Coalition formation in general NTU games

A general nontransferable utility (NTU) game is interpreted as a collection of pure bargaining games that can be played by individual coalitions. The threatpoints or claims points respectively, in these pure bargaining games reflect the players' opportunities outside a given coalition. We develop a solution concept for general NTU games that is consistent in the sense that the players' outside opportunities are determined by the solution to a suitably defined reduced game. For any general NTU game the solution predicts which coalitions are formed and how the payoffs are distributed among the players.     

May’s theorem in an infinite setting

We generalize May’s theorem to an infinite setting, preserving the elementary character of the original theorem. We define voting scenarios and generalized voting scenarios, and prove appropriate versions of May’s theorem. The case of generalized voting scenarios specialized to a countably infinite set of voters and the collections of all coalitions that have asymptotic density, shows that majority rule is the only aggregation rule that satisfies neutrality, irrelevance of null coalitions, anonymity, and positive responsiveness.     

Coalition structure values in differential information economies: is unity a strength?

The coalition structure (CS) value, introduced by Owen [G. Owen, Values of games with a priori unions, in: Essays in Mathematical Economics and Game Theory, Springer Verlag, Berlin, 1977] and Hart and Kurz [Econometrica 51 (1983) 1047], generalizes the Shapley value to social situations where coalitions form for the purpose of bargaining. This paper introduces the CS value to economies with differential information. We show that the private CS values exists and is Bayesian incentive compatible. Moreover, we construct examples that go against the intuitive viewpoint that “unity is strength”. In particular, we consider a three-person economy in which two agents bargain as a unit against the third agent. We show that bargaining as a unit is advantageous if and only if information is complete. This result sheds new light on bargaining under differential information.     

Countervailing power? Collusion in markets with decentralized trade

We consider the collective incentives of buyers and sellers to form cartels in markets with decentralized trade and pairwise bargaining. Cartels are coalitions of buyers or sellers that limit market participation and compensate inactive members for their abstention. In stable market outcomes, cartels set Nash equilibrium quantities and cartel memberships are immune to deviations. The set of stable market outcomes is non-empty and its full characterization is provided. Stable market outcomes are of two types: (i) at least one cartel restrains trade and market participation is balanced; (ii) only one cartel is active and it reduces trade slightly below the opponent’s.     

A non-cooperative interpretation of bargaining sets

This paper provides a non-cooperative interpretation for bargaining sets concepts in economic environments. We investigate the implementability of the Aumann-Maschler and Mas-Colell bargaining sets, and provide mechanisms whose subgame perfect equilibrium outcomes realize these sets. These mechanisms, in contrast to general mechanisms suggested in the implementation literature, have a natural structure closely related to that of the rationale underlying the bargaining sets. Furthermore, the strategy sets consist mainly of allocations and coalitions (thus avoiding any reference to preference parameters) and are finite dimensional. Received: 17 February 1997 / Accepted: 2 February 1999     

On the non-emptiness of the Mas-Colell bargaining set

We introduce an extension of the Mas-Colell bargaining set and construct, by an elaboration on a voting paradox, a superadditive four-person non-transferable utility game whose extended bargaining set is empty. It is shown that this extension constitutes an upper hemicontinuous correspondence. We conclude that the Mas-Colell bargaining set of a non-levelled superadditive NTU game may be empty.     

A noncooperative approach to the Mas-Colell bargaining set

We propose an extensive form game to give a noncooperative interpretation of the Mas-Colell bargaining set for transferable utility games. Based on the objection and counterobjection in the sense of the Mas-Colell bargaining set, a bilateral negotiation is designed in our model. We show that the equilibrium outcomes of our extensive form game coincide with the Mas-Colell bargaining set in the supperadditive environments.     

Negotiation games with unobservable mixed disagreement actions

A negotiation model combines an alternating offers bargaining game with a normal form stage game that determines players’ (interim) disagreement payoffs. Busch and Wen [Econometrica 63 (1995) 545] investigated this negotiation model under the assumption that players’ past mixed disagreement actions are observable. The question arises if this assumption is a substantial restriction. In this paper, we adopt the more plausible assumption that only the realizations of past mixed actions are observable, and find that the set of equilibrium payoffs shrinks, compared to that when mixed disagreement actions are observable. We precisely identify the effects of the unobservability and characterize the limiting set of equilibrium payoffs as the two players become sufficiently patient.     

A bargaining set for roommate problems

Since stable matchings may not exist, we propose a weaker notion of stability based on the credibility of blocking pairs. We adopt the weak stability notion of Klijn and Massó (2003) for the marriage problem and we extend it to the roommate problem. We first show that although stable matchings may not exist, a weakly stable matching always exists in a roommate problem. Then, we adopt a solution concept based on the credibility of the deviations for the roommate problem: the bargaining set. We show that weak stability is not sufficient for a matching to be in the bargaining set. We generalize the coincidence result for marriage problems of Klijn and Massó (2003) between the bargaining set and the set of weakly stable and weakly efficient matchings to roommate problems. Finally, we prove that the bargaining set for roommate problems is always non-empty by making use of the coincidence result.     

The veto mechanism in atomic differential information economies

We establish new characterizations of Walrasian expectations equilibria based on the veto mechanism in the framework of differential information economies with a complete finite measure space of agents. We show that it is enough to consider the veto power of a single coalition, consisting of the entire set of agents, to obtain the Aubin private core. Moreover, we investigate on the veto power of arbitrarily small and big coalitions, providing an extension to mixed markets of well known Schmeidler (1972) and Vind’s (1972) results in terms of Aubin private core allocations.     

Reject and renegotiate: The Shapley value in multilateral bargaining

This paper investigates three distinctive and intuitive renegotiation bargaining protocols that all yield the Shapley value as the unique subgame perfect equilibrium outcome. These protocols, built on the multi-bidding procedure of Pérez-Castrillo and Wettstein (2001), allow more freedom in multilateral bargaining where rejected players can further negotiate and form coalitions. The self-duality of the Shapley value plays a key role in the second and third results. Moreover, these renegotiation protocols allow an actual play along the equilibrium path to restore the Shapley value in case of a ‘mistake’ made before.     

Locally lipschitz cooperative games

A locally Lipschitz cooperative generalized game is described by its coalition worth function v defined on the set [0, 1]ⁿ of generalized (or fuzzy) coalitions of n players. We assume that v is positively homogeneous and locally Lipschitz. We propose the Clarke's generalized gradient ∂v(c^N) of v at the coalition c^N=(1,…,1) of all players as a set of solutions, and we study its property. We point out that it coincides with the core when v is super–additive and to the Shapley value when v is smooth.     

Time horizons matter: the hazard rate of coalition governments and the size of government

This study examines how coalition governments affect the size of government, measured by total central government expenditure as a share of GDP. Existing studies suggest that the presence of multiple political parties within ruling coalitions generate common pool resource problems or bargaining inefficiencies which, in turn, leads to more government spending when coalition governments are in office. We demonstrate that coalition governments have shorter time horizons than single party governments and use that finding to motivate a simple formal model. The model shows that coalition governments have greater incentives to increase government spending because of a lower discount factor in office. Results from empirical models estimated on a global sample of 111 democracies between 1975 and 2007 provide strong statistical support for the aforementioned theoretical prediction. The empirical results remain robust when we control for alternative explanations, employ different estimation techniques, and use different measures of government spending.     

Privatisation and vertical integration under a mixed duopoly

This paper analyses the privatisation of public firms when private firms may be vertically integrated with their suppliers. We consider a mixed duopoly with a vertically integrated public firm. The private firm bargains the price of the input with its supplier if they are not vertically integrated. We find that for a given bargaining power of the private firm, it vertically integrates with its supplier if goods are weak substitutes. We also find that there is less vertical integration in the mixed duopoly than in the private duopoly. Finally, in general, the public firm is privatised when goods are close substitutes and the bargaining power of the private firm is low enough.     

Measuring the set of blocking coalitions in infinite dimensional economies

The classical core-Walras equivalence is investigated via the measurement of the set of blocking coalitions. In the framework of continuum economies with an infinite dimensional space of commodities, we find the measure of the set of coalitions that block a non-competitive Pareto optimal allocation. Then, from the relation between coalitions of a continuum economy with a finite number of types and fuzzy coalitions of an economy with finitely many agents, the previous results are translated as results on the measure of blocking fuzzy coalitions. Both results imply classically formulated core-Walras equivalence theorems. Finally, the measure of blocking "social communication structures" is determined.     

Trading bargaining weights

We consider a model, in which two agents are engaged in two separate bargaining problems. We introduce a notion of bargaining weights (bargaining power), which is basically given by asymmetric versions of the Perles–Maschler bargaining solution. Thereby, we view bargaining power as ordinary goods that can be traded in an exchange economy. With equal initial endowment of bargaining power there exists a Walrasian equilibrium in this exchange economy such that the utility allocation in equilibrium coincides with the Perles–Maschler bargaining solution of the aggregate bargaining problem. Equilibrium prices are given by the primitives of the two bargaining problems.     

Trading bargaining weights

We consider a model, in which two agents are engaged in two separate bargaining problems. We introduce a notion of bargaining weights (bargaining power), which is basically given by asymmetric versions of the Perles–Maschler bargaining solution. Thereby, we view bargaining power as ordinary goods that can be traded in an exchange economy. With equal initial endowment of bargaining power there exists a Walrasian equilibrium in this exchange economy such that the utility allocation in equilibrium coincides with the Perles–Maschler bargaining solution of the aggregate bargaining problem. Equilibrium prices are given by the primitives of the two bargaining problems.     

Price and Quantity Competition in a Differentiated Duopoly with Upstream Suppliers

This paper analyzes the noncooperative game on the choice of strategic variable to set in duopoly in the presence of an upstream market for the input. For the case of labor input, the analysis shows that if the wage is the result of decentralized firm-union bargain, a duopoly producing substitutes may choose to compete either in the quantity space or in the price space, depending upon the distribution of bargaining power in the wage negotiation and the union's relative preference over the wage. For the case of input suppliers as profit-maximizing firms, the paper shows that a vertically differentiated duopoly may prefer to compete either in the quantity space or in a mixed strategy setting where the high-quality firm plays price and the low-quality firm plays quantity, depending upon the extent of substitutability, the degree of vertical product differentiation and the distribution of bargaining power in the input price negotiation.     

Stagnation proofness in n-agent bargaining problems

Journal of Economic Interaction and Coordination - Some bargaining solutions may remain unchanged under any extension of a bargaining set which does not affect the utopia point, despite the fact...