On the complexity of undominated core and farsighted solution concepts in coalition games

ABSTRACT In this paper, we study the computational complexity of solution concepts in the context of coalitional games. Firstly, we distinguish two different kinds of core, the undominated core and excess core, and investigate the difference and relationship between them. Secondly, we thoroughly investigate the computational complexity of undominated core and three farsighted solution concepts-farsighted core, farsighted stable set and largest consistent set

A recursive core for partition function form games

We present a new solution to partition function form games that is novel in at least two ways. Firstly, the solution exploits the consistency of the partition function form, namely that the response to a deviation is established as the same solution applied to the residual game, itself a partition function form game. This consistency allows us to model residual behaviour in a natural, intuitive way. Secondly, we consider a pair of solutions as the extrema of an interval for set inclusion. Taking the whole interval rather than just one of the extremes enables us to include or exclude outcomes with certainty.microeconomics ;

Simulating a Sequential Coalition Formation Process for the Climate Change Problem: First Come, but Second Served?

We analyze stability of self-enforcing climate agreements based on a data set generated by the CLIMNEG world simulation model (CWSM), version 1.2. We consider two new aspects which appear important in actual treaty-making. First, we consider a sequential coalition formation process where players can make proposals which are either accepted or countered by other proposals. Second, we analyze whether a moderator, like an international organization, even without enforcement power, can improve upon globally suboptimal outcomes through coordinating actions by making recommendations that must be Pareto-improving to all parties. We discuss the conceptual difficulties of implementing our algorithm.International Climate Agreements, Sequential Coalition Formation, Coordination through Moderator, Integrated Assessment Model, Algorithm for Computations

Sufficient conditions for unique stable sets in three agent pillage games

Pillage games (Jordan, 2006a) have two features that make them richer than cooperative games in either characteristic or partition function form: they allow power externalities between coalitions; they allow resources to contribute to coalitions’ power as well as to their utility. Extending von Neumann and Morgenstern’s analysis of three agent games in characteristic function form to anonymous pillage games, we characterise the core for any number of agents; for three agents, all anonymous pillage games with an empty core represent the same dominance relation. When a stable set exists, and the game also satisfies a continuity and a responsiveness axiom, it is unique and contains no more than 15 elements, a tight bound. By contrast, stable sets in three agent games in characteristic or partition function form may not be unique, and may contain continua. Finally, we provide an algorithm for computing the stable set, and can easily decide non-existence. Thus, in addition to offering attractive modelling possibilities, pillage games seem well behaved and analytically tractable, overcoming a difficulty that has long impeded use of cooperative game theory’s flexibility

Stationary Consistent Equilibrium Coalition Structures Constitute the Recursive Core

We study coalitional games where the proceeds from cooperation depend on the entire coalition structure. The coalition structure core (Kóczy, 2007) is a generalisation of the coalition structure core for such games. We introduce a noncooperative, sequential coalition formation model and show that the set of equilibrium outcomes coincides with the recursive core. In order to extend past results to games that are not totally balanced (understood in this special setting) we introduce subgame-consistency that requires perfectness in relevant subgames only, while subgames that are never reached are ignored.Partition Function, Externalities, Implementation, Recursive Core, Stationary Perfect Equilibrium, Time Consistent Equilibrium

Markets and Jungles

Economic institutions determine prospects for growth and development. This paper examines necessary conditions for an economy to support institutions that implement markets. Agents differ in land holdings, skill, and power. A competitive market assigns land to the skilled, not necessarily to the powerful. Therefore a market allocation needs to be robust to coalitional expropriation. In a dynamic setting, market payoffs may induce sufficient inequality in next period's endowments for markets to alternate with expropriation in a limit cycle, decreasing efficiency and amplifying macroeconomic fluctuations. Long run stability of markets is favored by higher social mobility, more initial equality, and less mismatch between demand and supply. --Expropriation,market institutions,inequality,fluctuations,coalition formation