Waiting to Cooperate? Cooperation in one-stage and two-stage games

Cooperation between two players often requires exactly one to take the available action, while the other acquiesces. If the decisions whether to pursue the action are made simultaneously, then neither or both may acquiesce leading to an inefficient outcome. However, inefficiency may be avoided if players move sequentially. We test experimentally whether two-stage versions of this entry-exit game enhance cooperation. In one version, players may wait in the first stage to see what their paired player did and then coordinate in the second stage. In another version, sequential decision-making is imposed by assigning one player to move in stage one and the other player in stage two. Although there are fewer cooperative decisions in the two-stage treatments, we show that subjects coordinate better on efficient cooperation and on avoiding both acquiescing. Consequently they achieve higher profits. Yet, the least cooperative pairs do worse in the two-stage games than their single-stage counterparts. They use the second stage not to facilitate coordination but to disguise their uncooperative play or to punish their opponents.