There are a number of different approaches to the modelling of biological markets. Our original model (Noë & Hammerstein 1994) and the model by Johnstone & Bshary (2008) are based on game theory
A boa constructor and two shadowbirds
(see Noë & Hammerstein 1994)
Other models, such as those published by Mark Schwartz and Jason Hoeksema and by Miro Kummel and Steve Salant, are based on David Ricardo's (1817) principle of 'comparative advantage'. Cowden & Peterson (2009) used cellular automata to build a model of nutrient exchange mutualisms, while Claire de Mazancourt and Mark Schwartz (2010) propose a model based on resource ratio theory. Song & Feldman (2013) propose a solution to the problem of markets heading for clearance with a reduction of variance in supply and reduced levels of choosiness as a result.
Campenni & Schino (2014), using agent-based modelling, very nicely show that positive correlations between investments given and received, which is often seen as a 'proof' for partner control mechanisms, such as reciprocal altruism, can in fact result from pure partner choice mechanisms without any need for partner control. Thus, proof for the existence of partner control is and remains in direct contingencies, e.g. alternation of giving and receiving in the case of reciprocal altruism.
Related theoretical approaches that also revolve around phenomena such as partner choice and competition by outbidding include: