Using Game Theory to Model the Evolution of Information: an Illustrative Game

The application of information theory to biology can be broadly split into three areas: (i) At the level of the genome; considering the storage of information using the genetic code. (ii) At the level of the individual animal; communication between animals passes information from one animal to another (usually, but not always, for mutual benefit). (iii) At the level of the population; the diversity of a population can be measured using population entropy. This paper is concerned with the second area. We consider the evolution of an individual's ability to obtain and process information using the ideas of evolutionary game theory. An important part of game theory is the definition of the information available to the participants. Such games tend to treat information as a static quantity whilst behaviour is strategic. We consider game theoretic modelling where use of information is strategic and can thus evolve. A simple model is developed which shows how the information acquiring ability of animals can evolve through time. The model predicts that it is likely that there is an optimal level of information for any particular contest, rather than more information being inherently better. The total information required for optimal performance corresponded to approximately the same entropy, regardless of the value of the individual pieces of information concerned.