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

Default risk in an interconnected banking system with endogeneous asset markets : [Version: August 2011]

This paper analyzes the emergence of systemic risk in a network model of interconnected bank balance sheets. Given a shock to asset values of one or several banks, systemic risk in the form of multiple bank defaults depends on the strength of balance sheets and asset market liquidity. The price of bank assets on the secondary market is endogenous in the model, thereby relating funding liquidity to expected solvency - an important stylized fact of banking crises. Based on the concept of a system value at risk, Shapley values are used to define the systemic risk charge levied upon individual banks. Using a parallelized simulated annealing algorithm the properties of an optimal charge are derived. Among other things we find that there is not necessarily a correspondence between a bank's contribution to systemic risk - which determines its risk charge - and the capital that is optimally injected into it to make the financial system more resilient to systemic risk. The analysis has policy implications for the design of optimal bank levies. JEL Classification: G01, G18, G33 Keywords: Systemic Risk, Systemic Risk Charge, Systemic Risk Fund, Macroprudential Supervision, Shapley Value, Financial Networ

Algorithms for Graph-Constrained Coalition Formation in the Real World

Coalition formation typically involves the coming together of multiple, heterogeneous, agents to achieve both their individual and collective goals. In this paper, we focus on a special case of coalition formation known as Graph-Constrained Coalition Formation (GCCF) whereby a network connecting the agents constrains the formation of coalitions. We focus on this type of problem given that in many real-world applications, agents may be connected by a communication network or only trust certain peers in their social network. We propose a novel representation of this problem based on the concept of edge contraction, which allows us to model the search space induced by the GCCF problem as a rooted tree. Then, we propose an anytime solution algorithm (CFSS), which is particularly efficient when applied to a general class of characteristic functions called $m+a$ functions. Moreover, we show how CFSS can be efficiently parallelised to solve GCCF using a non-redundant partition of the search space. We benchmark CFSS on both synthetic and realistic scenarios, using a real-world dataset consisting of the energy consumption of a large number of households in the UK. Our results show that, in the best case, the serial version of CFSS is 4 orders of magnitude faster than the state of the art, while the parallel version is 9.44 times faster than the serial version on a 12-core machine. Moreover, CFSS is the first approach to provide anytime approximate solutions with quality guarantees for very large systems of agents (i.e., with more than 2700 agents).Comment: Accepted for publication, cite as "in press