Hawthorn or blackthorn?

Author: István Scheuring

Recommended age: 10-99

Number of players: 10-40

Space needed for the game: classroom

Difficulty level: 1-2

Playing time: 10 minutes

Preparation time: 2 minutes

Accessories: Paper and ink for all players, one calculator.

Short description: We are birds living in an Autumn forest. We can eat hawthorn or blackthorn, but hawthorn is more nutrient-rich than blackthorn. However, if everybody eats hawthorn then only some remain for us. Then what should we eat, hawthorn or blackthorn?

Preparations: Ask players to take a sheet of paper and a pen.

Course of the game: The frame story of the game: We are birds and we are hungry. There is Autumn, only a few insects remain, but we can eat hawthorn or blackthorn. The nutrient content of hawthorn is twice the nutrient content of blackthorn. But if everybody eats hawthorn, then we have to share this food with others, and only little remains. So what should we do if we want to collect the most energy (the highest score)?

The score of the hawthorn eaters is 100/(number of hawthorn eaters) while the score of blackthorn eaters is 50/(number of blackthorn eaters). For example, if in a given round 18 players collected hawthorn and 11 players collected blackthorn, then hawthorn eaters receive 100/18=5.55 points, and blackthorn eaters get 50/11=4.54 points. (A calculator is helpful for this phase of the game.) The game leader notes these points on the blackboard and asks the players to note down their respective points.

Play 10-15 rounds in a similar manner. Check who won the game and applaud her. It is even more interesting to investigate how the collected points in the two groups changed. It is probable that with small fluctuations, but both groups (that is hawthorn and blackthorn eaters) will collect a similar number of points. On average, hawthorn will be selected about twice as many players as blackthorn. Discuss why we observe this! What kind of strategies did the players choose, and why?

Variant 1: Those who change their strategy, miss a round.

Variant 2: If someone chooses a resource the third or more time, he or she becomes twice as effective in using it. Thus, this player gets twice as many points. (He or she can simply raises both his/her hands.) Don’t forget that in these situations the scores should be calculated with the full score divided by all hands! This variant should be played together with variant 1.

Biological background: As the players, the animals in nature also try to select the most beneficial nutrient among the possible ones. The actual benefit of a nutrient depends on its nutrient content and the number of competitors. The animals, similar to the game situation, test the benefit of the different nutrients independently from each other. Then change their feeding strategy until the benefit becomes approximately equal in the two nutrient patches. Natural selection shaped the behavior of the animals to find this optimum fast.
Variant 1: With this variant we model the cost of switching between resource patches. If patches are far, the time spent travelling is not spent feeding.
Variant 2: This variant models that feeding on a resource for a long time can make the animal expert in handling and/or consuming the given resource.

References: own idea