Coalition structure generation in cooperative games with compact representations

This paper presents a new way of formalizing the coalition structure generation problem (CSG) so that we can apply constraint optimization techniques to it. Forming effective coalitions is a major research challenge in AI and multi-agent systems. CSG involves partitioning a set of agents into coalitions to maximize social surplus. Traditionally, the input of the CSG problem is a black-box function called a characteristic function, which takes a coalition as input and returns the value of the coalition. As a result, applying constraint optimization techniques to this problem has been infeasible. However, characteristic functions that appear in practice often can be represented concisely by a set of rules, rather than treating the function as a black box. Then we can solve the CSG problem more efficiently by directly applying constraint optimization techniques to this compact representation. We present new formalizations of the CSG problem by utilizing recently developed compact representation schemes for characteristic functions. We first characterize the complexity of CSG under these representation schemes. In this context, the complexity is driven more by the number of rules than by the number of agents. As an initial step toward developing efficient constraint optimization algorithms for solving the CSG problem, we also develop mixed integer programming formulations and show that an off-the-shelf optimization package can perform reasonably well

Heuristic methods for coalition structure generation

The Coalition Structure Generation (CSG) problem requires finding an optimal partition of a set of n agents. An optimal partition means one that maximizes global welfare. Computing an optimal coalition structure is computationally hard especially when there are externalities, i.e., when the worth of a coalition is dependent on the organisation of agents outside the coalition. A number of algorithms were previously proposed to solve the CSG problem but most of these methods were designed for systems without externalities. Very little attention has been paid to finding optimal coalition structures in the presence of externalities, although externalities are a key feature of many real world multiagent systems. Moreover, the existing methods, being non-heuristic, have exponential time complexity which means that they are infeasible for any but systems comprised of a small number of agents. The aim of this research is to develop effective heuristic methods for finding optimal coalition structures in systems with externalities, where time taken to find a solution is more important than the quality of the solution. To this end, four different heuristics methods namely tabu search, simulated annealing, ant colony search and particle swarm optimisation are explored. In particular, neighbourhood operators were devised for the effective exploration of the search space and a compact representation method was formulated for storing details about the multiagent system. Using these, the heuristic methods were devised and their performance was evaluated extensively for a wide range of input data

Computing optimal coalition structures in polynomial time

The optimal coalition structure determination problem is in general computationally hard. In this article, we identify some problem instances for which the space of possible coalition structures has a certain form and constructively prove that the problem is polynomial time solvable. Specifically, we consider games with an ordering over the players and introduce a distance metric for measuring the distance between any two structures. In terms of this metric, we define the property of monotonicity, meaning that coalition structures closer to the optimal, as measured by the metric, have higher value than those further away. Similarly, quasi-monotonicity means that part of the space of coalition structures is monotonic, while part of it is non-monotonic. (Quasi)-monotonicity is a property that can be satisfied by coalition games in characteristic function form and also those in partition function form. For a setting with a monotonic value function and a known player ordering, we prove that the optimal coalition structure determination problem is polynomial time solvable and devise such an algorithm using a greedy approach. We extend this algorithm to quasi-monotonic value functions and demonstrate how its time complexity improves from exponential to polynomial as the degree of monotonicity of the value function increases. We go further and consider a setting in which the value function is monotonic and an ordering over the players is known to exist but ordering itself is unknown. For this setting too, we prove that the coalition structure determination problem is polynomial time solvable and devise such an algorithm

Heuristic methods for optimal coalition structure generation

The problem of finding the optimal coalition structure arises frequently in multiagent systems. Heuristic approaches for solving this problem are needed because of its computational complexity. This paper studies two such approaches: tabu search and simulated annealing. Through simulations we show that tabu search generates better quality solutions than simulated annealing for coalition games in characteristic function form and those in partition function form

Advances in Negotiation Theory: Bargaining, Coalitions and Fairness

Bargaining is ubiquitous in real-life. It is a major dimension of political and business activities. It appears at the international level, when governments negotiate on matters ranging from economic issues (such as the removal of trade barriers), to global security (such as fighting against terrorism) to environmental and related issues (e.g. climate change control). What factors determine the outcome of negotiations such as those mentioned above? What strategies can help reach an agreement? How should the parties involved divide the gains from cooperation? With whom will one make alliances? This paper addresses these questions by focusing on a non-cooperative approach to negotiations, which is particularly relevant for the study of international negotiations. By reviewing non-cooperative bargaining theory, non-cooperative coalition theory, and the theory of fair division, this paper will try to identify the connection among these different facets of the same problem in an attempt to facilitate the progress towards a unified framework.Negotiation theory, Bargaining, Coalitions, Fairness, Agreements

A Good Opening: The Key to Make the Most of Unilateral Climate Action

In this paper we argue that when a subgroup of countries cooperate on emission reduction, the optimal response of non-signatory countries reflects the interaction between three potentially opposing factors, the incentive to free-ride on the benefits of cooperation, the incentive to expand the demand of fossil fuels, and the incentive to adopt cleaner technologies introduced by the coalition. Using an Integrated Assessment Model with a game theoretic structure we find that cost-benefit considerations would lead OECD countries to undertake a moderate, but increasing abatement effort (in line with the pledges subscribed in Copenhagen). Even if emission reductions are moderate, OECD countries find it optimal to allocate part of their resources to energy R&D and investments in cleaner technologies. International spillovers of knowledge and technology diffusion then lead to the deployment of these technologies in non-signatory countries as well, reducing their emissions. When the OECD group follows more ambitious targets, such as 2050 emissions that are 50% below 2005 levels, the benefits of technology externalities do not compensate the incentives deriving from the lower fossil fuels prices. This suggests that, when choosing their unilateral climate objective, cooperating countries should take into account the possibility to induce a virtuous behaviour in non-signatory countries. By looking at a two-phase negotiation set-up, we find that free-riding incentives spurred by more ambitious targets can be mitigated by means of credible commitments for developing countries in the second phase, as they would reduce lock-in in carbon intensive technologies.Technology Spillovers, Climate Change, Partial Cooperation

Energy Biased Technical Change: A CGE Analysis

This paper studies energy bias in technical change. For this purpose, we develop a computable general equilibrium model that builds on endogenous growth models. The model explicitly captures links between energy, the rate and direction of technical change, and the economy. We derive the equilibrium determinants of biased technical change and show the importance of feedback in technical change, substitution possibilities between final goods, and general-equilibrium effects for the equilibrium bias. If the feedback effect is strong, or the substitution elasticity large, or both, our model tends to a corner solution in which only technologies are developed that are appropriate for production of non-energy intensive goods.Computable general-equilibrium models, Endogenous technical change, Energy, Environment

Pairwise-Stability and Nash Equilibria in Network Formation

Suppose that individual payoffs depend on the network connecting them. Consider the following simultaneous move game of network formation: players announce independently the links they wish to form, and links are formed only under mutual consent. We provide necessary and sufficient conditions on the network link marginal payoffs such that the set of pairwise stable, pairwise-Nash and proper equilibrium networks coincide, where pairwise stable networks are robust to one-link deviations, while pairwise-Nash networks are robust to one-link creation but multi-link severance. Under these conditions, proper equilibria in pure strategies are fully characterized by one-link deviation checks.Network formation, Pairwise-stability, Proper equilibrium