Do Arabian babblers play mixed strategies in a “volunteer's dilemma”?

When group-living Arabian babbler songbirds hear a sentinel alarm call that indicates a raptor approach, they should instantaneously choose whether to flee to shelter, or rather to expose themselves while calling towards the raptor to communicate to it its detection. If enough group members thus signal to the raptor their vigilance, the raptor is likely to be dissuaded from attacking the group. Groupmates thus engage in a variant of the “volunteer's dilemma” game (Diekmann, 1985), whose symmetric equilibrium is in mixed strategies. We check whether in nature Arabian babblers indeed make independent randomized choices upon hearing alarm calls, in natural conditions as well as in a controlled field experiment in which recorded alarm calls were broadcast to group members. We use a resampling method to check for independence across group members in their reactions to sentinel alarm calls. In natural conditions independent mixed-strategy behaviour was refuted, and not refuted in the artificial conditions of the experiment. This is the first real-world test of mixed-strategy behaviour in games with more than two players.