The Strategic View of Biological Agents

What is a strategy? The term strategy has been used by many disciplines in a variety of contexts ranging, for example, from the game of chess and the Cuban missile crisis to markets, computer networks, political systems, cooperation, mating, parasitism, intragenomic conflict, and growth patterns. Despite this wide use of the term, only one discipline—game theory— has carefully examined the concept. In game theory, a pure strategy is a complete plan for a player’s choices in the game under consideration. A chess player’s pure strategy would thus have to specify all moves in all the situations that might arise on the chessboard during a match. Whereas in chess the pieces on the board are visible to both players, in many games players have only limited information about the objective state of affairs. In a number of card games, for example, a player’s one hand is not known to the other. Thus, players’ strategies must make use of the subjective state of affairs. This state is often referred to as the information situation or information set. Strategies can therefore be viewed as a map of information states to actions (adding the term “conditional” to “strategy” is thus redundant). For agents with memory, the information situation often includes knowledge about the course of play. This is of great importance to many applications and it demonstrates the richness of the strategy concept. A lot can be gained from widening the concept’s scope beyond that of pure strategies. What game theorists call a behavior strategy is a plan that assigns to each situation a probability distribution over the choices in that situation. This distribution may or may not place all weight on one choice. In a behavior strategy, the choices for different situations are stochastically independent. Another concept is that of a mixed strategy which differs from that of a behavior strategy as follows. In a mixed strategy, the player chooses among a number of pure strategies according to a probability distribution over these pure strategies—as opposed to choices during the game. To illustrate the difference, let us compare a behavior strategy with a cooking recipe. The recipe may at some stage contain the instruction to flip a coin in order to decide about mild or hot spicing. In contrast, a mixed strategy would flip a coin to decide between Italian and Mexican recipes. The concept of a mixed strategy can be extended to mixtures of behavior strategies.