Threat bargaining games with a variable population (Q922975)

The concept of a threat bargaining game with a variable population is developed and studied. Unlike the classical bargaining theory, the bargaining theory developed is built on a variable number of agents as well as a variable threat point. Assume that there exists an infinite population I of agents. For an arbitrarily finite subset P of I, a bargaining situation among agents indexed by the set P is defined to be a pair (S,d) where S is a compact convex comprehensive subset of \({\mathbb{R}}^ p_+\) and \(d\in S\) is the fixed threat point. A solution F is a function which associates with each bargaining game (S,d) a unique point F(S,d)\(\in S\). In the context of a variable threat point and a fixed set S of feasible alternatives, the agents must choose a threat point that belongs to a prespecified subset D(S) of S. The pair (S,D(S)) is called a threat bargaining game indexed by agents of some subset P of I. An equilibrium threat (e.t.) strategy for a threat bargaining situation (S,D(S),F) is defined to be a point of D(S) that is self- enforceable in the sense that no agent gains by unilaterally deviating from his component of the point involved. The aim of the final part of the paper is to show that peculiar properties of e.t. strategies follow from certain properties required for the solution F. Firstly, e.t. strategies are strategically stable whenever the solution F satisfies monotonicity with respect to the threat point. Secondly, e.t. strategies are strategically monotone with respect to changes in the number of agents whenever the solution F satisfies monotonicity with respect to the threat point as well as restricted monotonicity with respect to changes in the number of agents. Thirdly, e.t. strategies are strategically constant whenever the solution F satisfies multilateral stability.