Coordination.

• Author: Capra, C. Monica
• Position: Teaching Economics with Classroom Experiments: A Symposium - Coordination problems in economic games

1. Introduction

   Coordination problems arise naturally in many economic contexts. For example, in large organizations it is necessary to synchronize specialized divisions to avoid production bottlenecks. Low effort on the part of one worker or division can hold up the whole process, and it might not be worthwhile for a particular worker to exert high effort if others are not doing the same. In this sense, the organization can reach an equilibrium in which low effort prevails, even though all would be better off if they could share the gains from a high-effort, high-output situation. A similar problem can arise in macroeconomic contexts where high employment in one sector can increase the marginal product of labor in another. Some neo-Keynesians have used coordination games to justify the possible role of macroeconomic policies to move the economy to a better equilibrium.

   This paper describes how to use playing cards to set up a series of classroom coordination games with little advance preparation. Each player must make one of two decisions, which can be interpreted as "high" or "low" efforts, with high effort being more costly but potentially more productive if it is matched by others. There is an equilibrium in which all choose low efforts, and there is a better equilibrium in which all choose high efforts. These equilibria are not affected by noncritical changes in the cost of effort or in the number of participants. In contrast, intuition suggests that coordination on the high-effort outcome would be more difficult with more participants and higher effort costs. The classroom game helps students discover the essential tension in a coordination game between safe (e.g., low-effort) decisions and risky attempts to reach a better (e.g., high-effort) outcome. In more advanced classes, you can discuss the presence of multiple, Pareto-ranked Nash equilibria and the sensitivity of behavior to payoff parameters, such as effort costs or group size, which do not affect this set of equilibria. Depending on the level and nature of applications discussed, these games are appropriate for undergraduate and MBA courses in microeconomics or macroeconomics and for any course that uses applied game theory, such as industrial organization, law and economics, and managerial economics.

2. Procedures

   This exercise takes about 35 to 45 minutes to read instructions, play the game, and discuss results. Start by giving each student a copy of the instruction sheet and two playing cards - one red (Hearts or Diamonds) and one black (Clubs or Spades). Thus, each deck of cards can accommodate up to 26 participants. The instructor should begin by reading the instructions out loud to the class; this is a good way to anticipate questions and establish the appropriate atmosphere. In fact, an effective way for the instructor to prepare before class is to read the instructions to envision how the setup will appear from the students' point of view.

   As explained in the instructions, each student is matched with another person, and each chooses a card to play - red or black. A person who plays the red card earns $1 no matter what the other chooses. In contrast, a person who plays the black card earns $4 if the other also plays black but earns nothing if the other plays red. In this sense, playing the black (high-effort) card is riskier but potentially more profitable. Because only the colors of the cards matter, it is better to use decks with cover patterns that are neither red nor black. The use of the playing cards avoids suggestive terms such as "high effort," which emphasizes the basic incentive structure of the game. Finally, it helps to write the payoff rules (in words and dollar amounts) on the blackboard or on a transparency, perhaps using colored markers. We do not show a payoff matrix at this stage as its construction can arise naturally from the discussion that follows.

   The process begins when students are asked to play a card by holding it against their chests. This guarantees that they do not observe others' decisions. Moreover, the instructor can see who has already made a choice and who needs more time. Once students make their choices, the instructor can select pairings more or less randomly by pointing at two students spontaneously and saying, "You and you, please reveal your choices." If the class has fewer than 20 students, ask everyone to make choices at the same time before the random...