Defense against an opportunistic challenger: Theory and experiments

• We model a proportional contest where an attacker reacts to multiple defenders.
• Defenders can act independently or form an alliance to provide common protection.
• Acting independently, defenders face an all pay auction to not be the weakest target.
• Alliances lower defense spending yielding higher profits for defenders and attackers.
• Laboratory experiments largely confirm the theoretical predictions.

This paper considers a contest setting in which a challenger chooses between one of two contests to enter after observing the level of defense at each. Despite the challenger’s chance of success being determined by a proportional contest success function, the defenders effectively find themselves in an all-pay auction that largely dissipates the value of the defended resources because the challenger will target the weaker defender. However, if the defenders form a protective alliance then their expected profits increase despite the fact that a successful challenge is theoretically more likely, given the overall reduction in defense. Controlled laboratory experiments designed to test the model’s predictions are also reported. Observed behavior is generally consistent with the comparative static predictions although challengers exhibit the familiar overbidding pattern. Defenders appear to anticipate this reaction and adjust their behavior accordingly.