Ex­plan­a­tions of the games from "Play along? - Game the­ory at your fin­ger­tips"

Ad­jus­ted Win­ner

Your millionaire grandmother wants to part with a few valuables. Her two grandchildren (you and your fellow player) should therefore receive these goods and divide them up "fairly" between them. The grandchildren are asked to comment on which of the "heirlooms" seem more useful compared to the others. They then decide to draw up a list of points in which both people have 100 points to rate the goods (0 = no interest, high score = high interest).

Good Item Player A Player B
1 Motorbike 12 8
2 Fishing boat 8 4
3 Small car 14 12
4 Gold jewellery 14 8
5 Collection of photographs by Larry Yust 4 38
6 Antique crockery service 26 16
7 Fine furniture in country house style 6 6
8 Jet ski 16 8
Total points   100 100

Negotiate a distribution of goods with your fellow player based on the given preferences that both sides can agree on. If you cannot agree on a division, nobody inherits anything. It is also possible to divide an inheritance proportionally between you. You will then only receive the corresponding share of the points.

You can find the solution here.


At Paderby's auction house, it is a good tradition that the small change that was left on the floor during the last auction round is auctioned off in a jam jar. However, the bidders are not allowed to count the coins, only to estimate them. The jar is auctioned off in a first-price auction, which means that the bidder with the highest bid wins and must pay this bid.

You can find the solution here.

Pris­on­er's di­lemma

You and your team mate are taking part in a game show. You have successfully answered all the questions together and must now decide separately whether you would like to share the prize equally or each have everything for yourselves. Two packs of gummy bears are obligatory for the top prize. If you both decide to share the prize, you will each receive 1 pack. If you both decide to stab the other in the back and steal the prize, you both go away empty-handed. If only one of you wants to share and the other wants to steal the prize, the person who decides to steal gets the maximum prize (i.e. 2 packs of gummy bears).

For your decision, you are each given a red and a black playing card, which you do not show to your opponent. The red card indicates that you want to share the winnings and therefore trust your opponent. The black card means that you want to stab your opponent in the back and steal the winnings. Important: You must not collude with your fellow player!

After making your decision, place the corresponding card in the centre at the same time. You can then reveal the cards at the same time and see whether you go home as the lucky winner or the disappointed loser.

You can find the solution here.


You and your fellow players are ice cream vendors on a beach. You all have a mobile stand that allows you to move freely around the edge of the beach. There are people spread evenly across the entire beach. The aim is to supply them with ice cream, but the prices for the ice cream are set by the town and people always go to the stand that is closer to where they are lying. In order not to confuse the beach visitors, you and your fellow players move one after the other.

Look at the picture below: you and your two team-mates can move freely along the given line. Find the most promising location where you think you can sell the most ice cream. Take it in turns to move your pawns.

You can find the solution here.
This video also provides a clear explanation.


At the beginning of March, the traditional Paderfeld Paderbarbeque takes place in the Paderquell area. As is the case every year, a large number of people come to the festival. The Rehdame skat club and the Volle-Neune bowling club don't miss out on the spectacle either. The skat players and bowling fans quickly meet and get chatting. As the people of Paderfeld are known to be real party people, it doesn't take too long before the dance floor is just as busy as the drinks stands. Our protagonists are also all drawn towards the dance floor to dance until the next morning.

Look at the distributed preferences of the skat players (rectangles) and bowling fans (triangles).
Find a match between them in which each person finds a dance partner in the other club.

You can find the solutions here (10 people) and here (6 people).


The five pirates Anna, Ben, Christine, David and Emma have found a treasure of 100 gold coins. This is now to be divided up. The pirates have their own rules. Anna is the captain and is allowed to make the first suggestion as to how the treasure should be divided up. But beware: if this proposal is rejected by the majority, the pirates mutiny and Anna walks the plank! In this case, Ben is the new captain and makes the next suggestion. And he too is thrown overboard if a majority opposes him. After that, first Christine, then David and finally Emma would be captain.

Let's go back to the beginning. Anna, what division do you propose?

You can find the solution here.
This video also explains it clearly once again.

Pub­lic good

Four players play the public goods game. The game is played over several rounds. Each round, each of you receives two coins. You now have the choice: do you put the two new coins in the public pot or do you keep the coins for yourself?

The amount in the public pot is doubled and paid out equally to all players.
This means that if there are 8 coins in the pot, the amount is doubled to 16 coins. Each player now receives 4 coins.
If there are 6 coins in the pot, the amount is doubled to 12 coins and each player receives 3 coins.
If there are 4 coins in the pot, the amount is doubled to 8 coins and each player receives 2 coins.
If there are 2 coins in the pot, the amount is doubled to 4 coins and each player receives another coin.
How do you decide?

You can find the solution here.
This video also explains it clearly once again.