Cat's Dilemma

We study a simple example of a sequential game illustrating problems connected with making rational decisions that are universal for social sciences. The set of chooser's optimal decisions that manifest his preferences in case of a constant strategy of the adversary (the offering player), is investigated. It turns out that the order imposed by the player's rational preferences can be intransitive. The presented quantitative results imply a revision of the "common sense" opinions stating that preferences showing intransitivity are paradoxical and undesired.

Quantum Cat's Dilemma: an Example of Intransitivity in a Quantum Game

We study a quantum version of the sequential game illustrating problems connected with making rational decisions. We compare the results that the two models (quantum and classical) yield. In the quantum model intransitivity gains importance significantly. We argue that the quantum model describes our spontaneously shown preferences more precisely than the classical model, as these preferences are often intransitive.

Do transitive preferences always result in indifferent divisions?

The transitivity of preferences is one of the basic assumptions used in the theory of games and decisions. It is often equated with rationality of choice and is considered useful in building rankings. Intransitive preferences are considered paradoxical and undesirable. This problem is discussed by many social and natural sciences. The paper discusses a simple model of sequential game in which two players in each iteration of the game choose one of the two elements. They make their decisions in different contexts defined by the rules of the game. It appears that the optimal strategy of one of the players can only be intransitive! (the so-called \textsl{relevant intransitive strategies}.) On the other hand, the optimal strategy for the second player can be either transitive or intransitive. A quantum model of the game using pure one-qubit strategies is considered. In this model, an increase in importance of intransitive strategies is observed -- there is a certain course of the game where intransitive strategies are the only optimal strategies for both players. The study of decision-making models using quantum information theory tools may shed some new light on the understanding of mechanisms that drive the formation of types of preferences.Comment: 16 pages, 5 figure

Dimensional Consistency Analysis in Complex Algebraic Models

Relations in complex algebraic models include numerous variables and parameter that capture the physical dimensions of the objects represented in models (such as "mass", or "volume" of an object). A model developer must ensure the semantic correctness of the model, which includes consistency across physical dimensions and their units of measure in the model relations. Such dimensional consistency analysis is the subject of the research described in this paper. We propose a new methodological framework for this type of analysis which comprises: - a two-level structure for representing knowledge about physical dimensions and units of measure; and - the dimensional analysis algorithm that uses this structured knowledge for the verification of consistency. The proposed methodology allows us to resolve issues related to handling complex non-decomposable units of measure and the situation when instances of the same physical dimension are associated with different physical quantities. We illustrate the proposed methodological framework using mathematical relations from a comprehensive environmental model developed at IIASA