Clara Ponsati

The war of attrition with incomplete information

We present a continuous-time model of the war of attrition with exponential discounting and with two-sided incomplete information. We provide a full characterization of the Bayesian Equilibria of this game, without restricting strategies to be differentiable.

Bargaining one-dimensional social choices

We analyze bargaining over the one-dimension characteristic of a public good among n impatient players when decisions require q favorable votes, q 2. Stationary subgame perfect equilibrium strategies are characterized for all games with deterministic protocol. We provide a monotonicity condition (satisfied by all single-peak, strictly quasi-concave and concave utilities) that assures uniqueness for every q whenever player’s utilities are symmetric around the peak. Without symmetry, the monotonicity condition assures uniqueness for qualified majorities, q> n/2, provided that agents are sufficiently patient and utilities satisfy an additional regularity condition. Asymptotic uniqueness is assured for qualified majorities by imposing only the monotonicity condition.

Uniqueness of stationary equilibria in bargaining one-dimensional policies under (super) majority rules

We consider negotiations selecting one-dimensional policies. Individuals have instantaneous preferences represented by continuous, concave and single-peaked utility functions, and they are impatient. Decisions arise from a bargaining game with random proposers and (super) majority approval, ranging from the simple majority up to unanimity. We provide sufficient conditions that guarantee the existence of a unique stationary subgame perfect equilibrium, and we provide its explicit characterization. The uniqueness of the equilibrium permits an analysis of the set of Pareto optimal voting rules. For symmetric distributions of peaks and uniform recognition probabilities unanimity is the unanimously preferred majority rule.

Mediation: incomplete information bargaining with filtered communication

Abstract 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. Perfect Bayesian Equilibria are characterized. We show that an equilibrium using only the extreme agreements always exists and display the necessary and sufficient condition for the existence of 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 social welfare of the rest of the equilibria is decreasing in the number of compromise agreements used.

The deadline effect: A theoretical note

Abstract A two-person concession game with a deadline is presented. It is proved that along the Bayesian equilibrium players tend to reach an agreement at the deadline.

All in good time

Why is issue-by-issue bargaining a common phenomenon, even though it disallows the beneficial trade-offs across issues that are possible when negotiating a global solution? We show that under asymmetric information, issue-by-issue bargaining has two attractive features. First, it avoids bundling a good deal on one issue with a bad deal on another issue, when the lack of gains to agreement on the latter is not a priori common knowledge. Second, it avoids the imposition of the asymmetric information inefficiency of “harder” issues on issues which turn to be “easier” to solve. That’s why when the agenda is not imposed on the parties but is rather left for them to determine when negotiating, they may very well opt for issue-by-issue bargaining. We demonstrate this in a natural game where bargainers communicate, whenever they choose to do so, their willingness to discuss or make offers either on one of the issues or on a bundle of issues.

Bargaining over multiple issues with maximin and leximin preferences

Global bargaining problems over a finite number of different issues are formalized as cartesian products of classical bargaining problems. For maximin and leximin bargainers we characterize global bargaining solutions that are efficient and satisfy the requirement that bargaining separately or globally leads to equivalent outcomes. Global solutions in this class are constructed from the family of monotone path solutions for classical bargaining problems.

Robust Bilateral Trade and Mediated Bargaining

We consider bilateral trade problems subject to incomplete information on the reservation values of the agents. We address negotiations where the communication of proposals takes place through the filter of a third party, a mediator: traders submit proposals over continuous time to the mediator that receives bids and keeps them secret until they are compatible. A regular robust equilibrium (RRE) is an (undominated) ex post equilibrium where (with sufficient delay) all compatible traders reach agreement. We present a characterization of RRE for risk-neutral traders that discount the future at the same exponential rate. We show how to compute RRE strategy profiles, and we explicitly display the unique one where agreements split the net surplus in equal shares. Our results support the claim that bargaining through a mediator is an effective procedure to promote efficiency. (JEL: C78, D02, D74, D82) (c) 2008 by the European Economic Association.

Meritocracy, egalitarianism and the stability of majoritarian organizations

Egalitarianism and meritocracy are competing principles to distribute the joint benefits of cooperation. We examine the consequences of letting members of society vote between those two principles, in a context where individuals must join with others into coalitions of a certain size to become productive. Our setup induces a hedonic game of coalition formation. We study the existence of core stable partitions (organizational structures) of this game. We show that the inability of voters to commit to one distributional rule or another is a potential source of instability. But we also prove that, when stable organizational structures exist, they may be rich in form, and different than those predicted by alternative models of coalition formation. Non-segregated coalitions may arise within core stable structures. Stability is also compatible with the coexistence of meritocratic and egalitarian coalitions. These phenomena are robust, and persist under alternative variants of our initial model.

Stakeholder bargaining games

We study bilateral bargaining problems with an interested third party, the stakeholder, that enjoys benefits upon a bilateral agreement. To address the strategic implications of stakeholders over negotiations, we consider a model where two bargainers interact in the presence of a third party that (a) can transfer a share of her benefits to the bargainers but cannot receive a share of the bilateral surplus, and (b) while she may not participate in all periods of the negotiation, she cannot remain entirely inhibited. Our main findings are:(1) the stakeholder’s (reverse) liquidity constraint implies the existence of a multiplicity of stationary subgame perfect equilibria that include outcomes with very asymmetric bilateral agreements, and (2) the partial participation of the stakeholder may be the source of severe inefficiency