A Continuous-Time Model of Multilateral Bargaining † (original) (raw)

On continuous-time Markov processes in bargaining

Economics Letters, 2008

For bilateral stochastic bargaining procedures embedded in stable homogeneous continuous-time Markov processes, we show unusual limit results when time between rounds vanish. Standard convergence results require that some states are instantaneous.

Uniqueness of stationary equilibrium payoffs in coalitional bargaining

Journal of Economic Theory, 2013

We study a model of sequential bargaining in which, in each period before an agreement is reached, a proposer is randomly selected, the proposer suggests a division of a pie of size one, each other agent either approves or rejects the proposal, and the proposal is implemented if the set of approving agents is a winning coalition for the proposer. We show that stationary equilibrium outcomes of a coalitional bargaining game are unique. This generalizes Eraslan insofar as: (a) there are no restrictions on the structure of sets of winning coalitions; (b) different proposers may have different sets of winning coalitions; (c) there may be a positive probability that no proposer is selected. Running Title: Coalitional Bargaining J ournal of Economic Literature Classification Number D71.

Sequential Bargaining in a Stochastic Environment

2006

This paper investigates the uniqueness of subgame perfect (SP) payoffs in a sequential bargaining game. Players are completely informed and the surplus to be allocated follows a geometric Brownian motion. This bargaining problem has not been analysed exhaustively in a stochastic environment. The aim of this paper is to provide a technique to identify the subgame perfect equilibria, i.e. the timing of the agreement and the SP payoff at which agreement occurs. Even though the main focus is on the uniqueness of the equilibrium, we investigate other features of the equilibrium, such as the Pareto efficiency of the outcome and the relation with the Nash axiomatic approach. * Comments are welcome. We are very grateful to William Perraudin and Raymond Brummelhuis for helpful suggestions and discussions.

Markov Perfect Equilibrium in a Stochastic Bargaining Model

I present a model in which two players bargain using the alternating-offers protocol while costly fighting goes on according to a stochastic process that moves some player closer to complete victory. There are many Nash equilibria and a large range of payoffs can be supported in equilibrium. However, there is a unique Markov perfect equilibrium, which is efficient, and in which offers depend on players' prospects in war as well as the current military position.

Markov equilibria in a model of bargaining in networks

Games and Economic Behavior, 2012

We study the Markov perfect equilibria (MPEs) of an infinite horizon game in which pairs of players connected in a network are randomly matched to bargain. Players who reach agreement are removed from the network without replacement. We establish the existence of MPEs and show that MPE payoffs are not necessarily unique. A method for constructing pure strategy MPEs for high discount factors is developed. For some networks, we find that all MPEs are asymptotically inefficient as players become patient.

Dynamic Coalitional TU Games: Distributed Bargaining among Players' Neighbors

arXiv preprint arXiv:1101.4536, 2011

We consider a sequence of transferable utility (TU) games where, at each time, the characteristic function is a random vector with realizations restricted to some set of values. The game differs from other ones in the literature on dynamic, stochastic or interval valued TU games as it combines dynamics of the game with an allocation protocol for the players that dynamically interact with each other. The protocol is an iterative and decentralized algorithm that offers a paradigmatic mathematical description of negotiation and bargaining processes. The first part of the paper contributes to the definition of a robust (coalitional) TU game and the development of a distributed bargaining protocol. We prove the convergence with probability 1 of the bargaining process to a random allocation that lies in the core of the robust game under some mild conditions on the underlying communication graphs. The second part of the paper addresses the more general case where the robust game may have empty core. In this case, with the dynamic game we associate a dynamic average game by averaging over time the sequence of characteristic functions. Then, we consider an accordingly modified bargaining protocol. Assuming that the sequence of characteristic functions is ergodic and the core of the average game has a nonempty relative interior, we show that the modified bargaining protocol converges with probability 1 to a random allocation that lies in the core of the average game.

Markov equilibria in dynamic matching and bargaining games

Games and Economic Behavior, 2006

Rubinstein and Wolinsky (1990) show that a simple homogeneous market with exogenous matching has a continuum of (non-competitive) perfect equilibria; however, the unique Markov perfect equilibrium is competitive. By contrast, in the more general case of heterogeneous markets, we show there exists a continuum of (non-competitive) Markov perfect equilibria. However, a refinement of the Markov property, which we call monotonicity, does suffice to guarantee perfectly competitive behavior: we show that a Markov perfect equilibrium is competitive if and only if it is monotonic. The monotonicity property is closely related to the concept of Nash equilibrium with complexity costs.

Dynamic bargaining with action-dependent valuations

Journal of Economic Dynamics and Control, 2004

An inÿnite-horizon, dynamic bargaining model is presented in which actions a ect the expected future value of the buyer-seller match. Because actions directly a ect the future surplus to be bargained over, the model is unlike other models that tie the dynamic process to nature alone. Focusing on a subset of weak Markov equilibria, several results come about that are not found in static bargaining models using similar bargaining protocols. In particular, optimal price demands can be lower (higher) than the buyer's lowest (highest) possible valuation, and several empirical features concerning wage settlements and strike incidence from labor union contract negotiations can be explained. ?

Simple equilibria in dynamic bargaining games over policies

The paper constructs equilibria in a class of infinite horizon dynamic bar-gaining models in which players care about all the dimensions of a policy space. Both one-dimensional and multi-dimensional policy spaces are analysed. All the equilibria have attractive property in being simple and having intuitive structure. Equilibrium behaviour is a result of two opposing forces. One force pushes players into proposing policies as close as possible to their single period optimum. A second and strategic force pushes players in the opposite direc-tion, in an attempt to propose policies that constrain the future proposals of all other players. The resulting dynamics of the policies is shown to converge to the most preferred policy of the median player. The paper also uncovers the multiplicity of equilibria in certain environments, which greatly complicates their computational simulation.

Constrained consensus for bargaining in dynamic coalitional tu games

Decision and Control and European Control …, 2011

We consider a sequence of transferable utility (TU) games where, at each time, the characteristic function is a random vector with realizations restricted to some set of values. We assume that the players in the game interact only with their neighbors, where the neighbors may vary over time. The game differs from other ones in the literature on dynamic, stochastic or interval valued TU games as it combines dynamics of the game with an allocation protocol for the players that dynamically interact with each other. The protocol is an iterative and decentralized algorithm that offers a paradigmatic mathematical description of negotiation and bargaining processes. The main contributions of the paper are the definition of a robust (coalitional) TU game and the development of a distributed bargaining protocol. We prove the convergence with probability 1 of the bargaining protocol to a random allocation that lies in the core of the robust game under some mild conditions on the players' communication graphs.