Consider a situation in which surplus is produced by coalitions of players. Each player’s strategy incorporates
(a) A demand for a quantity of surplus, and
(b) A list of players with whom he is willing to work as part of some producing coalition.
Given the strategies of all the players, producing coalitions form which can satisfy the demands of their members. Players in any such coalition attain surplus equal to their demand. Players outside of any coalition get no surplus beyond what they can produce by themselves.
When strategy updating takes place under a coalitional dynamic with mistakes, in the long run we see surplus divisions that
(1) Maximize the wealth of the poorest player, and
(2) Minimize wealth inequality amongst the remaining players.
Depending on constraints, there may be some conflict between (1) and (2). In the special case where players have constant relative risk aversion, only consideration (1) matters and social evolution maximizes what economists call a Rawlsian social welfare function.
For more results, deeper analysis and further applications, please read:
Recontracting and stochastic stability, J.Newton, Journal of Economic Theory (2012).
For similar articles, please see our overview of the Evolutionary Nash Program and our post about the recent paper by Sawa.