieve your objectives.
Game Theory is an interesting subject. It has implications on all of our lives, and it’s not something that’s blatantly obvious all the time. It’s the science of strategy, and it’s pretty cool.
Game Theory is the study of strategic decision making.
Game Theory is a core principle of blockchain systems. If you’ve wondered how every individual Bitcoin node works together, Game Theory is your answer.
Game Theory incentivizes people who don’t know each other to work together successfully.
This video goes over the strategies and rules of thumb to help figure out where the Nash equilibrium will occur in a 2×2 payoff matrix. Generally you need to figure out what the dominant strategy is for each player and then use the dominant strategy of each player to see if a final cell ends up being the choice for both players.
In continuing on with our discussion on evolutionary game theory, in this video we will discuss network games.
The workings of evolution are typically told as a story of competition and the classical conception of the survival of the fittest.
But in reality, evolution is as much about cooperation as competition. A unicellular organism may have survived the course of history largely based upon its capacity to fight for resources with other unicellular organisms.
But the cells in multicellular organisms have survived based upon their capacity to cooperate. They form part of large systems of coordination and they are selected for based upon their capacity to interoperate with other elements within large networks that contribute to the workings of the whole organism.
Likewise, in a ghetto full of gangsters, it may be your capacity to look out for your own skin that will enable you to get ahead. But at the other end of town where people earn their living as part of large complex organizations, it is primarily your capacity to interoperate with others and form part of these large organizations that determine your payoff.
You form part of a large cooperative organization which is really what is supporting you and determining your payoff. In such an event one needs to be able to interoperate with others effectively, to be of value to the organization, and thus succeed in the overall game.
The idea is that evolution creates networks of cooperation that are able to intercept resources more effectively because of the coordinated effort.
People’s capacity to survive within such systems is then based upon their capacity for cooperation, instead of competition, as it might be if they were outside of these networks of cooperation, in the jungle so to speak.
Thus what we do, our choice of strategy and the payoff for cooperation or defection in the real world, depends hugely on the context outside of the immediate game and this context can be understood as a network of agents interacting.
When we form part of networks of coordination and cooperation our payoffs come to depend largely on what others around us are doing.
I want to buy a certain computer operating system but the payoff will depend on what operating system my colleagues are using. Or people want to learn a new language only if the other people around them also speak that language.
SPATIAL DISTRIBUTION
A key factor in the evolution of cooperation is spatial distribution. If you can get cooperators to cluster together in a social space, cooperation can evolve.
In research conducted by Christakis and Fowler, they have shown that our experience of the world depends greatly on where we find ourselves within the social networks around us. Particular studies have found that networks influence a surprising variety of lifestyle and health factors, such as how prone you are to obesity, smoking cessation, and even happiness.
The experiment they conducted took place in Tanzania with the Hadza people, one of the last remaining populations of hunter-gatherers on the planet whose lifestyle predates the invention of agriculture. They designed experiments to measure social ties and social cooperation within the communities.
To identify the social networks existing within the communities they first asked adults to identify individuals they would prefer to live with in their next encampment. Second, they gave each adult three straws containing honey and were told they could give these straws as gifts to anyone in their camp.
This generated 1,263 campmate ties and 426 gift ties.
In a separate activity, the researchers measured levels of cooperation by giving the Hadza additional honey straws that they could either keep for themselves or donate to the group.
When the networks were mapped and analyzed, the researchers found that co-operators and non-cooperators formed distinct clusters within the overall network. When they looked at individual traits with the ties that they formed they found clearly that cooperators clustered together, becoming friends with other cooperators.
The study’s findings describe elements of social network structures that may have been present early in human history. Suggesting how our ancestors may have formed ties with both kin and non-kin based on shared attributes, including the tendency to cooperate.
According to the paper, social networks likely contributed to the evolution of cooperation.
MODEL
The emerging combination of network theory and game theory offers us an approach to looking at such situations. The idea is that there are different individuals making decisions and they are on a network and people care about the actions of their neighbors.
As an example, we can think of an individual, Kate, choosing whether to go to university or not, and this action will depend upon how many of her friends are choosing to go to university also.
So the pay off for the individual will depend on how much she likes the idea of going to university as an individual, but also how many of her friends choose to go and on how many friends she has.
So in this networked game, the individual might have a threshold, say Kate will only go to the university if at least two of her friends are also going and her friends also have the same threshold.
This is an example of a strategic complements game. Meaning that the more of one’s neighbors that take an action the more attractive it becomes for one to also take it.
But we can also have the inverse, what are called games of strategic substitution, where the more of my neighbors that take the action the less attractive it is for me.
As an example, we might take Billy who is thinking of buying a car, but Billy is also part of a social network of friends and if one of his friends has a car then he can take rides with the friend and has no great need to purchase a car. If we assume the same is true for his friends we could use a social network model of the game to find where the equilibrium state is. So the payoff for Billy would look like a ranking where one of his friends having a car is best, then him having to buy one, then worst of all no one having a car.
An agent is only willing to take action 1 if no one they are connected to is also taking that action. So in the network, we can see that it is in equilibrium because all the players connected to a player taking strategy 1 do not take that strategy.
Our world is a complex place, especially when dealing with social interaction where people are embedded within a given social, cultural, economic and physical environment, all of which is affecting the choices they make. The combination of network theory and game theory takes us into this world of complex games which is much more representative of many real-world situations, but still very much at the forefront of research.
This video has hopefully given you a sense of how network game theory can help us look outside the box of standard games. To see how other factors in the environment may be influencing the games and how to potentially incorporate these other factors through the application of network modeling.
The Replicator equation is the first and most important game dynamic studied in connection with evolutionary game theory. The replicator equation and other deterministic game dynamics have become essential tools over the past 40 years in applying evolutionary game theory to behavioral models in the biological and social sciences.
REPLICATOR EQUATION
These models show the growth rate of the proportion of agents using a certain strategy. As we will illustrate, this growth rate is equal to the difference between the average payoff of that strategy and the average payoff of the population as a whole.
MODEL
There are three primary elements to a replicator model:
Firstly we have a set of agent types, each of which represents a particular strategy and each type of strategy has a payoff associated with it which is how well they are doing.
There is also a parameter associated with how many of each type there are in the overall population – each type represents a certain percentage of the overall population.
Now in deciding what they might do, people may adopt two approaches.
They may simply copy what other people are doing, in such a case the likelihood of an agent adopting any given strategy would be relative to its existing proportion of that strategy within the population. So if lots of people are doing some strategy the agent would be more likely to adopt that strategy over some other strategy that few are doing.
Alternatively, the agent might be more discerning and look to see which of other people’s strategies is doing well and adopt the one that is most successful, having the highest payoff.
The replicator dynamic model is going to try and balance these two potential approaches that agents might adopt, and hopefully, give us a more realistic model than one where agents simply adopt either strategy solely.
Given these rules, the replicator model is one way of trying to capture the dynamic of this evolutionary game, to see which strategies become more prevalent over time or how the percentage mix of strategies changes.
In a rational model, people will simply adopt the strategy that they see as doing the best amongst those present. But equally, people may simply adopt a strategy of simply copying what others are doing. If 10% are using strategy 1, 50% strategy 2, and 40% strategy 3, then the agent is more likely to adopt strategy 2 due to its prevalence.
So the weight that captures how likely an agent will adopt a certain strategy in the next round of the game is a function of the probability times the payoff.
If we wanted to think about this in a more intuitive way, we might think of having a bag of balls where the ball represents a strategy that will be played in the game. If a strategy has a better payoff then it will be a bigger ball and you will be more likely to pick that bigger ball.
Equally, if there are more agents using that strategy in the population, there will be more balls in the bag representing that strategy, meaning again you will be more likely to choose it. The replicator model is simply computing which balls will get selected and thus what strategies will become more prevalent.
One thing to note though is that the theory typically assumes large homogeneous populations with random interactions. The replicator equation differs from other equations used to model replication in that it allows the fitness function to incorporate the distribution of the population types rather than setting the fitness of a particular type constant. This important property allows the replicator equation to capture the essence of selection. But unlike other models, the replicator equation does not incorporate mutation and so is not able to innovate new types or pure strategies.
FISHERS FUNDAMENTAL THEOREM
An interesting corollary to this is what is called Fisher’s Fundamental Theorem, which is a model that tries to capture the role that variation plays in adaptation. The basic intuition is that a higher variation in the population will give it greater capacity to evolve optimal strategies given the environment.
Thus given a population of agents trying to adapt to their environment, the rate of adaptation of a population is proportional to the variation of types within that population. Fisher’s Fundamental Theorem then works to incorporate this additional important parameter, of the degree of variation among the population, so as to better model the overall process of strategy evolution.
GAMES
Static game-theoretic solution concepts, such as Nash equilibrium, play a central role in predicting the evolutionary outcomes of game dynamics.
Conversely, game dynamics that arise naturally in analyzing behavioral evolution lead to a more thorough understanding of issues connected to the static concept of equilibrium. That is, both the classical and evolutionary approaches to game theory benefit through this interplay between them.
Replicator Dynamic models have become a primary method for studying the evolutionary dynamics in games both social, economic and ecological.
John Nash, the US mathematician who has died at 86, is hailed with putting game theory at the heart of economics. Ferdinando Giugliano explains why his work is so important and how the Nash equilibrium theory works.
As we saw in the previous chapter on evolutionary games, when everyone was playing a random strategy it was best to play a Tit for Tat strategy. When everyone was playing a Tit for Tat strategy it was best to play Generous Tit for Tat. When people were playing this, it was then best to play an unconditional cooperative strategy. Once the game was in this state it was then best to play a defecting strategy, thus creating a cycle. This illustrates clearly the dynamic nature to the success of strategies within games.
Because evolutionary games are dynamic, meaning that agents’ strategies change over time, what is best for one agent to do often depends on what others are doing.
It is legitimate for us to then ask, are there any strategies within a given game that are stable and resistant to invasion?
In studying evolutionary games one thing that biologists and others have been particularly interested in is this idea of evolutionary stability, which are evolutionary games that lead to stable solutions or points of stasis for contending strategies.
Just as equilibrium is the central idea within static noncooperative games, the central idea in dynamic games is that of evolutionarily stable strategies, as those that will endure over time.
As an example, we can think about a population of seals that go out fishing every day. Hunting for fish is energy consuming and thus some seals may adopt a strategy of simply stealing the fish off those who have done the fishing. So if the whole population is fishing then if an individual mutant might be born that follows a defector strategy of stealing, it would then do well for itself because there is plenty of fishing happening. This successful defector strategy could then reproduce creating more defectors. At which point we might say that this defecting strategy is superior and will dominate. But of course, over time we will get a tragedy of the commons situation emerge as not enough seals are going out fishing. Stealing fish will become a less viable strategy to the point where they die out, and those who go fishing may do well again.
Thus the defector strategy is unstable, and likewise, the fishing strategy may also be unstable. What may be stable in this evolutionary game is some combination of both.
EVOLUTIONARILY STABLE STRATEGY
The Evolutionarily Stable Strategy is very much similar to Nash Equilibrium in classical Game Theory, with a number of additions.
Nash Equilibrium is a game equilibrium where it is not rational for any player to deviate from their present strategy.
An evolutionarily stable strategy here is a state of game dynamics where, in a very large population of competitors, another mutant strategy cannot successfully enter the population to disturb the existing dynamic.
Indeed, in the modern view, equilibrium should be thought of as the limiting outcome of an unspecified learning, or evolutionary process, that unfolds over time. In this view, equilibrium is the end of the story of how strategic thinking, competition, optimization, and learning work, not the beginning or middle of a one-shot game.
Therefore, a successful stable strategy must have at least two characteristics.
One, it must be effective against competitors when it is rare – so that it can enter the previous competing population and grow.
Secondly, it must also be successful later when it has grown to a high proportion of the population – so that it can defend itself.
This, in turn, means that the strategy must be successful when it contends with others exactly like itself. A stable strategy in an evolutionary game does not have to be unbeatable, it only has to be uninvadable and thus stable over time.
A stable strategy is a strategy that, when everyone is doing it, no new mutant could arise which would do better, and thus we can expect a degree of stability.
UNSTABLE CYCLING
Of course, we don’t always get stable strategies emerge within evolutionary games. One of the simplest examples of this is the game Rock, Paper, Scissors.
The best strategy is to play a mixed random game, where one plays any of the three strategies one-third of the time.
However in biology, many creatures are incapable of mixed behavior — they only exhibit one pure strategy. If the game is played only with the pure Rock, Paper and Scissors strategies the evolutionary game is dynamically unstable. Rock mutants can enter an all scissor population, but then – Paper mutants can take over an all Rock population, but then – Scissor mutants can take over an all Paper population – and so on.
Using experimental economic methods, scientists have used the Rock, Paper, Scissors game to test human social evolutionary dynamical behaviors in the laboratory. The social cyclic behaviors, predicted by evolutionary game theory, have been observed in various lab experiments.
Likewise, it has been recorded within ecosystems, most notably within a particular type of lizard that can have three different forms, creating three different strategies, one of being aggressive, the other unaggressive and the third some what prudent. The overall situation corresponds to the Rock, Scissors, Paper game, creating a six-year population cycle as new mutants enter and become dominant before another strategy invades and so on.
