Bidding and sequential coalition formation with externalities

We study coalition formation games with externalities where each agent’s payoff depends on the entire partition. As in Bloch (Games Econ Behav 14:90–123, 1996) and Ray and Vohra (Games Econ Behav 26:268–336, 1999), we assume that coalitions form sequentially and agreements are irreversible. Instead of a fixed order protocol, we use a “bidding mechanism” (see Pérez-Castrillo and Wettstein in Am Econ Rev 92(5):1577–1587, 2002) to determine proposals and transfers among the agents. We show that such a mechanism facilitates the attainment of efficiency; in particular, our game admits a Markov perfect equilibrium with the property of full dynamic efficiency. In addition, the aggregate equilibrium payoffs of our game exhibit monotonicity in time. Nevertheless, inefficient equilibria can also emerge.     

Sequential Formation of Coalitions Through Bilateral Agreements in a Cournot Setting

We study a sequential protocol of endogenous coalition formation based on a process of bilateral agreements among the players. We apply the game to a Cournot environment with linear demand and constant average costs. We show that the final outcome of any subgame perfect equilibrium of the game is the grand coalition, provided the initial number of firms is high enough and they are sufficiently patient.This research was partially conducted while the first authors were visiting the Department of Economics of the Norwegien School of Economics and Business Administration (Bergen).     

Trading water along a river

A set of agents is located along a river. Each agent consumes certain amount of water he receives from his part of the river basin and may sell certain amount to his downstream agent if it is mutually beneficial. Water trading is restricted to two neighboring agents and an agent can only pass water to his downstream agent. We ask if this restricted trade to neighboring agents can implement an efficient allocation of water. We show that the efficient allocation of water can be achieved through the process of downstream bilateral trading. Specifically, we show that this one way “downstream” trading process implements the unique efficient allocation as well as a welfare distribution. We also show that the welfare distribution is in the core of the associated game of the problem. Moreover, we show that the coalition of agents upstream any agent obtains more welfare with the bilateral trading than with the downstream incremental distribution proposed by Ambec and Sprumont (2002) and less than with the upstream incremental distribution proposed by [Ambec and Ehlers, 2008a] and [Ambec and Ehlers, 2008b].     

Emergent learning behaviour in a simulated organization faced with tasks requiring team effort

We conceptualize organizational learning as a result of the collective learning behaviour of knowledge agents in an organization. Each agent provides a range of attributes that may be required to perform organizational tasks. We devised a computational model consisting of three processes to simulate an organization's response to performing repeated tasks: (1) Expert Selection Process for selecting the winner knowledge agent or lead agent; (2) Plan Formation Process for deciding what additional attributes are needed, but not possessed by the winner expert agent, and iteratively selecting further agents with the needed attributes until the task can be accomplished by the combined attributes of the ‘coalition of agents’ so formed; and (3) Capital Modification Process for rewarding participating agents according to the success of their combined organizational performance. We observed the simulated results for different combinations of three levels of task difficulty (requiring, respectively, 5, 10 and, 15 different attributes, each at a sufficient level in the coalition or team to complete the task), and three levels of selection, during plan formation, for knowledge agent performance (the extent to which selection favours knowledge agents with much capital or large strength versus knowledge agents without much capital or large strength). The simulated organization exhibited aspects of both single loop and double loop learning, in repeatedly performing the same task, and ‘learning to perform the task’ with the smallest possible team.     

Groupstrategyproofness of the egalitarian mechanism for constrained rationing problems

Motivated by applications in many economic environments, Bochet et al. (2010) generalize the classic rationing model (Sprumont 1991) as follows: there is a moneyless market, in which a non-storable, homogeneous commodity is reallocated between agents with single-peaked preferences. Agents are either suppliers or demanders. Transfers between a supplier and a demander are feasible only if they are linked, and the links form an arbitrary bipartite graph. Information about individual preferences is private, and so is information about feasible links: an agent may unilaterally close one of her links if it is in her interest to do so. For this problem they propose the egalitarian transfer solution, which equalizes the net transfers of rationed agents as much as permitted by the bilateral constraints. Furthermore, they show that the egalitarian mechanism elicits a truthful report of both preferences and links. In the variant where demanders are not strategic but demands need to be exactly met Bochet et al. (2013), they propose a similar mechanism for which truthfully reporting the peaks is a dominant strategy, but truthful reporting of links is not.The key contribution of the paper is a comprehensive study of the egalitarian mechanism with respect to manipulation by a coalition of agents. Our main result is that the egalitarian mechanism is group strategyproof : no coalition of agents can (weakly) benefit from jointly misreporting their peaks. Furthermore, we show that the egalitarian mechanism cannot be manipulated – by misreporting links or by misreporting peaks – by any coalition of suppliers (or any coalition of demanders) in the model where both the suppliers and demanders are agents. Our proofs shed light on the structure of the two models and simplify some of the earlier proofs of strategyproofness. An implication of our results is that the well known algorithm of Megiddo (1977) to compute a lexicographically optimal flow in a network is group strategyproof with respect to the source capacities and sink capacities.     

Self-enforcing coalitions with power accumulation

Agents endowed with power compete for a divisible resource by forming coalitions with other agents. The coalition with the greatest power wins the resource and divides it among its members. The agents’ power increases according to their share of the resource.We study two models of coalition formation where winning agents accumulate power and losing agents may participate in further coalition formation processes. An axiomatic approach is provided by focusing on variations of two main axioms: self-enforcement, which requires that no further deviation happens after a coalition has formed, and rationality, which requires that agents pick the coalition that gives them their highest payoff. For these alternative models, we determine the existence of stable coalitions that are self-enforcing and rational for two traditional sharing rules. The models presented in this paper illustrate how power accumulation, the sharing rule, and whether losing agents participate in future coalition formation processes, shape the way coalitions will be stable throughout time.     

Hedonic coalition formation games with variable populations: core characterizations and (im)possibilities

We consider hedonic coalition formation games with variable sets of agents and extend the properties competition sensitivity and resource sensitivity (introduced by Klaus, Games Econ Behav 72:172–186, 2011, for roommate markets) to hedonic coalition formation games. Then, we show that on the domain of solvable hedonic coalition formation games, the Core is characterized by coalitional unanimity and Maskin monotonicity (see also Takamiya, Maskin monotonic coalition formation rules respecting group rights. Niigata University, Mimeo, 2010, Theorem 1). Next, we characterize the Core for solvable hedonic coalition formation games by unanimity, Maskin monotonicity, and either competition sensitivity or resource sensitivity (Corollary 2). Finally, and in contrast to roommate markets, we show that on the domain of solvable hedonic coalition formation games, there exists a solution not equal to the Core that satisfies coalitional unanimity, consistency, competition sensitivity, and resource sensitivity (Example 2).     

Computational complexity in additive hedonic games

We investigate the computational complexity of several decision problems in hedonic coalition formation games and demonstrate that attaining stability in such games remains NP-hard even when they are additive. Precisely, we prove that when either core stability or strict core stability is under consideration, the existence problem of a stable coalition structure is NP-hard in the strong sense. Furthermore, the corresponding decision problems with respect to the existence of a Nash stable coalition structure and of an individually stable coalition structure turn out to be NP-complete in the strong sense.     

Sticks and carrots for the design of international climate agreements with renegotiations

This paper examines renegotiations of international climate agreements for carbon abatement. We explore coalition stability under ‘optimal transfers’ that have been suggested to stabilise international environmental agreements (e.g. McGinty in Oxford Economic Papers 59, 45–62, 2007). Such transfer schemes need to be refined when agreements are renegotiated. We determine the requirements that transfers between signatories of an international climate agreement must satisfy in order to stabilise the sequence of agreements that performs best in terms of provision of the public good ‘carbon abatement’. If these requirements are met, no country wants to change its membership status at any stage. In order to demonstrate the applicability of our result we use the STACO model, a 12-regions global model, to assess the impact of well-designed transfer rules on the stability of an international climate agreement. Although there are strong free-rider incentives, we find a stable grand coalition in the first commitment period in a game with one round of renegotiations if renegotations take place sufficiently early.