Abstract
In this chapter I discuss the definitions of complexity that emerged in different areas of science and their relevance to the economic theory of optimal contracts.
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Notes
- 1.
This is similar to possibility to approximate any of uncountable number of real number by a sequence of rational numbers, which belong to a countable set.
- 2.
Turing machine is essentially an idealized version of a computer with an infinite memory.
- 3.
See, for example, Cutland (1980).
- 4.
Some real numbers allow for two different binary expansions, for example, 0.1(0) and 0.0(1), where (a) denotes an infinite series of a, both correspond to 0.5 in the decimal notation. In this case the authors use the one with biggest number of zeros, in this case the first one.
- 5.
For example, one can think of the potential state as a countably infinite set of characteristics, each of which can be either present or absent in the realized state.
- 6.
This definition at first glance seems different from a more standard definition that defines a contract to be incomplete if it does not prescribe actions in some states of nature. See, Anderlini and Felli (1994) for a thorough response to this critique.
- 7.
Some additional care should be taken if the agents' common prior is not absolutely continuous with respect to Lebesgue measure, but this is a purely technical consideration that should not concern as here.
- 8.
Due to risk neutrality of the parties only the expected payments matter.
- 9.
From here on by cost I mean the cost of production of the special widget, unless specified otherwise.
- 10.
The constraint is expressed in terms of the seller’s payoffs. This can be done since the sum of the seller’s and buyer's payoffs conditional on the cost realization is fixed.
- 11.
It is still an open question in the computer science whether \(P = {\text{NP}}\).
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Basov, S. (2016). Complexity Constraints and Optimal Contracts. In: Social Norms, Bounded Rationality and Optimal Contracts. Studies in Economic Theory, vol 30. Springer, Singapore. https://doi.org/10.1007/978-981-10-1041-5_4
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