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Coalition formation as a dynamic process: Journal of Economic Theory, Vol. 110, No. 1. (May 2003), pp. 1-41.We study coalition formation as an ongoing, dynamic process, with payoffs generated as coalitions form, disintegrate, or regroup. A process of coalition formation (PCF) is an equilibrium if a coalitional move to some other state can be "justified" by the expectation of higher future value, compared to inaction. This future value, in turn, is endogenous: it depends on coalitional movements at each node. We study existence of equilibrium PCFs. We connect deterministic equilibrium PCFs with unique absorbing state to the core, and equilibrium PCFs with multiple absorbing states to the largest consistent set. In addition, we study cyclical as well as stochastic equilibrium PCFs.Hideo Konishi, Debraj Ray

Source: Journal of Economic Theory, Vol. 110, No. 1. (May 2003), pp. 1-41.
Buying Supermajoritie s: The American Political Science Review, Vol. 90, No. 2. (1996), pp. 303-315.Minima l winning coalitions have appeared as a key prediction or as an essential assumption of virtually all formal models of coalition formation, vote buying, and logrolling. Notwithstandin g this research, we provide a model showing that supermajority coalitions may be cheaper than minimal winning coalitions. Specifically, if vote buyers move sequentially, and if the losing vote buyer is always granted a last chance to attack the winner's coalition, then minimal winning coalitions will generally not be cheapest, and equilibrium coalitions will generally not be minimal winning. We provide results relating equilibrium coalition size with preferences of the legislators and vote buyers, and we show that minimal winning coalitions should occur in only rare cases. We discuss these results in light of empirical work on coalition size and suggest other possible avenues for testing our model.Tim Groseclose, James Snyder

Source: The American Political Science Review, Vol. 90, No. 2. (1996), pp. 303-315.
Coalition Formation in Non-Democracie s: Review of Economic Studies, Vol. 75, No. 4. (2008), pp. 987-1009.We study the formation of a ruling coalition in non-democratic societies where institutions do not enable political commitments. Each individual is endowed with a level of political power. The ruling coalition consists of a subset of the individuals in the society and decides the distribution of resources. A ruling coalition needs to contain enough powerful members to win against any alternative coalition that may challenge it, and it needs to be self-enforcing , in the sense that none of its subcoalitions should be able to secede and become the new ruling coalition. We present both an axiomatic approach that captures these notions and determines a (generically) unique ruling coalition and the analysis of a dynamic game of coalition formation that encompasses these ideas. We establish that the subgame-perfec t equilibria of the coalition formation game coincide with the set of ruling coalitions resulting from the axiomatic approach. A key insight of our analysis is that a coalition is made self-enforcing by the failure of its winning subcoalitions to be self-enforcing . This is most simply illustrated by the following example: with "majority rule", two-person coalitions are generically not self-enforcing and consequently, three-person coalitions are self-enforcing (unless one player is disproportiona tely powerful). We also characterize the structure of ruling coalitions. For example, we determine the conditions under which ruling coalitions are robust to small changes in the distribution of power and when they are fragile. We also show that when the distribution of power across individuals is relatively equal and there is majoritarian voting, only certain sizes of coalitions (e.g. with majority rule, coalitions of size 1, 3, 7, 15, etc.) can be the ruling coalition.Daro n Acemoglu, Georgy Egorov, Konstantin Sonin

Source: Review of Economic Studies, Vol. 75, No. 4. (2008), pp. 987-1009.
Cohesion in Legislatures and the Vote of Confidence Procedure: The American Political Science Review, Vol. 92, No. 3. (1998), pp. 611-621.We present a framework to analyze the effects of constitutional features on legislative voting with respect to cohesion and the distribution of payoffs. We then apply this framework to parliamentary democracies and show how a prominent feature of decision making in parliaments, the vote of confidence procedure, creates an incentive for ruling coalitions to vote together on policy issues that might otherwise split them. The key feature that creates cohesive voting is the fact that votes on bills are treated as votes on who controls floor access in future periods. As a consequence, legislative majorities capture more of the legislative rents from the minority in parliamentary democracies than in nonparliamenta ry settings.Danie l Diermeier, Timothy Feddersen

Source: The American Political Science Review, Vol. 92, No. 3. (1998), pp. 611-621.
The Time Structure of Self-Enforcing Agreements: Econometrica, Vol. 70, No. 2. (2002), pp. 547-582.A principal and an agent enter into a sequence of agreements. The principal faces an interim participation constraint at each date, but can commit to the current agreement; in contrast, the agent has the opportunity to renege on the current agreement. We study the time structure of agreement sequences that satisfy participation and no-deviation constraints and are (constrained) efficient. We show that every such sequence must, after a finite number of dates, exhibit a continuation that maximizes the agent's payoff over all such efficient, self-enforcing sequences. Additional results are provided for situations with transferable payoffs.Debraj Ray

Source: Econometrica, Vol. 70, No. 2. (2002), pp. 547-582.
Unique stability in simple coalition formation games: Games and Economic Behavior, Vol. 48, No. 2. (August 2004), pp. 337-354.We investigate the uniqueness of stable coalition structures in a simple coalition formation model, for which specific coalition formation games, such as the marriage and roommate models, are special cases that are obtained by restricting the coalitions that may form. The main result is a characterizati on of collections of permissible coalitions which ensure that there is a unique stable coalition structure in the corresponding coalition formation model. In particular, we show that only single-lapping coalition formation models have a unique stable coalition structure for each preference profile, where single-lapping means that two coalitions cannot have more than one member in common, and coalitions do not form cycles. We also give another characterizati on using a graph representation , explore the implications of our results for matching models, and examine the existence of strategyproof coalition formation rules.Szilvia Pápai

Source: Games and Economic Behavior, Vol. 48, No. 2. (August 2004), pp. 337-354.
Coalition and Party Formation in a Legislative Voting Game: Journal of Economic Theory, Vol. 103, No. 1. (March 2002), pp. 49-87.We examine a legislative voting game where decisions are to be made over both ideological and distributive dimensions. In equilibrium legislators prefer to make proposals for the two dimensions together, despite having preferences that are separable over the two dimensions. The equilibria exhibit interaction between the ideological and distributive dimensions, and the set of legislators who approve winning proposals does not always consist of ideologically adjacent legislators. There is more than one ideological decision that has a positive probability of being proposed and approved. We show that legislators can gain from forming political parties, and consider examples where predictions can be made about the composition of parties. Journal of Economic Literature Classification Numbers: D72, C71, C78.Matthew Jackson, Boaz Moselle

Source: Journal of Economic Theory, Vol. 103, No. 1. (March 2002), pp. 49-87.
On the voting power of an alliance and the subsequent power of its members: Social Choice and Welfare, Vol. 28, No. 2. (February 2007), pp. 181-207.Feix, Marc, Lepelley, Dominique, Merlin, Vincent, Rouet, Jean-Louis

Source: Social Choice and Welfare, Vol. 28, No. 2. (February 2007), pp. 181-207.
Coalition Formation with Binding Agreements: The Review of Economic Studies, Vol. 74, No. 4. (October 2007), pp. 1125-1147.Kyle Hyndman, Debraj Ray

Source: The Review of Economic Studies, Vol. 74, No. 4. (October 2007), pp. 1125-1147.
Legislative Bargaining and Coalition Formation: Journal of Economic Theory, Vol. 102, No. 2. (February 2002), pp. 322-353.The finite horizon version of D. P. Baron and J. Ferejohn's [1989, Amer. Polit. Sci. Rev.83, 1181-1206] legislative bargaining model is investigated. With three or more periods, a continuum of divisions is supportable as subgame perfect equilib- ria. There exist equilibria where coalitions larger than a minimal winning coalition receive strictly positive shares. With sufficiently patient players and a sufficiently long horizon, any interior distribution is supportable as an equilibrium. In contrast, a generic uniqueness result applies when introducing heterogenous time preferences. The unique backwards induction equilibrium in the perturbed game is nonstationary, and neither the original (symmetric) nor the perturbed game provides guidance for equilibrium selection in the infinite game. Journal of Economic Literature Classification Numbers: C73, C78, D72, D78, H49.Peter Norman

Source: Journal of Economic Theory, Vol. 102, No. 2. (February 2002), pp. 322-353.

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