Bargaining in a long-term relationship and the Rubinstein solution

In a recent paper, Muthoo (1995) discusses whether the Rubinstein solution carries over on repeated bargaining situations. He concludes that stationary equilibria for such a repeated bargaining game do not imply the Rubinstein solution and that several non-stationary equilibria may exist. This paper demonstrates that the Rubinstein solution applies not only to unique bargaining problems but to repeated bargaining problems as well. It demonstrates that stationarity holds also in Muthoo's model, and it shows that a certain result of Muthoo which makes the split of bargaining gains independent of the discount factors is no relevant case as the discounted sum of each agent's utility is infinite. The paper introduces an alternative approach which takes into account that offers may cover also future realizations by employing future contracts. It shows that the agreement depends crucially on the enforceability of contracts if bargaining behavior fulfils a rationality condition.Strategic bargaining,repeated games,rational bargaining behavior

Money and price dynamics in a market with strategic bargaining

This paper studies a strategic bargaining model of money and prices to complement the results reported in Coles and Wright (1998). The probability of a bargaining breakdown is chosen to be consistent with market conditions in the spirit of Rubinstein and Wolinsky (1985). The unique monetary steady state coincides with the one under asymmetric Nash bargaining. The dynamics of the price level are determined without any reference to the value of search. The dynamic properties of the model resemble those of traditional monetary models.money, bargaining, price dynamics.

Wage bargaining with non-stationary preferences under strike decision

In this paper, we present a non-cooperative wage bargaining model in which preferences of both parties, a union and a firm, are expressed by the sequences of discount rates varying in time. For such a wage bargaining with non-stationary preferences, we determine subgame perfect equilibria between the union and the firm for the case when the union is supposed to go on strike in each period in which there is a disagreement. A certain generalization of the original Rubinstein bargaining model is applied to determine these equilibria.union - firm bargaining ; alternating offers ; varying discount rates ; subgame perfection

Bargaining in a long-term relationship and the Rubinstein solution

In a recent paper, Muthoo (1995) discusses whether the Rubinstein solution carries over on repeated bargaining situations. He concludes that stationary equilibria for such a repeated bargaining game do not imply the Rubinstein solution and that several non-stationary equilibria may exist. This paper demonstrates that the Rubinstein solution applies not only to unique bargaining problems but to repeated bargaining problems as well. It demonstrates that stationarity holds also in Muthoo's model, and it shows that a certain result of Muthoo which makes the split of bargaining gains independent of the discount factors is no relevant case as the discounted sum of each agent's utility is infinite. The paper introduces an alternative approach which takes into account that offers may cover also future realizations by employing future contracts. It shows that the agreement depends crucially on the enforceability of contracts if bargaining behavior fulfils a rationality condition

Sequential Share Bargaining

This paper presents a new extension of the Rubinstein-St°ahl bargaining model to the case with n players, called sequential share bargaining. The bargaining protocol is natural and has as its main feature that the players’ shares in the cake are determined sequentially. The bargaining protocol requires unanimous agreement for proposals to be implemented. Unlike all existing bargaining protocols with unanimous agreement, the resulting game has unique subgame perfect equilibrium utilities for any value of the discount factor. In equilibrium, agreement is reached immediately. The results are therefore qualitatively the same as in the two player case. The result builds on an analysis of so-called one-dimensional bargaining problems. We show that also one-dimensional bargaining problems have unique subgame perfect equilibrium utilities for any value of the discount factor, and that also in one-dimensional bargaining problems agreement is reached immediately.microeconomics ;

Patience and Ultimatum in Bargaining

This study investigates in a two-stage two-player model how the decision to make an ultimatum and how much to demand depends on the impatience of the agents and the pie uncertainty. First, players simultaneously decide on their ultimatums. If the ultimatum(s) are compatible then the player(s) receive his (their) demand(s) in the second period and the eventually remaining player becomes residual claimant. If no ultimatums are made then there is a Rubinstein-Ståhl bargaining. Relative impatience induces ultimatums but does not affect the demanded amount. In a discrete (continuous) setting there exist no equilibrium without an ultimatum (with mutual ultimatums).Ultimatum; Bargaining; Patience; Rubinstein-Ståhl

A Game Theoretical Model of Land Contract Choice

In most of the land tenancy literature the type of contract is exogenous. Also even though these contracts vary a lot among farms, between regions and over time, the theoretical literature has not always acknowledged this idiosyncrasy. Building on the strategic bargaining theory initiated by Rubinstein, this model not only makes the type of contract endogenous, but also provides the surplus sharing rules and the conditions giving rise to each type of contract, showing how the type and terms of the contract are tailored to fit the characteristics of the parties and their economic environment. Pairwise bargaining is embedded into a market context by putting “competitive pressure” on the players through the opportunity they have to break up bargaining and look for alternative partners. Because of this threat of opting out, the outcome of the bargaining process depends not only on the characteristics of the players, but also on events outside their match and the information they have about them. The model departs from price-taking assumptions. Type and terms of the contract result from negotiation and are shaped by the “relative bargaining powers” of the players whose relevant components are identified in a precise way in the model.land tenancy, contract choice, game theory

Bilateral Oligopoly

In intermediate goods markets, both buyers and sellers normally have market power, and sales are based on bilaterally negotiated contracts specifying both price and quantity. In our model, pairs of buyers and sellers meet in bilateral but interdependent Rubinstein-Ståhl negotiations. The outcome has a simple characterization (a Nash equilibrium in Nash bargaining solutions) suitable for applied work. Equilibrium quantities are efficient regardless of concentration and also with few “trading links”. The law of one price does not hold. In addition to relation-specific characteristics, prices depend on both upstream and downstream concentration and on the structure of trading links. The requirements necessary for Walrasian prices are stronger than usually believed.Bilageral Oligopoly; Bargaining; Intermediate Goods; Decentralized Trade; Walrasian Outcome

The Role of Mediation in Peacemaking and Peacekeeping Negotiations.

We develop a model of bargaining that provides a rationale for the difference in the method of negotiation, depending on the nature of the conflict. We distinguish those negotiations that take place previous to a potential conflict (peacekeeping), and negotiations inside the conflict (peacemaking). In these contexts, we study the role of a mediator that tries to achieve a certain balance between the efficiency of the agreement and the equality of the sharing. We show that the credibility of the mediator comes from her willingness to impose delays in the negotiation, even if that implies costs. We also find how the “weak” player in the conflict can strategically profit from the mediator’s quest for equality. Finally, we show how the capacity of the mediator to induce a higher equality in the sharing is always higher in a peacemaking situation than in a peacekeeping one..Mediation, Rubinstein bargaining.

Alternating offers bargaining with loss aversion

The Rubinstein alternating offers bargaining game is reconsidered under the assumption that each player is loss averse and the associated reference point is equal to the highest turned down offer of the opponent in the past. This makes the payoffs and therefore potential equilibrium strategies dependent on the history of play. A subgame perfect equilibrium is constructed, in which the strategies depend on the history of play throughthe current reference points. It is shown that this equilibrium is unique under some assumptions that it shares with the equilibrium in the classical model: immediate acceptance of equilibrium offers, indifference between acceptance and rejection of such offers, and strategies depending only on the current reference points. It is also shown that in this equilibrium loss aversion is a disadvantage. Moreover, a relation with asymmetric Nashbargaining is established, where a player’s bargaining power is negatively related to own loss aversion and positively to the opponent’s loss aversion.mathematical economics;