A link between a no-side-payment (NSP) market game and a side-payment (SP) market game can be established by introducing a suﬀicient amount of an ideal utility-money of constant marginal utility to all agents. At some point when there is “enough money” in the system, if it is “well distributed” the new game will be a SP game. This game can also be related to a pure NSP game where a set of default parameters have been introduced. These parameters play a role similar to the parameters specifying the interpersonal comparisons in the side-payment game. We study this game for the properties of the delta-core and consider both the conditions for the uniqueness of competitive equilibria and a new approach to the second welfare theorem. A discussion of the relationship between market games and strategic market games is also noted.
Qin, Cheng-Zhong; Shapley, Lloyd S.; and Shubik, Martin, "Marshallian Money, Welfare, and Side-Payments" (2009). Cowles Foundation Discussion Papers. 2051.