Who is the winner, who is the proper?

Author: István Scheuring

Recommended age: 12-99

Number of players: 4-40

Space needed for the game: classroom

Difficulty level: 3

Playing time: 15-30 minutes

Preparation time: 15 minutes

Accessories: Reward table (either on paper or projector), voting cards (two different cards for each team, apple and a pear in our example, but anything will do). A large bowl with water, a smaller bowl that floats, pebbles, and something as a prize.

Short description: You can only win if you are greedy. However, if everybody is greedy then nobody wins at the end. How can we solve this discrepancy?

Preparations: We form equally large groups of players. The groups can sit down, separately from each other. We present the rules of the game. Then, we give voting cards and reward tables for each group. We position the large bowl with the water so that everyone can see it. Then we put the smaller bowl afloat, and the pebbles next to them.

Course of the game:
We form equally large groups of players. We present the reward table and analyze it together with the players as long as everyone understands it properly (Table 1.) Don’t rate or judge the strategies, and ask the players not to do that, either. Only the quiet within-group conversation is allowed. There will be ten rounds in the game. One round consists of the groups voting synchronously (showing one of the cards), receiving their respective scores and putting the respective amount of pebbles in the floating bowl. The group that reaches the highest score after ten rounds is the winner of the game. However, if the floating bowl sinks, because of the weight of the pebbles, then the game ends with all groups losing. It is important to set the size of the floating bowl and/or the size of the pebbles so that an intermediate number of “pear votes” sinks the bowl. For example, in our presented case, if 3*10=30 pebbles sink the bowl with high probability, then the game is strictly challenging. At that setup, players sink the pot in most cases before the tenth round. The failure and the behavior of the others are frustrating, so players frequently become angry or disappointed. We have to take this into consideration, and have to resolve the remaining frustration somehow at the very end of the game.

Table 1. The table shows the reward scores and the number of respective pebbles needed to put into the bowl for all possible combinations in the case of 6 teams. We have to make a similar table if we form more or less teams. (When creating new tables we have to follow these rules: More the pear votes, more the pebbles needed to put into the bowl. If everybody votes apple, then we can take a pebble from the bowl.) The greedy strategy is denoted by the pear and the cooperative one by the apple.

An important element of the game is that we change the rules after some unsuccessful series of rounds (that is, when the bowl sinks before the end of the game). We change the rules and study the effect of these modifications.

Variant 1: After every (or every second, third, etc..) round, each team sends a representative to negotiate with the other team representatives. The negotiation is short (e.g. 30 seconds) and takes place further away from the teams, but in the same room. When the representatives have returned, for another 30 seconds the teams can discuss the result of the negotiation and decide which card they will show in the next round. This frequently helps to avoid failure, however, if some teams repeatedly break the agreement, then strong emotions and fast sinking will follow.

Variant 2: We can stay at the basic game or we can play Variant 1. However, before beginning the game, teams have the opportunity to modify any rules, except the reward table, which is unchangeable. That is, there is no way to take away or add points according to an additional rule. Practically, only one option is allowed to them: the winner should share the prize. Our aim is to help them find this solution.

Variant 3: We can stay at the basic game or we can play Variant 1. However, there already are an unknown number of pebbles in the floating bowl. That is, the bowl with the pebbles is in a covered place. Teams can check the number of pebbles in the bowl, but this is a costly action. Each team that checks it, loses two points.

Variant 4: Same as Variant 2., but it is now allowed to take away from or add points to teams, according to some additional rule, defined by the teams before the game. Table 1. remains valid, but teams can be punished or rewarded additionally. In this manner, players can modify the game so that not the greedy strategy will be the preferred one. Thus the conflict gets resolved immediately.

After finishing the game, do not forget to discuss how the players felt during the game. What did help them to reach the ten rounds without sinking the bowl, and why? Discuss how this is a difficult social conflict present in human societies and even in biological systems. We also recommend to close and dissolve the tension of this game with a short funny game (see Warm up games).

Biological background: The essence of the game is that irrespective of what the other teams do, the greedy strategy (pear card) is always the winner. The temptation is high to choose this strategy. As a consequence, it is highly probable that the bowl will sink before the end. Competition between animals can lead to a similar self-destructive situation. For example, male common toads fight each other on the back of the female in the mating period. Meanwhile, they frequently hold the female so long under the water that the female drowns. The competition among males decreases the number of females in this manner, which increases the competition for the females even further. Thus, females will have an increasing chance to get drowned. The dramatic decrease in the number of females can even cause the extinction of the population. There are several reasons why these situations are not so frequent in biology. In the case of toads, fortunately, the drowning of the females is relatively rare. However, in other cases, the most frequent reason is that the cooperative (apple strategy in the game) behavior has a direct benefit. For example, if a bacterial cell emits food decomposing enzymes, then all cells in the neighborhood will profit from that. We might think that greedy cells don’t have to produce the costly enzyme, thus they will replicate faster than the producers. However, the producers themselves benefit more than the neighboring cells, especially if the other cells are a little bit further from the producer.
The other motivation of the game, at least as important, is to understand the social dilemma connected with the global climate catastrophe. Those countries and firms that behave greedily will always profit more than those who spend on decreasing the CO2 emission. As a consequence, the CO2 level increases continuously, but its disastrous effect will probably emerge abruptly (e.g. the melting of the arctic ice or the stopping or the reordering of the ocean currents). This then will cause a much larger damage for all participants, than the profit the greedy strategy earned earlier.

References: Kyburz-Gragel, Nagel, Odermatt: Spiel Eisbaer. in: Handeln statt Hoffen, ISBN 978-3-265-83945-6 2010 Klett und Balmer Verlag Zug.