Noncooperative Foundations of Stable Sets in Voting Games.

This note investigates the noncooperative foundations of von Neumann-Morgenstern (vN-M) stable sets in voting games. To do so, we study subgame perfect equilibria of a noncooperative legislative bargaining game, based on underlying simple games. The following results emerge from such an exercise: Every stable set of the underlying simple game is the limit set of undominated pure-strategy Markov perfect equilibria, and of strategically stable sets of undominated subgame perfect equilibria of the bargaining game with farsighted voters.Legislative bargaining, committee, strategic stability, stable set.

Existence and indeterminacy of Markovian equilibria in dynamic bargaining games

The paper studies stationary Markov perfect equilibria in multidimensional models of dynamic bargaining, in which the alternative chosen in one period determines the status quo for the next. We generalize a sufficient condition for existence of equilibrium due to Anesi and Seidmann (2015). We then use this existence result to show that if a weak gradient restriction holds at an alternative, then when players are sufficiently patient, there is a continuum of equilibria with absorbing sets arbitrarily close to that alternative. A sufficient condition for our gradient restriction is that the gradients of all players' utilities are linearly independent at that alternative. When the dimensionality of the set of alternatives is high, this linear independence condition holds at almost all alternatives, and equilibrium absorbing sets are dense in the set of alternatives. This implies that constructive techniques, which are common in the literature, fail to identify many plausible outcomes in dynamic bargaining games

Stable cores in information graph games

In an information graph situation, a finite set of agents and a source are the set of nodes of an undirected graph with the property that two adjacent nodes can share information at no cost. The source has some information (or technology), and agents in the same component as the source can reach this information for free. In other components, some agent must pay a unitary cost to obtain the information. We prove that the core of the derived information graph game is a von Neumann-Morgenstern stable set if and only if the information graph is cycle-complete, or equivalently if the game is concave. Otherwise, whether there always exists a stable set is an open question. If the information graph consists of a ring that contains the source, a stable set always exists and it is the core of a related situation where one edge has been deleted.Xunta de Galicia | Ref. ED431B 2019/34Generalitat de Catalunya | Ref. 2017SGR778Agencia Estatal de Investigación | Ref. ECO2017-82241-RAgencia Estatal de Investigación | Ref. PID2020-113110GB-I0

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

Existence and indeterminacy of Markovian equilibria in dynamic bargaining games

The paper studies stationary Markov perfect equilibria in multidimensional models of dynamic bargaining, in which the alternative chosen in one period determines the status quo for the next. We generalize a sufficient condition for existence of equilibrium due to Anesi and Seidmann (2015). We then use this existence result to show that if a weak gradient restriction holds at an alternative, then when players are sufficiently patient, there is a continuum of equilibria with absorbing sets arbitrarily close to that alternative. A sufficient condition for our gradient restriction is that the gradients of all players' utilities are linearly independent at that alternative. When the dimensionality of the set of alternatives is high, this linear independence condition holds at almost all alternatives, and equilibrium absorbing sets are dense in the set of alternatives. This implies that constructive techniques, which are common in the literature, fail to identify many plausible outcomes in dynamic bargaining games

Coalition formation and history dependence

Farsighted formulations of coalitional formation, for instance, by Harsanyi and Ray and Vohra, have typically been based on the von Neumann-Morgenstern stable set. These farsighted stable sets use a notion of indirect dominance in which an outcome can be dominated by a chain of coalitional "moves" in which each coalition that is involved in the sequence eventually stands to gain. Dutta and Vohra point out that these solution concepts do not require coalitions to make optimal moves. Hence, these solution concepts can yield unreasonable predictions. Dutta and Vohra restricted coalitions to hold common, history-independent expectations that incorporate optimality regarding the continuation path. This paper extends the Dutta-Vohra analysis by allowing for history-dependent expectations. The paper provides characterization results for two solution concepts that correspond to two versions of optimality. It demonstrates the power of history dependence by establishing nonemptyness results for all finite games as well as transferable utility partition function games. The paper also provides partial comparisons of the solution concepts to other solutions.Peer reviewe

Bargaining over an endogenous agenda

We present a model of bargaining in which a committee searches over the policy space, successively amending the default by voting over proposals. Bargaining ends when proposers are unable or unwilling to amend the existing default, which is then implemented. Our main goal is to study the policies that can be implemented from any initial default in a pure-strategy stationary Markov perfect equilibrium for an interesting class of environments including multidimensional and infinite policy spaces. It is convenient to start by characterizing the set of immovable policies that are implemented, once reached as default. These policies form a weakly stable set and, conversely, any weakly stable set is supported by some equilibrium. Using these results, we show that minimum-winning coalitions may not form and that a player who does not propose may nevertheless earn all of the surplus from agreement. We then consider how equilibrium outcomes change as we vary the order in which players propose, the identity of proposers, and the set of winning coalitions. First, if the policy space is well ordered, then the committee implements the ideal policy of the last proposer in a subset of a weakly stable set, but this result does not generalize to other cases. We also show, surprisingly, that a player may prefer not to be given the opportunity to propose and that the set of immovable policies may shrink as the quota increases. Finally, we derive conditions under which immovable policies in semi-Markovian equilibria form a consistent choice set

Endogenous agenda formation processes with the one-deviation property

Peer reviewe

Dynamic legislative bargaining with veto power: theory and experiments

In many domains, committees bargain over a sequence of policies and a policy remains in effect until a new agreement is reached. In this paper, I argue that, in order to assess the consequences of veto power, it is important to take into account this dynamic aspect. I analyze an infinitely repeated divide-the-dollar game with an endogenous status quo policy. I show that full appropriation by the veto player is the only stable policy when legislators are sufficiently impatient; and that, irrespective of legislators' patience and the initial division of resources, there is always an equilibrium where policy eventually gets arbitrarily close to full appropriation by the veto player. In this equilibrium, increasing legislators' patience or decreasing the veto player's proposal power makes convergence to this outcome slower and the veto player supports reforms that decrease his allocation. The main predictions of the theory find support in controlled laboratory experiments