ABSTRACT
Most evolutionary game-theoretic models that we have considered fall into the class of normal form games (see Section 2.1) with perfect information. In this chapter we consider two key departures from this structure which are still highly relevant to biological modelling. First we consider games in extensive form. Although they apply to a wider class, such games can be most usefully thought of as modelling interactions where individuals make sequential decisions, so the second player can choose a strategy based upon the observed choice of the first player. An example is a revised version of the game of brood care and desertion introduced in Section 8.4.2, which we consider below. Secondly we consider games where individuals do not have perfect information; either no player has perfect information, or some players do but others do not. Thus in the asymmetric Hawk-Dove game of Section 8.4.1 where individuals vary in size, perfect information would involve knowing the size of both yourself and your opponent. It is possible that an individual knows its own size, but that it has only an estimate of its opponent’s size. Alternatively, in the kleptoparasitism models of Chapter 17 it is possible that food varies in quality (or in how much remains to be consumed) and the handler of the item may know this and the attacker may not (Broom and Rychta´rˇ, 2009). We then consider a type of game which can be thought to be both in extensive form and with imperfect information, repeated games.
