Compensatory Transfers in Two-Player Decision Problems

Abstract

This paper presents an axiomatic characterization of a family of solutions to two-player quasi-linear social choice problems. In these problems the players select a single action from a set available to them. They may also transfer money between themselves.The solutions form a one-parameter family, where the parameter is a nonnegative number, t.The solutions can be interpreted as follows: Any efficient action can be selected. Based on this action, compute for each player a "best claim for compensation". A claim for compensation is the difference between the value of an alternative action and the selected efficient action, minus a penalty proportional to the extent to which the alternative action is inefficient. The coefficient of proportionality of this penalty is t. The best claim for compensation for a player is the maximum of this computed claim over all possible alternative actions. The solution, at the parameter value t, is to implement the chosen efficient action and make a monetary transfer equal to the average of these two best claims.The characterization relies on three main axioms. The paper presents and justifies these axioms and compares them to related conditions used in other bargaining contexts. In Nash Bargaining Theory, the axioms analagous to these three are in conflict with each other. In contrast, in the quasi-linear social choice setting of this paper, all three conditions can be satisfied simultaneously.

Resource allocation with partial responsibilities for initial endowments

“…The class of income redistribution codes we have characterized violates so‐called recursive invariance (except when ), which states in the context of quasi‐linear bargaining that once the prescribed allocation is taken to be the initial endowment, reapplying the rule does not change the allocation (see Chun ; Green ). This shows that where the original endowments are coming from really does matter in our argument.…”

Cooperative strategic games

“…Indeed, the Nash solution——exhibits a side payment from player 2 to player 1, as does Shapley's original notion of value (see Section 2 for details.) Other authors, for example, Green (2005) have also emphasized the impact of inferior strategies on the cooperative‐competitive outcome.…”