Grouping in animals is ubiquitous and thought to provide group members antipredatory advantages and foraging efficiency. However, parasitic foraging strategy often emerges in a group. The optimal parasitic policy has given rise to the producer-scrounger (PS) game model, in which producers search for food patches, and scroungers parasitize the discovered patches. The N-persons PS game model constructed by Vickery et al. (1991. Producers, scroungers, and group foraging. American Naturalist 137, 847-863) predicts the evolutionarily stable strategy (ESS) of frequency of producers (q;) that depends on the advantage of producers and the number of foragers in a group. However, the model assumes that the number of discovered patches in one time unit never exceeds one. In reality, multiple patches could be found in one time unit. In the present study, we relax this assumption and assumed that the number of discovered patches depends on the producers' variable encounter rate with patches (lambda). We show that q; strongly depends on lambda within a feasible range, although it still depends on the advantage of producer and the number of foragers in a group. The basic idea of PS game is the same as the information sharing (parasitism), because scroungers are also thought to parasitize informations of locations of food patches. Horn (1968) indicated the role of information-parasitism in animal aggregation (Horn, H.S., 1968. The adaptive significance of colonial nesting in the Brewer's blackbird (euphagus cyanocephalus). Ecology 49, 682-646). Our modified PS game model shows the same prediction as the Horn's graphical animal aggregation model; the proportion of scroungers will increase or animals should adopt colonial foraging when resource is spatiotemporally clumped, but scroungers will decrease or animals should adopt territorial foraging if the resource is evenly distributed.

Larvae of Acanthoscelides obtectus show two contrasting behaviors when entering a bean. One is pioneer behavior in which a larva enters the bean through an entrance hole made by itself; the other is follower behavior in which a larva enters the bean through an entrance hole made by a pioneer. Previous studies have shown that the number of followers is much greater than that of pioneers. If there is a cost to being a pioneer, and if larvae can choose either of the two strategies, there is a dilemma: to be a pioneer or not. This dilemma is similar to the chicken game because if all larvae avoid choosing the risky pioneer strategy in favor of the follower strategy, none of the larvae can enter a bean, and they will die. In the present study, in order to investigate whether the larvae of A. obtectus are facing a dilemma of entry order, we experimentally measured the cost to pioneers and tested the flexibility of larval entering strategies. Pioneers' costs were measured by entrance success rate, and the flexibility of larval strategies was tested by gauging the proportion of pioneers at various larval densities. The entrance success of pioneers was lower than that of followers, and the proportion of pioneers decreased as the number of competing larvae increased. These results suggest that the Pioneer-Follower interaction in A. obtectus satisfies the conditions for a dilemma game: the larvae of A. obtectus are in a dilemma of entry order.