Prince or dragon?

Author: István Scheuring

Recommended age: 10-99

Number of players: 8-40

Space needed for the game: classroom

Difficulty level: 1

Playing time: 10-15 minutes

Preparation time: 5 minutes

Accessories: sheets of papers, pen and ink, buttons or pebbles or any other small object that can be hidden in your fist

Short description: It is good to be a prince if the opponent is a dragon, and it is better to be a dragon than a prince if the opponent is a prince. However, if two dragons or two princes meet, that is really bad. What should I do then? Be a prince or a dragon?

Preparations: I suggest forming a long desk-line which you can walk around. The players will sit or stand at the two sides of this desk-line. Every player has a sheet of paper, a pen, and a button or a pebble in one of her hands. Present the score table of the game on the blackboard or the projector.

Course of the game: Players sit or stand in pairs at the two opposite sides of the desk-line. Their sheets and pens are in front of them on the desk. They hide both of their hands behind their back, show their closed right fists, and then open their hands. The empty hand means dragon, the button/pebble/etc means prince. Finally, everyone records their scores from the last round on their sheets, according to the score table presented below.

What is the rationale behind these scores? If two princes meet, they start fighting each other to decide which of them will marry the kidnapped princess. It takes a lot of time and energy, and has little benefit, as the princess is kidnapped by the dragon. This is the reason they receive -2 points each. If a prince meets a dragon, then he frees the princess and can marry her. Thus the prince receives 5 points, and the dragon 0 points, since the princess is gone. If two dragonPrince or dragon?s meet, they have a nice conversation about dangerous princes and beautiful princesses, so they receive 1 point each.

Following each round, the players move one place to the right or the left around the deskline. Thus there will be new pairs that play the same game against each other. This continues for 10-20 rounds. The questions are: Who collected the most points? What kind of strategies can lead to high scores?

Biological background: The presented game is the well-known hawk-dove game with a funnier frame story. The essential element of the game is that for a high score the player has to change the prince and dragon strategies. If too many players choose the prince strategy, then they often receive -2 points. If somebody plays a dragon, in this case, it will receive 0 points, which is more favorable. However, if the majority plays dragon, then their benefit will be mostly 1 point, while the prince strategy generally receives 5 points. Consequently, (similar to the rock-paper-scissors game) the rare strategy is always advantageous. This situation in biology is called a negative frequency-dependent selection or an advantage of rarity. A natural example for such a situation are house sparrows searching for food in a flock. Individuals can search actively, or can only scrounge active searchers. It can be shown that if there are too many searchers then scroungers are better off, but if there are too many scroungers in the flock, then the searchers can collect more food. Negative frequency dependent selection maintains the balance between these two strategies.

At the end of the game ask the players to count the number of cases when they played prince and dragon and then compute the frequencies of these strategies (divide the number of a strategy by the sum of all rounds). Then study whether there is any connection between the high score received by a player and the frequency of choosing the dragon strategy. What is your experience? The prince and dragon strategies receive the same score if the prince strategy is chosen with frequency 2/3, and the dragon strategy with frequency 1/3. Then the average score per round for a prince is (-2 x 2/3) + (5 x 1/3) = 1/3. Similarly, the dragon strategy’s average score per round is (0 x 2/3) + (1 x 1/3) = 1/3. Thus, the player who plays prince with frequency 2/3 and dragon with frequency 1/3, receives ⅓ points on average per round. If the majority of the players chooses the prince strategy more frequently than 2/3, then those individuals collect more points who choose the prince strategy less frequently than 2/3. And vice versa, if the majority chooses the prince strategy less frequently than 2/3, then those individuals collect more points who choose the prince strategy more frequently than 2/3.

References: Barnard, C.J.; R.M. Sibly (May 1981). "Producers and scroungers: A general model and its application to captive flocks of house sparrows". Animal Behaviour. 29 (2): 543–550. doi:10.1016/S0003-3472(81)80117-0