The strategy structure of some coalition formation games

In coalitional games with side payments, the core predicts which coalitions form and how benefits are shared. The predictions however run into difficulties if the core is empty or if some coalitions benefit from not blocking truthfully. These difficulties are analyzed in games in which an a priori given collection of coalitions can form, as the collection of pairs of buyer-seller in an assignment game. The incentive properties of the core and of its selections are investigated in function of the collection. Furthermore the relationships with Vickrey-Clarke-Groves mechanisms are drawn.coalition formation ; assignment ; manipulability ; substitutes ; incremental value ; Vickrey-Clarke-Groves mechanism

A Theory of Political Influence and Economic Organization

I propose a cooperative game theory model of economic reform in a political environment with interest groups. Agents in a better economic position have strategic advantage in formulating economic policy. Agents bargain over policies because they are associated with different income distributions. In this context I examine the robustness of the `Coase Theorem' prediction of efficient bargaining. I use the Aspiration Core and the Aspiration Bargaining Set as solutions to the cooperative game. Even under zero transaction costs, if endogenous coalition formation is allowed, bargaining between interest groups need not result in efficient economic change because the core may be empty. Indeed, I show that there are inefficient equilibrium outcomes if and only if the core is empty.Political Economy, Interest Groups, Institutional Change, Coalition Formation, Cooperative Games, Aspiration Solution Concepts

Platform Competition with Endogenous Multihoming

A model of two-sided market (for credit cards) is introduced and discussed. In this model, agents can join none, one, or more than one platform (multihoming), depending on access prices and the choices made by agents on the opposite market side. Although emerging multihoming patterns are, clearly, one aspect of equilibrium in a two-sided market, this issue has not yet been thoroughly addressed in the literature. This paper provides a general theoretical framework, in which homing partitions are conceived as one aspect of market equilibrium, rather than being set ex-ante, through ad-hoc assumptions. The emergence of a specific equilibrium partition is a consequence of: (1) the structure of costs and benefits, (2) the degree and type of heterogeneity among agents, (3) the intensity of platform competition.Two-sided markets, Network externalities, Standards, Platforms, Multihoming

Market games and clubs

The equivalence of markets and games concerns the relationship between two sorts of structures that appear fundamentally different -- markets and games. Shapley and Shubik (1969) demonstrates that: (1) games derived from markets with concave utility functions generate totally balanced games where the players in the game are the participants in the economy and (2) every totally balanced game generates a market with concave utility functions. A particular form of such a market is one where the commodities are the participants themselves, a labor market for example. But markets are very special structures, more so when it is required that utility functions be concave. Participants may also get utility from belonging to groups, such as marriages, or clubs, or productive coalitions. It may be that participants in an economy even derive utility (or disutility) from engaging in processes that lead to the eventual exchange of commodities. The question is when are such economic structures equivalent to markets with concave utility functions. This paper summarizes research showing that a broad class of large economies generate balanced market games. The economies include, for example, economies with clubs where individuals may have memberships in multiple clubs, with indivisibile commodities, with nonconvexities and with non-monotonicities. The main assumption are: (1) that an option open to any group of players is to break into smaller groups and realize the sum of the worths of these groups, that is, essential superadditivity is satisfied and :(2) relatively small groups of participants can realize almost all gains to coalition formation. The equivalence of games with many players and markets with many participants indicates that relationships obtained for markets with concave utility functions and many participants will also hold for diverse social and economic situations with many players. These relationships include: (a) equivalence of the core and the set of competitive outcomes; (b) the Shapley value is contained in the core or approximate cores; (c) the equal treatment property holds -- that is, both market equilibrium and the core treat similar players similarly. These results can be applied to diverse economic models to obtain the equivalence of cooperative outcomes and competitive, price taking outcomes in economies with many participants and indicate that such results hold in yet more generality.Markets; games; market games; clubs; core; market-game equivalence; Shapley value; price taking equilibrium; small group effectiveness; inessentiality of large groups; per capita boundedness; competitive equilibrium; games with side payments; balanced games; totally balanced games; local public goods, core convergence; equal treatment property; equal treatment core; approximate core; strong epsilon core; weak epsilon core; cooperative game; asymptotic negligibility

Approximate Cores of Games and Economies with Clubs

This presentation focuses on new approachs to large games introduced in five papers by the authors (one with the same title as this abstract). In a new framework of parameterised collections of games with and without side payments, we provide nonemptiness of approximate core, a law of scarcity, and convergence results. The parameters bound (a) the number of approximate types of players and the size of the approximation and (b) the size of nearly effective groups of players and their distance from exact effectiveness. Our nonemptiness theorems are based on a new notion of partition-balanced profiles and approximately partition-balanced profiles. Our convergence results provide a new sort of application of standard theorems from linear programming. The results are applied to a model of an economy with clubs. In contrast to the extant literature, our approach allows widespread externalities -- that is, the payoffs to members of a club may depend on the economy in which the club is situated.

The strategy structure of some coalition formation games

In coalitional games with side payments, the core predicts which coalitions form and how benefits are shared. The predictions however run into difficulties if the core is empty or if some coalitions benefit from not blocking truthfully. These difficulties are analyzed in games in which an a priori given collection of coalitions can form, as the collection of pairs of buyer-seller in an assignment game. The incentive properties of the core and of its selections are investigated in function of the collection. Furthermore the relationships with Vickrey-Clarke-Groves mechanisms are drawn.Dans un jeu coopératif à paiements latéraux, le coeur prédit quels arrangements de la société sont stables vis-à-vis des possibilités de blocage par les coalitions. Ces prédictions ne sont pas opérationnelles si tout arrangement est bloqué (le coeur est vide) ou si les coalitions n'ont pas d'incitation à bloquer comme le suppose la théorie. Nous analysons ces difficultés dans des jeux où la collection des coalitions qui peuvent se former est a priori restreinte. C'est par exemple le cas dans un jeu de marché lorsque seules les paires acheteur-vendeur sont essentielles. Les propriétés stratégiques du coeur et de ses sélections sont étudiées en fonction de la collection des coalitions admissibles. De plus, les relations avec les mécanismes de Vickrey-Clarke-Groves sont développées

The Cooperative Theory of Two Sided Matching Problems: A Re-examination of Some Results

We show that, given two matchings of which say the second is stable, if (a) no firm prefers the first matching to the second, and (b) no firm and the worker it is paired with under the second matching prefer each other to their respective assignments in the first matching, then no worker prefers the second matching to the first. This result is a strengthening of a result originally due to Knuth (1976). A theorem due to Roth and Sotomayor (1990), says that if the number of workers increases, then there is a non-empty subset of firms and the set of workers they are assigned to under the F – optimal stable matching, such that given any stable matching for the old two-sided matching problem and any stable matching for the new one, every firm in the set prefers the new matching to the old one and every worker in the set prefers the old matching to the new one. We provide a new proof of this result using mathematical induction. This result requires the use of a theorem due to Gale and Sotomayor (1985 a,b), which says that with more workers around, firms prefer the new optimal stable matchings to the corresponding ones of the old two-sided matching problem, while the opposite is true for workers. We provide an alternative proof of the Gale and Sotomayor theorem, based directly on the deferred acceptance procedure.Two-sided matching, Stable

Politics in coalition formation of local governments

We analyze empirically the coalition formation of local governments using a novel reduced form econometric procedure that allows for multi-partner mergers. Using Finnish municipal merger data where mergers were decided independently at the local level, we find that merger decisions are largely in line with voter preferences. Most importantly, mergers are clearly less likely when the distance of the median voter to the coalition centre is large. However, councillors seem also to prefer mergers where post-merger political competition is lower which indicates a concern for re-election. Interestingly, municipalities do not seem to be seeking economies of scale through merging. This is possibly due to existing cooperation in service production which we find to be a strong predictor of merging

Fractional solutions for capacitated NTU-games, with applications to stable matchings

Abstract. In this paper we investigate some new applications of Scarf’s Lemma. First, we introduce the notion of fractional core for NTU-games, which is always nonempty by the Lemma. Stable allocation is a general solution concept for games where both the players and their possible cooperations can have capacities. We show that the problem of finding a stable allocation, given a finitely generated NTU-game with capacities, is always solvable by a variant of Scarf’s Lemma. Then we describe the interpretation of these results for matching games. Finally we consider an even more general setting where players ’ contributions in a joint activity may be different. We show that a stable allocation can be found by the Scarf algorithm in this case as well, and we demonstrate the usage of this method for the hospitals resident problem with couples. This problem is relevant in many practical applications, such as NRM

Core-stable Rings in Auctions with Independent Private Values

We propose a semi-cooperative game theoretic approach to check whether a given coalition is stable in a Bayesian game with independent private values. The ex ante expected utilities of coalitions, at an incentive compatible (noncooperative) coalitional equilibrium, describe a (cooperative) partition form game. A coalition is core-stable if the core of a suitable characteristic function, derived from the partition form game, is not empty. As an application, we study collusion in auctions in which the bidders’ final utility possibly depends on the winner’s identity. We show that such direct externalities offer a possible explanation for cartels’ structures (not) observed in practice.auctions, Bayesian game, collusion, core, partition function game