Extensions of The Evolutionary Game Theory Model
A mathematical model analysing the behaviour of a system needs initially to be as simple as possible to aid in developing a base understanding the fundamentals, or “first order effects”, pertaining to what is being studied. With this understanding in place it is then appropriate to see if other, more subtle, parameters (second order effects) further impact the primary behaviours or shape additional behaviours in the system. Following Maynard Smith’s seminal work in EGT, the subject has had a number of very significant extensions which have shed more light on understanding evolutionary dynamics, particularly in the area of altruistic behaviors. Some of these key extensions to EGC are:
| Spatial Games | There are several very important influences attributable to geographic factors in the field of evolution – not least of which is gene flow and horizontal gene transfer. Spatial game models take geometry into effect by locating contestants in a lattice of cells over a two dimensional plane to represent this geographic element. In spatial games contests take place only with immediate neighbours. Winning strategies take over these immediate neighbourhoods and then go on to interact further with adjacent neighbourhoods. This model has been especially useful in showing how pockets of co-operators can invade and introduce altruism in the Prisoners Dilemma game, where for example Tit for Tat (TFT) is a Nash Equilibrium but NOT also an ESS. TFT cannot normally invade an all Defector population yet in spatial games this becomes possible. |
| Effects of having information | In conventional Game Theory the effect of Signalling (the acquisition of information) is of critical importance in outcomes. This can also be the case in EGT. Nowhere is this more important that in the area of studying Indirect Reciprocity in Prisoners Dilemma (where contests between the SAME paired individuals is NOT repetitive). This models the reality of most normal social interactions which are non-kin related. It has been shown that unless a probability measure of REPUTATION is available in Prisoners Dilemma only DIRECT reciprocity can be achievable. With this information INDIRECT reciprocity is also supported. |
| Finite populations | Many evolutionary games have been modelled in finite populations rather than infinite to see the effect this may have. Though in many cases this does not significantly alter game dynamics in others significant differences can and do occur, for example being in the prevalence of mixed strategies. |
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