Dynamic multilateral markets

We study dynamic multilateral markets, in which players' payoffs result from intra-coalitional bargaining. The latter is modeled as the ultimatum game with exogenous (time-invariant) recognition probabilities and unanimity acceptance rule. Players in agreeing coalitions leave the market and are replaced by their replicas, which keeps the pool of market participants constant over time. In this infinite game, we establish payoff uniqueness of stationary equilibria and the emergence of endogenous cooperation structures when traders experience some degree of (heterogeneous) bargaining frictions. When we focus on market games with different player types, we derive, under mild conditions, an explicit formula for each type's equilibrium payoff as the market frictions vanish

Incomplete Contracts with Asymmetric Information: Exclusive v. Optional Remedies

Law and economics scholars have always had a strong interest in contract remedies. Perhaps the most explored issue in contract law has been the desirability of various contract remedies, such as expectation damages, specific performance, or liquidated damages, to name the most common. Scholars have been debating for years, from various perspectives, the comparative advantage of these remedies. Yet, most scholars have assumed that each of these remedies is exclusive, and their work has compared a single remedy contract to another single remedy contract. Interestingly, an analysis that assumes these remedies are optional (or cumulative) has not yet been explored, in spite of the fact that contract law provides the non-breaching party with a variety of optional remedies to choose from in case of a breach, and in spite of the fact that parties themselves write contracts which provide such an option. In this paper we attempt to start filling in this gap by studying the relationship between these remedies. Specifically, we study the conditions at which a contract that grants the non-breaching party an option to choose from optional remedies is superior to an exclusive remedy contract. We show that under conditions of double-sided uncertainty and asymmetric information between a seller (who might breach) and a buyer (who never breaches) the interaction of the parties\u27 distributions should determine whether a contract provides for exclusive or optional remedies. Specifically, if the buyer\u27s conditional expected valuation is larger than the seller\u27s conditional expected valuation (in both cases - conditional that their expected valuation is above the buyer\u27s mean valuation), then a contract which provides the buyer an option to choose between liquidated damages or specific performance (or actual damages) is superior. Our analysis in this paper informs transactional lawyers of the relevant economic factors they should consider when deciding the optimal composition of remedies in a given context. Moreover, our analysis is relevant for courts that interpret contracts because it will help them to better understand whether rational parties would have agreed that a particular remedy would be an exclusive remedy or an optional remedy when the language of the contract is ambiguous. Lastly, our analysis provides yet another economic rationale for why courts should enforce parties\u27 liquidated damages clauses even if it seems ex-post over, or under, compensatory. We present a model which shows when parties will agree on a non-exclusive liquidated damages clause. Under such a contract the parties stipulate ex-ante that the buyer will have the option to choose upon breach whether she prefers an optional remedy, such as actual damages or specific performance, to the pre-determined liquidated damages. We focus on the ex-ante design of the contract in light of the new information that the parties anticipate they will gain after they draft the contract. Therefore, we assume that no renegotiation or investments are involved. We demonstrate the optimal way to design contract clauses which takes advantage of the information that the seller and the buyer receive between the time they enter into the contract and the time of the actual breach. We further suggest that parties indeed use such clauses and that courts honor them. After laying out the basic model we provide some extensions to it. As is well known, an exclusive liquidated damages contract is equivalent to granting the seller a call option to breach and pay, where the exercise price is equal to the amount of the agreed liquidated damages. What is perhaps less known is that a non-exclusive, or optional, contract, where the buyer can choose performance, is equivalent to giving the buyer a consecutive call option with the same exercise price. Yet, the consecutive call option to the buyer does not have to have the same exercise price but can rather have a higher one. We call this new contract a two-price contract and show that it is even more efficient than the basic contract we have explored before. Next, we introduce more rounds of sequential options and show that while the regular ex-ante contract can achieve on average about 4 Indeed, in an environment of asymmetric information renegotiation costs are high. More on this below. 90% of the first-best allocative efficiency, an n-rounds contract approaches the first best, as n goes to infinity. We show numerically that within just 4 rounds, 96% of the allocative efficiency can be achieved. Section two describes the legal background against which we have designed our model. Section three surveys the literature that evaluates contract remedies from an economic perspective. Section four presents a simple model with two-sided incomplete information and with a liquidated damages clause. In section four we compare the performance of a regime with optional remedies with a regime of exclusive remedy and then determine the conditions at which each regime should be applied. Section five discusses some interesting extensions meant to approach the first-best allocative efficiency. The appendix provides a more rigorous mathematical demonstration of the model

Vertical Coordination Through Renegotiation

This paper analyzes the strategic use of bilateral supply contracts in sequential negotiations between one manufacturer and two differentiated retailers. Allowing for general contracts and retail bargaining power, I show that the first contracting parties have incentives to manipulate their contract to shift rent from the second contracting retailer and these incentives distort the industry profit away from the fully integrated monopoly outcome. To avoid such distortion, the first contracting parties may prefer to sign a contract which has no commitment power and can be renegotiated from scratch should the manufacturer fail in its subsequent negotiation with the second retailer. Renegotiation from scratch induces the first contracting parties to implement the monopoly prices and might enable them to capture the maximized industry profit. A slotting fee, an up-front fee paid by the manufacturer to the first retailer, and a menu of tariff-quantity pairs are sufficient contracts to implement the monopoly outcome. These results do not depend on the type of retail competition, the level of differentiation between the retailers, the order of sequential negotiations, the level of asymmetry between the retailers in terms of their bargaining power vis-à-vis the manufacturer or their profitability in exclusive dealing

What Factors Determine the Number of Trading Partners?

The purpose of the paper is to provide a simple model explaining buyer-supplier relationships and show what factors determine the number of trading partners. We show that when the supplier is able to determine the number of trading partners, the optimal number is small if the supplier's bargaining power with them is weak, the economy of scope in the supplier's variable costs is significant, and that in its sunk investment is weak. Investment may be greater when the number of trading partners is small. The results may be consistent with the formation of Japanese buyer-supplier relations