Abstract
We introduce Transformation Games (TGs), a form of coalitional game in which players are endowed with sets of initial resources, and have capabilities allowing them to derive certain output resources, given certain input resources. The aim of a TG is to generate a particular target resource; players achieve this by forming a coalition capable of performing a sequence of transformations from its combined set of initial resources to the target resource. After presenting the TG model, and discussing its interpretation, we consider possible restrictions on the transformation chain, resulting in different coalitional games. After presenting the basic model, we consider the computational complexity of several problems in TGs, such as testing whether a coalition wins, checking if a player is a dummy or a veto player, computing the core of the game, computing power indices, and checking the effects of possible restrictions on the coalition. Finally, we consider extensions to the model in which transformations have associated costs.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Babaioff, M., Walsh, W.E.: Incentive-compatible, budget-balanced, yet highly efficient auctions for supply chain formation. Decision Support Systems (2005)
Bachrach, Y., Markakis, E., Resnick, E., Procaccia, A.D., Rosenschein, J.S., Saberi, A.: Approximating power indices: theoretical and empirical analysis. The Journal of Autonomous Agents and Multi-Agent Systems 20(2), 105–122 (2010)
Bachrach, Y., Rosenschein, J.S.: Coalitional skill games. In: AAMAS 2008 (2008)
Bachrach, Y., Rosenschein, J.S.: Power in threshold network flow games. The Journal of Autonomous Agents and Multi-Agent Systems 18(1), 106–132 (2009)
Bachrach, Y., Rosenschein, J.S., Porat, E.: Power and stability in connectivity games. In: AAMAS 2008 (2008)
Chen, R., Roundy, R., Zhang, R., Janakiraman, G.: Efficient auction mechanisms for supply chain procurement. Manage. Sci. 51(3), 467–482 (2005)
Deng, X., Papadimitriou, C.H.: On the complexity of cooperative solution concepts. Mathematics of Operations Research 19(2), 257–266 (1994)
Denzinger, J., Kronenburg, M.: Planning for distributed theorem proving. In: Görz, G., Hölldobler, S. (eds.) KI 1996. LNCS (LNAI), vol. 1137, pp. 43–56. Springer, Heidelberg (1996)
Elkind, E., Goldberg, L., Goldberg, P., Wooldridge, M.: Computational complexity of weighted threshold games. In: AAAI 2007 (2007)
Fisher, M., Wooldridge, M.: Distributed problem-solving as concurrent theorem proving. In: Boman, M., Van de Velde, W. (eds.) MAAMAW 1997. LNCS, vol. 1237. Springer, Heidelberg (1997)
Genesereth, M.R., Nilsson, N.: Logical Foundations of Artificial Intelligence. Morgan Kaufmann Publishers, San Mateo (1987)
Lenat, D.B.: BEINGS: Knowledge as interacting experts. In: IJCAI 1975, pp. 126–133 (1975)
Osborne, M.J., Rubinstein, A.: A Course in Game Theory. MIT Press, Cambridge (1994)
Ostrovsky, M.: Stability in supply chain networks. American Economic Review 98(3), 897–923 (2008)
Wooldridge, M., Dunne, P.E.: On the computational complexity of coalitional resource games. Artificial Intelligence 170(10), 853–871 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bachrach, Y., Zuckerman, M., Wooldridge, M., Rosenschein, J.S. (2010). Proof Systems and Transformation Games. In: Hliněný, P., Kučera, A. (eds) Mathematical Foundations of Computer Science 2010. MFCS 2010. Lecture Notes in Computer Science, vol 6281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15155-2_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-15155-2_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15154-5
Online ISBN: 978-3-642-15155-2
eBook Packages: Computer ScienceComputer Science (R0)