this paper is to study equilibrium binding agreements, the coalition structures that form under such agreements, and the efficiency of the outcomes that result. The approach that we take is in the spirit of cooperative game theory, in the sense that the concept of blocking" by a coalition is one of the primitive features of our analysis. A companion article no. ET962236 0022-0531#97 #25.00 Copyright # 1997 by Academic Press All rights of reproduction in any form reserved

In an electronic marketplace coalition formation allows buyers to enjoy a price discount for each item while combinatorial auction enables buyers to place bids for a bundle of items that are complementary. Coalition formation and combinatorial auction both help to improve the efficiency of a market and have received much attention from economists and computer scientists. But neither in laboratories nor in practice has there been literature on the situations where both coalition formation and combinatorial auctions exist. In this paper we consider an e-market where each buyer places a bid on a combination of items with a reservation cost, and sellers offer price discounts for each item based on volumes. We call coalition formation under this condition a Combinatorial Coalition Formation (CCF) problem since coalition formation is motivated by price discounts on single items while multiple items are complementary for buyers. By artificially dividing the reservation cost of each buyer appropriately among the items we can construct optimal coalitions with respect to each item. We then try to make these coalitions satisfy the complementarity of the items, and thus induce the optimal solution. Based on this idea we present polynomial-time algorithms to find a semi-optimal solution of CCF and a payoff division scheme that is in the core of the coalition when linear price functions are applied, and in the pseudo-core when general price functions are applied. Simulation results show that the algorithms obtain solutions in a satisfactory ratio to the optimal value.

This paper proposes a model for multilateral contracting, where contracts are written and renegotiated over time, and where contracts may impose externalities on other agents. Equilibria always exist and the equilibrium value function is linear and monotonically increasing on the contracts. If the grand coalition, or contracting among all agents, is inefficient we show that bargaining delays arise in positive-externality games and equilibrium inefficiency may remain bounded away from zero even as bargaining frictions converge to zero. Otherwise, if the grand coalition is efficient, there are no bargaining delays, convergence to the grand coalition occurs in a finite number of contracting rounds, and the outcome becomes efficient as players become more patient.

In a Shapley-Shubik assignment problem with a supermodular output matrix, we consider games in which each firm makes a take-it-or-leave-it salary offer to one applicant, and a match is made only when the offer is accepted by her. We consider both one-shot and multistage games. In either game, we show that there can be many equilibrium salary vectors which are higher or lower than the minimal competitive salary vector. If we exclude artificial equilibria, applicants’ equilibrium salary vectors are bounded above by the minimal competitive salary vector, while firms’ equilibrium payoff vectors are bounded below by the payoff vector under the minimal competitive salary vector. This suggests that adopting the minimal competitive salary vector as the equilibrium outcome in decentralized markets does not have a strong justification.

In an oligopoly, prior to choosing quantities/prices, each firm has an opportunity to form pair-wise collaborative links with other firms. These pair-wise links lower costs of production of the firms which form a link. The collection of pair-wise links defines a collaboration network. We study stable and efficient networks under different types of market competition. We find that except under extreme competition, a la Bertrand, firms have an incentive to collaborate with their competitors to lower costs of production. We find that two simple architectures, the complete network, where every firm has a collaboration link with every other firm, and the network with a dominant group, which contains a large number of completely connected firms and several isolated firms, are stable under different market conditions. We also observe that stable networks are often efficient from a social point of view.

Connections seem to matter both at the individual level, in terms how well a person, a firm, or a country does, as well as for the aggregate performance of the system. The advantages that accrue from connections suggest that individuals will find it attractive to invest in forming links with others. However, an individual's links influence the payoffs of other players and hence their incentives to form links. These considerations lead us to formulate a strategic model of link formation.

If agents negotiate openly and form coalitions, can they reach efficient agreements? We address this issue within a class of coalition formation games with externalities where agents' preferences depend solely on the coalition structures they are associated with. We derive Ray and Vohra's (1997) notion of equilibrium binding agreements using von Neumann and Morgenstern abstract stable set and then extend it to allow for arbitrary coalitional deviations (as opposed to nested deviations assumed originally). We show that, while the new notion facilitates the attainment of efficient agreements, inefficient agreements can nevertheless arise.

This paper studies an extensive form game of coalition formation with random proposers in a situation where coalitions impose externalities on other players. It is shown that an agreement will be reached without delay provided that any set of coalitions profit from merging. Even under this strong condition, the formation of the grand coalition is not guaranteed. Therefore, the resulting coalition structure will not necessarily be efficient. The results of this model are compared with the related work of Ray and Vohra (GEB, 1999), which assumes that players move in a predetermined order. The game with random proposers tends to give a large advantage to the proposer, whereas the game with a rule of order tends to favour the responders and may not capture the competition between players. The game with random proposers yields more ecient results for some specific classes of games. However, the results of the two games cannot be ranked in general in terms of efficiency.

The advertising agency business is well known for its highly customized and unorthodox products and production processes, low overhead costs, high turnover, and the importance of knowledge (information) and creative ideas. We develop a model of network formation based on the common practice search process in the advertising industry. This model provides a micro-foundation for knowledge sharing among the advertising agencies despite the severe competition in the industry. Under incomplete information, a costly search by advertisers most likely does not end in the best match. However, agencies have more information than do advertisers about other agencies. This puts agencies in a position to provide an additional service to advertisers by undertaking a part of the search on behalf of advertisers toward the betterment of the match. Early elimination of many agencies in the search process eases the competition among agencies and opens the door for cooperation. A “network ” provides a platform for such cooperation and (strategic) knowledge sharing among the agencies. We define “network ” as a rather small number of tightly related agencies, usually connected by personal friendship, that share their knowledge and creative ideas when there is no conflict of interest. Networks improve the quality of matches and reduce the inefficiency in the advertisers ’ search process. We argue that these informal networks are only

Casual observation reveals that groups of people interact on many levels simultaneously. Examples include political party formation and interaction; the interaction of Sunnis, Shias and Kurds in the Government of Iraq; and labor union and confederation formation. In this paper, a model of hierarchical group structures is developed. The model generalizes the existing coalitional theory in several ways and reveals a new connection between characteristic and partition function theories; that they are both valuable components of an overall theory. The stability concept that emerges is called the core of cores. Several results are presented, including necessary and sufficient conditions for the existence of the core of cores and a theorem that demonstrates the relationship between the cores of each level of the organizational structure and the core of cores. The results establish that stability can arise from any combination of stable and unstable components, and suggest a re-thinking of existing coalitional models, taking into account the effect of “nearby” games. The framework developed here has immediate applications to various topics in political economy and industrial organization, such as representative voting and corporate mergers.