Sir Philip Sidney game
Sir Philip Sidney game
thumb|Sir Philip Sidney, after Antonis Mor
In biology and game-theory, the Sir Philip Sidney game is used as a model for the evolution and maintenance of informative communication between relatives. Developed by john-maynard-smith as a model for chick begging behavior, it has been studied extensively including the development of many modified versions.
It was named after a story about Sir Philip Sidney who, fatally wounded, allegedly gave his water to another, saying, "thy necessity is yet greater than mine." Since parents respond differentially, chicks have an incentive to overstate their need since it will result in them receiving more food. If all chicks overstate their need, parents have an incentive to ignore the begging and give food using some other rule.
This situation represents a case of animal signaling where there arises an evolutionary question to explain the maintenance of the signal. The Sir Philip Sidney game formalizes a signalling theory suggestion from Amotz Zahavi, the handicap principle, that reliability is maintained by making the signal costly to produce—chicks expend energy in begging. Since it requires energy to beg, only chicks in dire need should be willing to expend the energy to secure food.
The game There are two individuals, the signaler and the responder. The responder has some good which can be transferred to the signaler or not. If the responder keeps the good, the responder has a fitness of 1, otherwise the responder has a fitness of (1-d). The signaler can be in one of two states, healthy or needy. If the signaler receives the good, his fitness will be 1. Otherwise his fitness will be (1-b) or (1-a) if healthy or needy respectively (where a>b). The signaler can send a signal or not. If he sends the signal he incurs a cost of c regardless of the outcome.
If individuals maximize their own fitness the responder should never transfer the good, since he is reducing his own fitness for no gain. However, it supposed that the signaler and responder are related by some degree r. Each individual attempts to maximize his inclusive fitness, and so in some cases the responder would like to transfer the good.
The case of interest is where the responder only wants to transfer the good to the needy signaler, but the signaler would want the good regardless of his state. This creates a partial conflict of interest, where there would be an incentive for deception. Maynard Smith showed, however, that for certain values of c, honest signaling can be an evolutionarily-stable-strategy. This suggests that it might be sustained by evolution.