Strategic Cautiousness as an Expression of Robustness to Ambiguity
Economic predictions often hinge on two intuitive premises: agents rule out the possibility of others choosing unreasonable strategies (‘strategic reasoning’), and prefer strategies that hedge against unexpected behavior (‘cautiousness’). These two premises conflict and this undermines the compatibility of usual economic predictions with reasoning-based foundations. This paper proposes a new take on this classical tension by interpreting cautiousness as robustness to ambiguity. We formalize this via a model of incomplete preferences, where (i) each player's strategic uncertainty is represented by a possibly non-singleton set of beliefs and a (ii) rational player chooses a strategy that is a best-reply to every belief in this set. We show that the interplay between these two features precludes the conflict between strategic reasoning and cautiousness and therefore solves the inclusion-exclusion problem raised by Samuelson (1992). Notably, our approach provides a simple foundation for the iterated elimination of weakly dominated strategies.
In this paper, we propose an interpretation of the Hilbert space method used in quantum theory in the context of decision making under uncertainty. For a clear comparison we will stay as close as possible to the framework of SEU suggested by Savage (1954). We will use the Ellsberg (1961) paradox to illustrate the potential of our approach to deal with well-known paradoxes of decision theory.
The law of accelerating returns can be viewed as a concept that describes acceleration of technological progress. The idea is that tools are used for developing more advanced tools that are applied for creating even more advanced tools etc. A similar idea has been implemented in algorithms for advancing artificial intelligence. In this paper, the results of applying these algorithms in games are discussed. Nevertheless, real life tasks seem more complicated. The game theoretic approach can be applied for transition from theoretical and unrealistic games to more complex and practical tasks. Applications of the game theoretic approach to advance artificial intelligence in solving tasks in the credit industry are proposed.
The authors suggest the organization method of the educational process for system engineers training in blended learning. The concept of a command file, which sets the scenario of on-line and face-to-face course studying parts, is introduced in order to automate the discipline learning. The command file should be developed taking into account the features of the educational trajectory. The paper describes the choosing methods of the most efficient educational trajectory for a specific training group based on the decision theory that can accumulate the opinions of teachers, experts and students.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.