Sir Philip Sidney game
Encyclopedia
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 Philip Sidney who allegedly, fatally wounded, gave his water to another, saying, "thy necessity is greater than mine."
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 suggestion from Amotz Zahavi
that reliability is maintained by making the signal costly to produce—chicks expend energy in begging. Since it requires energy to beg, only those chicks who are in dire need should be willing to expend the energy to secure food.
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 her 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 her 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.
as an explanation for chick begging behavior. Several empirical studies have attempted to measure the cost of begging, in effect measuring c. These studies have found that although there is a cost, it is far lower than would be sufficient to sustain honesty. Since the actual benefits of food are hard to calculate, the required value of c cannot be determined exactly, but it nonetheless has raised concern.
In addition to the empirical concern, there has been theoretical concern. In a series of papers, Carl Bergstrom
and Michael Lachmann suggest that in many biologically possible cases we should not expect to find signaling despite the fact that it is an evolutionarily stable strategy
. They point out that whenever a signaling strategy is evolutionarily stable, non-signaling equilibria are as well. As a result, evolutionary stability alone does not require the evolution of signaling. In addition, they note that in many of these cases the signaling equilibrium is pareto inferior
to the non-signaling one – both the chick and parent are worse off than if there was no signaling. Since one would expect non-signalling to be the ancestral state, it is unclear how evolution would move a population from a superior equilibrium to an inferior one.
Both of these concerns led Bergstrom and Lachmann to suggest a modified game where honesty is maintained, not by signal cost, but instead by the common interest inherent in interaction among relatives. In their partial pooling model, individuals have no incentive to lie, because the lie would harm their relative proportionally more than it would help them. As a result, they do better by remaining honest.
Biology
Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...
and game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
, the Sir Philip Sidney
Philip Sidney
Sir Philip Sidney was an English poet, courtier and soldier, and is remembered as one of the most prominent figures of the Elizabethan Age...
game is used as a model for the evolution and maintenance of informative communication between relatives. Developed by John Maynard Smith
John Maynard Smith
John Maynard Smith,His surname was Maynard Smith, not Smith, nor was it hyphenated. F.R.S. was a British theoretical evolutionary biologist and geneticist. Originally an aeronautical engineer during the Second World War, he took a second degree in genetics under the well-known biologist J.B.S....
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 Philip Sidney who allegedly, fatally wounded, gave his water to another, saying, "thy necessity is greater than mine."
The phenomenon
Young birds and other animals beg for food from their parents. It appears that in many species the intensity of begging varies with the need of the chick and that parents give more food to those chicks that beg more. 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
Animal communication
Animal communication is any behavior on the part of one animal that has an effect on the current or future behaviour of another animal. The study of animal communication, is sometimes called Zoosemiotics has played an important part in the...
where there arises an evolutionary question to explain the maintenance of the signal. The Sir Philip Sidney game formalizes a suggestion from Amotz Zahavi
Handicap principle
The handicap principle is a hypothesis originally proposed in 1975 by biologist Amotz Zahavi to explain how evolution may lead to "honest" or reliable signaling between animals who have an obvious motivation to bluff or deceive each other...
that reliability is maintained by making the signal costly to produce—chicks expend energy in begging. Since it requires energy to beg, only those chicks who are 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, her fitness will be 1. Otherwise her 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 she sends the signal she 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 her inclusive fitness
Inclusive fitness
In evolutionary biology and evolutionary psychology, the inclusive fitness of an organism is the sum of its classical fitness and the number of equivalents of its own offspring it can add to the population by supporting others...
, 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 her 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
Evolutionarily stable strategy
In game theory and behavioural ecology, an evolutionarily stable strategy , which is sometimes also called an evolutionary stable strategy, is a strategy which, if adopted by a population of players, cannot be invaded by any alternative strategy that is initially rare. An ESS is an equilibrium...
. This suggests that it might be sustained by evolution.
Criticisms
The empirical study of chick begging has cast some doubt on the appropriateness of the Sir Philip Sidney game and on the handicap principleHandicap principle
The handicap principle is a hypothesis originally proposed in 1975 by biologist Amotz Zahavi to explain how evolution may lead to "honest" or reliable signaling between animals who have an obvious motivation to bluff or deceive each other...
as an explanation for chick begging behavior. Several empirical studies have attempted to measure the cost of begging, in effect measuring c. These studies have found that although there is a cost, it is far lower than would be sufficient to sustain honesty. Since the actual benefits of food are hard to calculate, the required value of c cannot be determined exactly, but it nonetheless has raised concern.
In addition to the empirical concern, there has been theoretical concern. In a series of papers, Carl Bergstrom
Carl Bergstrom
Carl T. Bergstrom is a theoretical and evolutionary biologist and a professor at the University of Washington , with a secondary appointment at the Santa Fe Institute. His work concerns the flow of information through biological and social networks and the ecology and evolution, including the...
and Michael Lachmann suggest that in many biologically possible cases we should not expect to find signaling despite the fact that it is an evolutionarily stable strategy
Evolutionarily stable strategy
In game theory and behavioural ecology, an evolutionarily stable strategy , which is sometimes also called an evolutionary stable strategy, is a strategy which, if adopted by a population of players, cannot be invaded by any alternative strategy that is initially rare. An ESS is an equilibrium...
. They point out that whenever a signaling strategy is evolutionarily stable, non-signaling equilibria are as well. As a result, evolutionary stability alone does not require the evolution of signaling. In addition, they note that in many of these cases the signaling equilibrium is pareto inferior
Pareto efficiency
Pareto efficiency, or Pareto optimality, is a concept in economics with applications in engineering and social sciences. The term is named after Vilfredo Pareto, an Italian economist who used the concept in his studies of economic efficiency and income distribution.Given an initial allocation of...
to the non-signaling one – both the chick and parent are worse off than if there was no signaling. Since one would expect non-signalling to be the ancestral state, it is unclear how evolution would move a population from a superior equilibrium to an inferior one.
Both of these concerns led Bergstrom and Lachmann to suggest a modified game where honesty is maintained, not by signal cost, but instead by the common interest inherent in interaction among relatives. In their partial pooling model, individuals have no incentive to lie, because the lie would harm their relative proportionally more than it would help them. As a result, they do better by remaining honest.