On the complexity of cooperative solution concepts
Mathematics of Operations Research
An automated prover for Zermelo-Fraenkel set theory in Theorema
Journal of Symbolic Computation
First-order logic formalisation of Arrow's theorem
LORI'09 Proceedings of the 2nd international conference on Logic, rationality and interaction
The Seventeen Provers of the World
A qualitative comparison of the suitability of four theorem provers for basic auction theory
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
The ForMaRE project: formal mathematical reasoning in economics
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
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Theoretical economics makes use of strict mathematical methods. For instance, games as introduced by von Neumann and Morgenstern allow for formal mathematical proofs for certain axiomatized economical situations. Such proofs can--at least in principle--also be carried through in formal systems such as Theorema. In this paper we describe experiments carried through using the Theorema system to prove theorems about a particular form of games called pillage games. Each pillage game formalizes a particular understanding of power. Analysis then attempts to derive the properties of solution sets (in particular, the core and stable set), asking about existence, uniqueness and characterization. Concretely we use Theorema to show properties previously proved on paper by two of the co-authors for pillage games with three agents. Of particular interest is some pseudo-code which summarizes the results previously shown. Since the computation involves infinite sets the pseudocode is in several ways non-computational. However, in the presence of appropriate lemmas, the pseudo-code has sufficient computational content that Theorema can compute stable sets (which are always finite). We have concretely demonstrated this for three different important power functions.