Barry O'Neill

Bargaining with an agenda

Gradual bargaining is represented by an agenda: a family of increasing sets of joint utilities, parameterized by time. A solution for gradual bargaining specifies an agreement at each time. We axiomatize an ordinal solution, i.e., one that is covariant with order-preserving transformations of utility. It can be viewed as the limit of step-by-step bargaining in which the agreement of the last negotiation becomes the disagreement point for the next. The stepwise agreements may follow the Nash solution, the Kalai–Smorodinsky solution or many others and still yield the ordinal solution in the limit.

Risk Aversion in International Relations Theory

|When international relations theorists use the concept of risk aversion, they usually cite the economics conception involving concave utility functions. However, concavity is meaningful only when the goal is measurable on an interval scale. International decisions are usually not of this type, so that many statements appearing in the literature are formally meaningless. Applications of prospect theory face this difficulty especially, as risk aversion and acceptance are at their center. This paper gives two definitions of risk attitude that do not require an interval scale. The second and more distinctive one uses the property of submodularity in place of concavity. R. D. Luce has devised a theory of choice with features of prospect theory but not requiring on an interval scale, and the second definition in combination with this theory yields the traditional claim that decision makers are risk-averse for gains and risk-seeking for losses.

Lexicographic composition of simple games

A two-house legislature can often be modelled as a proper simple game whose outcome depends on whether a coalition wins, blocks or loses in two smaller proper simple games. It is shown that there are exactly five ways to combine the smaller games into a larger one. This paper focuses on one of the rules, lexicographic composition, where a coalition wins G_1 => G_2 when it either wins in G_1, or blocks in G_1 and wins in G_2. It is the most decisive of the five. A lexicographically decomposable game is one that can be represented in this way using components whose player sets partition the whole set. Games with veto players are not decomposable, and anonymous games are decomposable if and only if they are decisive and have two or more players. If a players benefit is assessed by any semi-value, then for two isomorphic games a player is better off from having a role in the first game than having the same role in the second. Lexicographic decomposability is sometimes compatible with equality of roles. A relaxation of it is suggested for its practical benefits. (This abstract was borrowed from another version of this item.)