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This paper proposes a new solution concept to three-player coalitional bargaining problems where the underlying economic opportunities are described by a partition function. This classic bargaining problem is modeled as a dynamic non-cooperative game in which players make conditional or unconditional offers, and coalitions continue to negotiate as long as there are gains from trade. The theory yields a unique stationary perfect equilibrium outcome—the negotiation value—and provides a unified framework that selects an economically intuitive solution and endogenous coalition structure. For such games as pure bargaining games the negotiation value coincides with the Nash bargain- ing solution, and for such games as zero-sum and majority voting games the negotiation value coincides with the Shapley value. However, a novel situation arises where the out- come is determined by pairwise sequential bargaining sessions in which a pair of players forms a natural match. In addition, another novel situation exists where the outcome is determined by one pivotal player bargaining unconditionally with the other players, and only the pairwise coalitions between the pivotal player and the other players can form. Download Paper
This paper considers the efficiency and convergence properties of dynamic processes of social and economic interactions such as exchange economies, multilateral negotiations, merger and divestiture transactions, or legislative bargaining. The key general feature of the economy is that agents can implement any move from one state to another as long as a pre-specified subset of agents approve of it. By means of examples, we show that inefficiencies may occur even in the long run. Persistent inefficiencies take the form of cycles between states or of convergence to an inefficient state. When agents are sufficiently patient, we show very generally that the initial state from which the process starts plays no role in the long run properties of equilibria. Also, when there exists an efficient state that is externality free (in the sense that a move away from that state does not hurt the agents whose consent is not required for the move), then the system must converge to this efficient state in the long run. Conversely, long run efficiency can only be attained in a robust way if there exists an efficient externality-free state. It is thus more important to design transitions guaranteeing the existence of an efficient externality-free state rather than to implement a fine initialization of the process. Download Paper
This paper studies multilateral negotiations among n players in an environment where there are externalities and where contracts forming coalitions can be written and renegotiated. The negotiation process is modeled as a sequential game of offers and counteroffers, and we focus on the stationary subgame perfect equilibria, which jointly determine both the expected value of players and the Markov state transition probability that encodes the path of coalition formation. The existence of equilibria is established, and Pareto efficiency is guaranteed if the grand coalition is efficient, despite the existence of externalities. Also, for almost all games (except in a set of measure zero) the equilibrium is locally unique and stable, and the number of equilibria is finite and odd. Global uniqueness does not hold in general (a public good provision example has seven equilibria), but a sufficient condition for global uniqueness is derived. Using this sufficient condition, we show that there is a globally unique equilibrium in three-player super-additive games. Comparative statics analysis can be easily carried out using standard calculus tools, and some new insights emerge from the investigation of the classic apex and quota games. Download Paper
This paper develops a dynamic model of tender offers in which there is trading on the target's shares during the takeover, and bidders can freeze out target shareholders (compulsorily acquire remaining shares not tendered at the bid price), features that prevail on almost all takeovers. We show that trading allows for the entry of arbitrageurs with large blocks of shares who can hold out a freezeout - a threat that forces the bidder to offer a high preemptive bid. There is also a positive relationship between the takeover premium and arbitrageurs' accumulation of shares before the takeover announcement, and the less liquid the target stock, the strong this relationship is. Moreover, freezeouts eliminate the free-rider problem, but front-end loaded bids, such as two-tiered and partial offers, do not benefit bidders because arbitrageurs can undo any potential benefit and eliminate the coerciveness of these offers. Similarly, the takeover premium is also largely unrelated to the bidder's ability to dilute the target's shareholders after the acquisition, also due to potential arbitrage activity. Download Paper
We study strategic three-player coalitional bargaining problems in an environment with externalities where contracts forming coalitions can be written and renegotiated. The theory yields a unique stationary subgame perfect Nash equilibrium outcome (the coalitional bargaining value). This solution has an intuitive economic interpretation using outside options, and it can be either the Nash bargaining solution, for games where the worth of all pairwise coalition is less than a third of the grand coalition value; the Shapely value, for games where the sum of the values created by all pairwise coalitions is greater than the grand coalition value; or the nucleolus, for games where only the 'natural coalition' among two 'natural partners' creates significant value, and those where only the pairwise coalitions including 'a pivotal player' create significant value. Download Paper
This paper identifies a new corporate governance mechanism: sharing control. We show that bargaining problems among multiple controlling shareholders may prevent inefficient investment decisions that harm minority shareholders. The same bargaining problems may block efficient investment decisions, though. By solving this trade-off, we show that the likelihood that shared control is efficient increases with three firm characteristics: overinvestment problems, the cost of verifying cash flows, and financing requirements. The model provides testable implications for the role that large shareholders play in corporate governance, contrasting shared control and monitoring as alternative governance mechanisms. Download Paper