Evolution Games (PLUS)

Public summary: 

Simulate populations and explore stable and unstable equilibrium by using Game Theory to model animal behaviour in sharing a food supply.

Modelling Evolution by Game Theory
Useful information
Kit List: 

A selection of strategy cards with various bird pictures
A whiteboard and pen (optional)
Some lego brick success counters
A photocopy of Chapter 5 of the Selfish Gene by Richard Dawkins (source of experiment)

Packing Away: 

In the maths box.

Frequency of use: 

Talk about peoples ideas about evolution. Try and say how most competition is in between members of the same species. Competition for mates etc. We can model with maths.

Moles and blackbirds compete for worms, blackbirds and blackbirds compete for worms and everything else. Why don't blackbirds just kill off their competition (and eat them) there's a risk to it and it might help other people more than me.

Good examples is elephants being hunted for tusks, those with larger tusks die and hence tusk size decreases. I introduced genes as parts of the DNA encoding some feature, you could go into more detail if you wanted.

First talk about how science works, we observe something and try and create a model of how it works. This can be linked nicely to Hand model and Handy engineering. It's often best to start with a simple model and add in more elements to improve it. That's what we do here for evolution. You could ask why they think a game is a good model for evolution? Some people win/propagate genes, chance, you make decisions/moves etc. Thankfully the mathematical and normal notion of games match well.

First of all give everyone 10 lego bricks, these are a measure of how 'successful' you have been at life. The game works by two people in the population 'randomly' meeting and competing over a resource (this could be a mate, food, nest). The resource is worth 5 blocks to whoever gets it however only one can get it (no sharing). How can we decide who gets it? Two ways we either have a fight, this is risky as the loser will come out badly hurt so takes a -10, or we can have a argument/show off/staring contest, think peacocks with their tails over mates or pacing in circles in cats, this is risk free but in the time it takes we could have found something elsewhere so we loose -1 for this time. If someone tries to fight you you're able to run away so you don't get injured. If there is a fight/staring then flip a coin/rock-paper-scissors for who wins.

We consider individuals behaving in a very simple way. They are either an aggressive hawk or a peaceful dove (this is firstly untrue as doves are aggressive and secondly unhelpful as this is inter-species competition...). Hawks always fight never run away, doves never fight and will just stare off and run away from fights.

We can now consider various different encounters...
Between a hawk and a dove it's obvious a hawk does well and a dove doesn't do badly.
Between a dove and a dove one gets a win and the other a slight loss. On average though across two fights both are in profit.
Between a hawk and a hawk, one does well and one takes a massive loss. On average neither is doing too well.

You can now ask what would happen if:
-We had one hawk in lots of doves => the hawk would always win and hence the number of hawks would increase (they have lots of offspring).
-We had one dove in lots of hawks => slightly more tricky, the dove would never win, it always scores zero, but the hawks loose 2.5 points a fight on average, so the dove is actually winning by not suffering major injuries.

So from all hawks we're pushed towards more doves and all doves pushes towards more hawks. We can convince them this might have a stable point in the middle which both these push against. In fact it does when the population is 7/12 hawks and 5/12 doves. With 6 people you can simulate this using one of the random cards (explaining it's like half hawk half dove) this also leads into the idea of polymorphism, not that individuals are intrinsically a hawk but they sometimes decide to be one.

Phase plane diagram
0%doves Stable 100%doves

Now they've seen a simple model ask them how they think you could change it, thinking about how they see animals and themselves behaving:

- You could vary the rewards, this only really shifts the equilibrium, we pick them with a reasonable weighting. In fact we can actually back calculate these numbers from observing populations too. Increasing penalty for wasting time incentives hawks who never waste time, increasing loosing penalty incentives doves for the same reason. Changing the win value is more complicated. We could also make these random but we can take the expectation and it turns out to be equivalent in the long run. We can observe this in populations of very venomous snakes, they're very unlikely to attack as the risks are high.

- We can introduce new strategies, ask them for ideas. The simpler the better (we don't want to make our model too complicated). The next ones we normally consider are conditional strategists. They make decisions based on what the other person is doing. For example the retaliator stares off like a dove against a dove and fights like a hawk if fought against. Strategies like retaliator and prober-retaliator form a (nearly) Evolutionary Stable Strategy (ESS). They're vulnerable to slight invasions by each other and doves and we get a polymorphism between them.

- We can also "break the symmetry" of the game. So far all fights are 50-50 who wins, in reality this is really not the case. Some members of the species are bigger, more experience fighters or are in home territory giving them an advantage in the fight. The idea of "bigger animal acts like a hawk, smaller a dove" is a stable strategy. Weirdly so is the reverse "smaller acts like a hawk, bigger a dove" as anyone who choose to break it is going to end up in lots of fights. Mexican Social Spiders are a species stuck in one of these paradoxical strategies, "if your nest is invaded act like a dove, if your invading act like a hawk" one invasion leads to many which is very costly however the risk of fighting manages to outweigh it in this species. Also rewards might be worth different amounts to different individuals, older ones might take more risks as they have less to loose, if you have a large stash of food you're less likely to risk much on getting more.

-Memory. Crickets have past memory but can't identify individuals. They remember how well they've done previously and rank themselves on this (I lose 30% of fights). Monkeys can start doing individual rankings, I always loose to Frank and Phil always runs away. This gives you ideas of what strategy other players are using.

We can work out optimal values for these games too, at the simple equilibrium in the original game on average everyone gets 0.625 points/encounter. We can now talk conspiracy theories. If everyone agreed to be a dove they'd average a reward of 1.5 which is much better, however individuals have no incentive to stick to it, become a hawk in this group and they rake in the points. "stable not because it's good for the individuals within but because it's immune to treachery". (There are actually even better conspiracies to have)

If we want somewhere to go next we can go for wars of attrition. Like an auction but all bidders pay their bid and only the highest bidder gets the item. E.g. staring competition for a piece of food, both waste time staring and the loser gets nothing. Lots of things are unstable. Value how much it's worth, stare that long then give up is outdone by someone who stares a second longer than it's worth. If you're not going to win ever you might as well never try so max bid population infiltrated by immediate quitters, then infiltrated by people who wait a second etc.

Imagine there was an indication you might give up, e.g. a whisker flicker when you'll give up in a minute. Strategy where you continued as you would but as soon as your opponent's whisker flickered you wait 61 secs optimal if you're going to give up in a min and they haven't flickered give up now (and don't flick your whiskers!) is optimal. Hence evolution of the poker face. Lying is unstable. Imagine people sat down if they were in for the long game, people would give up if their opponent sat down, then liars emerge who sit down anyway, the people emerge to call the bluff. Lies and truth both unstable.

There's also competition inter species. A lion wants to eat an antelope. An antelope would prefer to not be eaten by a lion. These are mutually incompatible. Obviously lions could instead try to eat other lions but there's no much risk of retaliation. Antelopes don't fight back as it's too risky to attack the lion so they try and improve their running away. This is really just an example of (a rather large) asymmetry in participants.

There is often questions which actually highlight the one major flaw in this model. Humans are actually very bad at following it. There are various good examples in the Public Goods Game, Ultimatum game, Dictator (Trust) 'game' which give very counter intuitive results.

Risk Assessment
Date risk assesment last checked: 
Tue, 01/01/2019
Risk assesment checked by: 
Date risk assesment double checked: 
Mon, 04/02/2019
Risk assesment double-checked by: 
Conor Cafolla
Risk Assessment: 

Modelling evolution via game theory.

Hazard Risk Likelihood Severity Overall Mitigation Likelihood Severity Overall
Duplo/Lego Children swallowing Duplo or Lego pieces 1 2 2 The Duplo pieces should be sufficiently large to discourage swallowing. Do not use Lego with very small children and keep a close eye on the box of Lego.
Call first aider if child swallows, if choking encourage child to cough.
1 2 2
Coins Tossed coins flying off and hitting someone. 1 1 1 Check you can flip a coin without losing control of it, otherwise just spin it on the table. It's perfectly fine to let the children toss the coin themselves, but make sure they're capable of doing it safely with a trial flip first.
In case of injury call first aider.
1 1 1