Advertise effectively!

Author: István Scheuring

Recommended age: 10-99

Number of players: 3-12

Space needed for the game: a space that can comfortably accommodate the given number of players

Difficulty level: 2

Playing time: 10-15 minutes

Preparation time: 5 minutes (+ time needed to prepare the accessories)

Accessories: six small and different ornaments, or any other signs with numbers from 1 to 6 (12*6), dice, paper, pencils

The “ornaments” for the game. One can also hang them around her neck by tying a string around them.

Short description: Increasing the number of attractive ornaments increases the chance of being chosen as a mating partner, but decreases the number of offspring. How costly signals should we choose to achieve the highest fitness?

Preparations: Put ornaments, pencils and paper on each table to record the points.

Course of the game: Each player receives 6 different ornaments. This can be 6 different bird feathers made of paper, which you can hang on your wrist or neck with a string or stick on yourself with a sticky note. But you can also have six syllabuses (bird's song elements) visually displayed. Each of the 6 elements has a number from 1 to 6. Each player can decide how many ornaments to hang on themselves. These advertise how attractive he is. The referee then rolls one die. Whoever has a number of ornaments that match the number rolled, scores the number of points equaling the number of ornaments they have not used as an ornament. (Unused ornaments indicate the amount of energy left to use for reproduction, and used ornaments indicate the cost of the signal by which the other sex chooses mating partners.) Then another round follows. The aim is to collect the most points after 10-12 rounds. Each player's score is kept on paper or on a board. Let's see who will be the winner and why!

The expected value of the scores depending on the decisions can be calculated as follows: number of ornaments kept * probability of winning. In other words, if 1,2,3..5 ornaments are used for advertising, the average collected points are : 5 x 1/6, 4 x 2/6, 3 x 3/6, 2 x 4/6, 1 x 5/6. Consequently, it is best to use 3 ornaments on average, but obviously we don't tell the players this in advance.

Variant: We chose some players randomly (or all of the players) who are in a better physical condition. Therefore, the number of unused ornaments + 2 points will be awarded if their number is selected by a dice roll. If they do not use any ornaments, they will still surely get 2 points each turn. Thus, their expected payoff is (5+2) x 1/6, (4+2) x 2/6, (3+2) x 3/6, (2+2) x 4/6, (1+2) x 5/6, (0+2) x 6/6. That is, it is best to use four ornaments. So, those in better shape should incur higher advertising costs. We can introduce rules for individuals in worse physical condition in a similar fashion.

Biological background: When choosing a mating partner, the choosy sex, which in most birds is the female, selects from individuals of the opposite sex on the basis of reliable signals that predict well the viability and reproductive ability of the individual. Because these signals are costly, if an individual advertises itself more intensively, it will leave him less energy for reproduction. Together, these two effects select different optimal levels of advertisement depending on the viability of the individual. The game's variation shows that individuals in better condition will advertise themselves with brighter colours and more intense vocalizations than less viable individuals.

References: own idea