Abstract
We adopt an algorithmic approach in characterizing complete markets and complete contracts. We define a free market to be a market where private ownership is positively valued by market members. In an economy with zero transaction costs, if the market is algorithmically complete, ownership will be worthless. Accordingly, the market can be either free or complete, but not both. For the same reason, the market can be either efficient or complete, but not both.
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Notes
- 1.
This is in accordance with the Church–Turing thesis that states that any intuitively computable task can be performed by a suitable TM.
- 2.
A Turing Machine is total if it executes the code and halts over a “halting state,” i.e. it does not come to abrupt halt nor goes on an infinite computation [7].
- 3.
We of course require that our formal background, represented by our theory, include enough arithmetic. Axioms for \(+\) and \(\times \) plus the so–called trichotomy axiom suffices.
- 4.
For similar theorems see [2].
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Al-Suwailem, S., Doria, F.A. (2020). Can a Free Market Be Complete?. In: Bucciarelli, E., Chen, SH., Corchado, J. (eds) Decision Economics: Complexity of Decisions and Decisions for Complexity. DECON 2019. Advances in Intelligent Systems and Computing, vol 1009. Springer, Cham. https://doi.org/10.1007/978-3-030-38227-8_27
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DOI: https://doi.org/10.1007/978-3-030-38227-8_27
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