The Doughnut Negotiation: Win-Sets with Sprinkles

Today we have a guest post from Dr. Patricia Blocksome, Assistant Professor of Social Science, US Army School of Advanced Military Studies. She can be reached via her LinkedIn profile at


Putnam argues that international negotiations between states occur simultaneously with domestic negotiations between intrastate coalitions – the two-level game. At the domestic level, politicians have to form coalitions large enough to ratify an international agreement. These domestic coalitions establish the win-set, the spectrum of acceptable outcomes for the state. At the international level, each state attempts to achieve an agreement that falls within its domestic win-set. When states have overlapping domestic win-sets, an international agreement is possible. Negotiations can occur concurrently over two or more different issues, leading to potential trade-offs, where a gain in one area can offset a loss in another.

So how does this apply to doughnuts?

If a class has, for example, sixteen students, bring in eleven doughnuts of various types. You want an odd number of doughnuts, and fewer doughnuts than students; this prevents students from evenly distributing doughnuts across the class. Providing a variety of doughnuts makes the pastries less substitutable, so that negotiations can occur over doughnuts with specific attributes, such as sprinkles.

The class gets split into two groups, and each group chooses a chief negotiator. The class is shown the doughnuts, and I encourage students to think about their preferences for different doughnut attributes. Students are informed that there will be a series of negotiations, with the following rules:

  • No fractional division of doughnuts is allowed (i.e. no half-doughnuts).
  • Negotiations can include items other than doughnuts. In the past, students have negotiated an exchange between responsibility for answering questions in the class that day and receiving extra doughnuts. You could also offer a certain number of extra credit points to be divided between the two groups.
  • For a successful negotiation, where the two groups agree on a division of doughnuts, each chief negotiator will receive a two-doughnut reward (this allows for side-payoffs). This leaves seven doughnuts available for distribution. Which specific four doughnuts the chief negotiators will receive is also up for negotiation.
  • For an unsuccessful negotiation, where the groups do not achieve an agreement on the distribution of doughnuts, the doughnuts are taken away to be eaten by faculty.

After explaining the rules, negotiations begin. First, there is a five-minute within-group negotiation to determine the initial win-set for each group. This can take place with both groups in the classroom, but if you can send one group to a different room, this prevents eavesdropping on the other group’s strategy.

Next, the chief negotiators meet for two minutes in my office. By bringing them into my office, the groups cannot overhear what is discussed, permitting side-payoffs between the negotiators (remember, each negotiator has two doughnuts of their own to do with as they choose). Once this round of negotiations is over, the chief negotiators return to the classroom and report back to their groups. There is a second five-minute within-group negotiation to discuss the other group’s offer and reassess win-sets.

The chief negotiators have a final two-minute round in my office. At the end of this round, the chief negotiators return to class and announce the results of their negotiation. If the chief negotiators’ agreement is not approved by either group, the negotiation is declared unsuccessful. If the agreement is approved, the negotiation is declared successful and the doughnuts are distributed accordingly.

Following the negotiation, the students are usually happy to talk about their win-sets and what happened in the negotiations, and this discussion can be used to transition into discussion of two-level games in the international arena.