## Using Theorema in the Formalization of Theoretical Economics

Venue: | Proceedings CICM 2011, pages 58–73, 2011. + 11] [KW11] [Lan11] [Lib10 |

Citations: | 2 - 1 self |

### BibTeX

@INPROCEEDINGS{Kerber_usingtheorema,

author = {Manfred Kerber and Colin Rowat and Wolfgang Windsteiger},

title = {Using Theorema in the Formalization of Theoretical Economics},

booktitle = {Proceedings CICM 2011, pages 58–73, 2011. + 11] [KW11] [Lan11] [Lib10},

year = {}

}

### OpenURL

### Abstract

Abstract. 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. 1

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Citation Context ...omic theory which have been formalized. Arrow’s theorem in social choice has attracted the most attention, including studies by Wiedijk [18] using Mizar, Nipkow [15] using HOL, and Grandi and Endriss =-=[6]-=- using Prover9. Noncooperative game theory has also received attention, including by Vestergaard and co-authors [16] with Coq. The formalization of a particular game form in economics can be interesti... |

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Citation Context ...tive game. Related is work on other axiomatic proofs within economic theory which have been formalized. Arrow’s theorem in social choice has attracted the most attention, including studies by Wiedijk =-=[18]-=- using Mizar, Nipkow [15] using HOL, and Grandi and Endriss [6] using Prover9. Noncooperative game theory has also received attention, including by Vestergaard and co-authors [16] with Coq. The formal... |

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Citation Context ...ency of swapping, which is trivial but still automatically verified based on the definition of σ1,2. These proofs, and all that will follow, have been generated by the Theorema set theory prover, see =-=[20]-=-. Equipped with Lemma[“perm swap”] and Lemma[“ANswap”] in the knowledge base, a three page humanunderstandable proof of the two directions of Lemma 2 is obtained. Note, however that the introduction o... |

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(Show Context)
Citation Context ... general properties about pillage games (such as the finiteness of the stable set) and investigated the possibilities of three particular power functions for arbitrarily many agents. Kerber and Rowat =-=[10]-=- studied an infinite class of power functions for three agents. In particular they gave a complete characterization of the stable set for arbitrary power functions (with three agents) which satisfy th... |