It is not always wise to form an alliance while in a conflict or at war, especially when there is something to be shared afterward. Economists from the Max Planck Institute for Tax Law and Public Finance have now shown by game theory experiments that, as soon as the enemy is gone, in-group solidarity of alliances vanishes rapidly. Former brothers in arms fight even more vigorously over the spoils of a victory than strangers do. During the conflict, they expend together only half the effort of their enemy. Furthermore, when anticipating a future distributional conflict, they reduce their contribution even more.

It can be useful to fight in alliances, however. Psychologists know that an individual shouldn't confront a group alone. They emphasize the importance of interaction inside the group as well as the emergence of solidarity in the face of an adversary; although, as contest theory shows, alliances face a collective action problem. Free-riding incentives cause alliance members to reduce their commitment during the conflict. Moreover, expecting disputes over the distribution of the spoils, they will less appreciate the victory over the enemy.

History has shown that alliances tended to break apart after the enemy is defeated. After the Second World War and the defeat of Nazi Germany, for example, the Cold War was quick to turn the former allied superpowers, the United States and the Soviet Union, into adversaries. The same may happen when it comes to a promotion in a firm or to sporting competitions: loyal teammates can quickly turn into acrimonious enemies.

In their experimental study, Changxia Ke, Kai A. Konrad and Florian Morath, all from the Max Planck Institute for Tax Law and Public Finance, asked whether allies who anticipate a later distributional conflict mobilize less effort than allies who know from the beginning how the prize will be shared. Furthermore, they wanted to know whether in-group solidarity that can be observed during the competition still persists after the enemy is defeated. What effect will shoulder-to-shoulder fighting have on the readiness of allies to turn against each other in a distributional conflict?

Whoever expects a conflict contributes less to the alliance effort

In laboratory experiments, the researchers modelled a contest between an alliance – consisting of two players – and a single player. They compared the combat efforts of alliance members who still had to figure out how to split the gains with the efforts of players who already had a peaceful solution for the division of the prize. The researchers demonstrated that alliances suffer from a collective action problem in general. Even though it was made clear that the spoils of the victory would be divided peacefully, the alliance members together provided only half the fighting effort that the single players did. This commitment decreased even more when a later distributional conflict was expected. In anticipation of the future conflict, they attributed less value to the pending prize and, hence, contributed less to the overall result.

When it comes to the spoils, friends quickly become enemies

In further experiments, the researchers examined distributional conflicts inside victorious alliances. They compared the efforts that two former "brothers in arms" on the one hand and previously non-allied players on the other each expended while contesting for comparable prizes. They found that in-group solidarity breaks down as soon as the joint enemy is defeated. Former "brothers in arms" will not fight less against each other than strangers will. On the contrary: They fight even more vigorously for their share in the loot than strangers do. Therefore, allies should agree ahead of the conflict on how the prize or the spoils will be divided. That would not only strengthen the alliance and enhance the efforts made during the fight against the external enemy but it would also dissuade former "brothers in arms" from turning into fierce adversaries.

More information: Changxia Ke, Kai A. Konrad and Florian Morath, Brothers in arms – An experiment on the alliance puzzle, Games and Economic Behavior 77 (2013), p. 61-76