Regularity of Pure Strategy Equilibrium Points in a Class of Bargaining Games

For a class of n-player (n ? 2) sequential bargaining games with probabilistic recognition and general agreement rules, we characterize pure strategy Stationary Subgame Perfect (PSSP) equilibria via a finite number of equalities and inequalities. We use this characterization and the degree theory of Shannon, 1994, to show that when utility over agreements has negative definite second (contingent) derivative, there is a finite number of PSSP equilibrium points for almost all discount factors. If in addition the space of agreements is one-dimensional, the theorem applies for all SSP equilibria. And for oligarchic voting rules (which include unanimity) with agreement spaces of arbitrary finite dimension, the number of SSP equilibria is odd and the equilibrium correspondence is lower-hemicontinuous for almost all discount factors. Finally, we provide a sufficient condition for uniqueness of SSP equilibrium in oligarchic games.Local Uniqueness of Equilibrium, Regularity, Sequential Bargaining.

International organisation analysed with the power index method

The period of globalisation has seen more and more of international and regional organisation. Setting up an organisation with a group of state entails a resolution to the following two questions: (1) How are votes to be allocated? (2) What aggregation rule is to be employed? International and regional organisations display some interesting differences in how they have approached these two questions choosing a regime. The power index framework offers a convenient method for analysing these constitutional differences. It may be linked with the basic framework in constitutional economics – Wicksell’s classic approach, which entails that players very much use their preferences for the power to act and the power to prevent action when deciding the regime to be employed

Coalitional Bargaining Equilibria

This paper takes up the foundational issue of existence of stationary subgame perfect equi- libria in a general class of coalitional bargaining games that includes many known bargaining models and models of coalition formation. General sufficient conditions for existence of equilib- ria are currently lacking in many interesting environments: bargaining models with non-concave stage utility functions, models with a Pareto optimal status quo alternative and heterogeneous discount factors, and models of coalition formation in public good economies with consumption lower bounds. This paper establishes existence of stationary equilibrium under compactness and continuity conditions, without the structure of convexity or comprehensiveness used in the extant literature. The proof requires a precise selection of voting equilibria following different proposals. The result is applied to obtain equilibria in models of bargaining over taxes, coalition formation in NTU environments, and collective dynamic programming problems.

Fallback Bargaining

Fallback bargaining is a bargaining procedure under which bargainers begin by indicating their preference rankings over all alternatives. They then fall back, in lockstep, to less and less preferred alternatives - starting with first choices, then adding second choices, and so on - until an alternative is found on which all bargainers agree. This common agreement, which becomes the outcome of the procedure, may be different if a decision rule other than unanimity is used.BARGAINING ; SOCIAL CHOICE ; NASH EQUILIBRIUM

Persistence of power: Repeated multilateral bargaining with endogenous agenda setting authority

We extend a simple repeated, multilateral bargaining model to allow successful agenda setters to hold on to power as long as they maintain the support of a majority of other committee members. Theoretically and experimentally, we compare this Endogenous Power environment with a standard Random Power environment in which agenda setters are appointed randomly each period. Although the theoretical analysis predicts that the two environments are outcome equivalent, the experimental analysis shows substantial differences in behavior and outcomes across the games. The Endogenous Power environment results in the formation of more stable coalitions, less-equitable budget allocations, the persistence of power across periods, and higher long-run inequality than the Random Power environment. We present evidence that the stationary equilibrium refinements traditionally used in the literature fail to predict behavior in either game

A Theory of coalition Bargaining

When voting takes place in democratic institutions, we find (either explicitly or implicitly) that there is an agenda setter or a formateur. Such players are uniquely able to make substantive proposals for given topics. Their statuses remain intact even after rejection of proposals, but they must revise rejected proposals constructively (e.g. towards a compromise). We model this in a general environment, show that the equilibrium outcome is generically unique, and characterize it explicitely. The equilibrium outcome is robust to (partially) binding communication between the formateur and the voters. As illustrations, we consider majority bargaining about a cake (leaned on Baron and Ferejohn,1989),where the formateur ends up being a perfect dictator, and a model of legislative voting (leaned on Jackson and Moselle,2002), where he is a dictator if his ideological position is within the quartiles of the parliament. In these cases, our model implements (reversed) McKelvey majority path. Depending on the valuations, the formateur´s power may be weakened when parliamentary decisions can be revised, as this may faciliate tacit collusion amongst the voters. --coalitional bargaining,legislature,non-cooperative

Bargaining Foundations of the Median Voter Theorem

We provide game-theoretic foundations for the median voter theorem in a one-dimensional bargaining model based on Baron and Ferejohn’s (1989) model of distributive politics. We prove that, as the agents become arbitrarily patient, the set of proposals that can be passed in any subgame perfect equilibrium collapses to the median voter’s ideal point. While we leave the possibility of some delay, we prove that the agents’ equilibrium continuation payoffs converge to the utility from the median, so that delay, if it occurs, is inconsequential. We do not impose stationarity or any other refinements. Our result counters intuition based on the folk theorem for repeated games, and it contrasts with the known result for the distributive bargaining model that, as agents become patient, any division of the dollar can be supported as a subgame perfect equilibrium outcome.