Bargaining with Incomplete Information

A central question in economics is understanding the difficulties that parties have in reaching mutually beneficial agreements. Informational differences provide an appealing explanation for bargaining inefficiencies. This chapter provides an overview of the theoretical and empirical literature on bargaining with incomplete information. The chapter begins with an analysis of bargaining within a mechanism design framework. A modern development is provided of the classic result that, given two parties with independent private valuations, ex post efficiency is attainable if and only if it is common knowledge that gains from trade exist. The classic problems of efficient trade with one-sided incomplete information but interdependent valuations, and of efficiently dissolving a partnership with two-sided incomplete information, are also reviewed using mechanism design. The chapter then proceeds to study bargaining where the parties sequentially exchange offers. Under one-sided incomplete information, it considers sequential bargaining between a seller with a known valuation and a buyer with a private valuation. When there is a "gap" between the seller's valuation and the support of buyer valuations, the seller-offer game has essentially a unique sequential equilibrium. This equilibrium exhibits the following properties: it is stationary, trade occurs in finite time, and the price is favorable to the informed party (the Coase Conjecture). The alternating-offer game exhibits similar properties, when a refinement of sequential equilibrium is applied. However, in the case of "no gap" between the seller's valuation and the support of buyer valuations, the bargaining does not conclude with probability one after any finite number of periods, and it does not follow that sequential equilibria need be stationary. If stationarity is nevertheless assumed, then the results parallel those for the "gap" case. However, if stationarity is not assumed, then instead a folk theorem obtains, so substantial delay is possible and the uninformed party may receive substantial surplus. The chapter also briefly sketches results for sequential bargaining with two-sided incomplete information. Finally, it reviews the empirical evidence on strategic bargaining with private information by focusing on one of the most prominent examples of bargaining: union contract negotiations.Bargaining; Delay; Incomplete Information

Mediation: Incomplete information bargaining with

We analyze a continuous-time bilateral double auction in the presence of two-sided incomplete information and a smallest money unit. A distinguishing feature of our model is that intermediate concessions are not observable by the adversary: they are only communicated to a passive auctioneer. An alternative interpretation is that of mediated bargaining. We show that an equilibrium using only the extreme agreements always exists and display the necessary and sufficient condition for the existence of (perfect Bayesian) equilibra which yield intermediate agreements. For the symmetric case with uniform type distribution we numerically calculate the equilibria. We find that the equilibrium which does not use compromise agreements is the least efficient, however, the rest of the equilibria yield the lower social welfare the higher number of compromise agreements are used.Noncooperative games, bargaining theory

Rhetoric in legislative bargaining with asymmetric information

We analyze a three-player legislative bargaining game over an ideological and a distributive decision. Legislators are privately informed about their ideological intensities, i.e., the weight placed on the ideological decision relative to the weight placed on the distributive decision. Communication takes place before a proposal is offered and majority rule voting determines the outcome. We show that it is not possible for all legislators to communicate informatively. In particular, the legislator who is ideologically more distant from the proposer cannot communicate informatively, but the closer legislator may communicate whether he would \compromise "or flight" on ideology. Surprisingly, the proposer may be worse off when bargaining with two legislators (under majority rule) than with one (who has veto power), because competition between the legislators may result in less information conveyed in equilibrium. Despite separable preferences, the proposer is always better off making proposals for the two dimensions together

Markets with bilateral bargaining and incomplete information

We study the relationship between bargaining and competition with incomplete information. We consider a model with two uninformed and identical buyers and two sellers. One of the sellers has a privately-known reservation price, which can either be Low or High. The other seller’s reservation price is commonly known to be in between the Low and High values of the privately-informed seller. Buyers move in sequence, and make offers with the second buyer observing the offer made by the first buyer. The sellers respond simultaneously. We show that there are two types of (perfect Bayes) equilibrium. In one equilibrium, the buyer who moves second does better. In the second equilibrium, buyers’ expected payoffs are equalised, and the price received by the seller with the known reservation value is determined entirely by the equuilibrium of the two-player game between a single buyer and an informed seller. We also discuss extensions of the model to multiple buyers and sellers, and to the case where both sellers are privately informed

Bargaining and Conflict with Incomplete Information

This paper studies bargaining and conflict under incomplete information, provides an overview and a critical account of the literature on the topic and contributes with original research. We first revise models of mechanism design and sequential bargaining that take confrontation as final. Conflict and inefficiencies are to be expected in these models whenever parties have optimistic prospects on the outcome of the all-out conflict. After examining the causes and reasons for this optimism, we move to the analysis of the recent literature that considers the existence of limited confrontations that allow bargaining to resume. In the presence of private information, these limited conflicts convey information and thus become a bargaining instrument. The paper closes with a discussion on the related empirical literature, the challenges that it faces and some potential avenues for further research.Bargaining, Conflict, Incomplete information, Power, Optimism, Hicks paradox, Uneven contenders paradox.

Learning from Strikes

This paper reports on an experimental study of the influence of asymmetric information and information spillovers on bargaining outcomes. It develops and tests Kuhn and Gu's model (1999) of learning in sequential wage negotiations, by means of two Ultimatum Bargaining Games with uncertainty on the proposer's side. Evidence shows that Dunlop's assertion of inflationary wage demands does not systematically hold and strike incidence is lowered by information spillovers, since demands are revised according to previous bargaining outcomes. However, in the presence of fairness concerns, the ability to observe outcomes but not the bargaining process does not entail a sufficient reduction in information asymmetry to a point of guaranteeing Pareto-improved bargaining outcomes.asymmetric information; experimental economics; learning; strikes; ultimatum bargaining games

Collective Bargaining under Complete Information

In this paper, we build and structurally estimate a complete information bargaining model of collective negotiation for Spain. For large firms, the assumption of complete information seems a sensible one, and it matches the collective bargaining environment better than the one provided by private information models. The specification of the model with players having different discount factors allows us to measure their relative bargaining power, a recurrent question in the theory of bargaining. We find that both entrepreneurs and workers have high discount factors, and no evidence that entrepreneurs have bigger bargaining power as usually assumed.Delays, sequential bargaining, structural estimation

Mediation: Incomplete information bargaining with filtered communication

We analyze a continuous-time bilateral double auction in the presence of two-sided incomplete information and a smallest money unit. A distinguishing feature of our model is that intermediate concessions are not observable by the adversary: they are only communicated to a passive auctioneer. An alternative interpretation is that of mediated bargaining. We show that an equilibrium using only the extreme agreements always exists and display the necessary and sucient condition for the existence of (perfect Bayesian) equilibra which yield intermediate agreements. For the symmetric case with uniform type distribution we numerically calculate the equilibria. We find that the equilibrium which does not use compromise agreements is the least ecient, however, the rest of the equilibria yield the lower social welfare the higher number of compromise agreements are used.

The Dynamics of Bargaining Postures: The Role of a Third Party

In many real world negotiations, from wage contract bargaining to product liability disputes, the bargaining parties often interact repeatedly and have the option of seeking outside judgement. This paper studies a model of repeated bargaining with a third party to analyze how and why bargaining postures endogenously evolve over time. A privately informed long-lived player bargains with a sequence of short-lived players, one at a time. Should the players fail to reach an agreement, an unbiased yet imperfect third party is called upon to make a judgement. The uninformed short-lived players learn through two channels: observed behavior of the informed player (\soft" information) and, if any, verdicts of the third party (\hard" information). The long-lived player wants to guard his private information by bargaining tough but at the expense of more information disclosure from the third party. As a result of the strategic use of these two sources of information, the players' bargaining postures change as the uninformed players' beliefs evolve. Interestingly, as third party information becomes more precise, the players adopt tough bargaining postures for a wider range of beliefs. Many repeated bargaining problems can be analyzed in this framework. In particular, the equilibrium dynamics provide an explanation for the puzzling contrast between the bargaining postures of Merck and Pfizer in their recent high-profile product liability litigations. The results also help us understand several other phenomena documented in the related literature.bargaining posture, repeated bargaining, third party information, reputation

Rhetoric in Legislative Bargaining with Asymmetric Information

In this paper we analyze a legislative bargaining game in which parties privately informed about their preferences bargain over an ideological and a distributive decision. Communication takes place before a proposal is offered and majority rule voting determines the outcome. When the private information pertains to the ideological intensities but the ideological positions are publicly known, it may not be possible to have informative communication from the legislator who is ideologically distant from the proposer, but the more moderate legislator can communicate whether he would "compromise" or fight" on ideology. If instead the private information pertains to the ideological positions, then all parties may convey whether they will "cooperate," "compromise," or fight" on ideology. When the uncertainty is about ideological intensity, the proposer is always better on making proposals for the two dimensions together despite separable preferences, but when the uncertainty is about ideological positions, bundling can result in informational loss which hurts the proposer.