Attitudes and motivations of Economics students: Some recent evidence

There is disagreement amongst economists regarding whether economics students are more self-interested than other students in economic and non-economic contexts. Econometric analysis of the choice to share in a Prisoner´s Dilemma game suggests that it may not be economics students per se that have a lower probability of choosing share rather than compete, but instead that individuals with attitudes, motivations and values similar to those assumed by standard economic theory have a lower probability of choosing share. The experimental evidence here of 1,701 students suggests that it is the motivations and attitudes of subjects that are important for determining economic choices rather than simply whether the individual studies economics. The results confirm that a higher proportion of economics students have motivations in a game theory context that are similar to those assumed by standard economic theory, yet that their related general attitudes and values are not significantly different. Overall the results suggest that the assumptions of standard economic theory are appropriate for a subset of individuals, and for many individuals who do not study economics

Supertropical matrix algebra III: Powers of matrices and generalized eigenspaces

We investigate powers of supertropical matrices, with special attention to the role of the coefficients of the supertropical characteristic polynomial (especially the supertropical trace) in controlling the rank of a power of a matrix. This leads to a Jordan-type decomposition of supertropical matrices, together with a generalized eigenspace decomposition of a power of an arbitrary supertropical matrix.Comment: 21 page

Are people ethical? An experimental approach

Do ethical motivations and attitudes affect behaviour? We examine this issue in six Prisoner´s Dilemma and Prisoner´s Dilemma related games using an online experiment where individuals were asked to make choices and subsequently to express the motivations for their choices and their general attitudes. The experimental evidence of 1,701 students suggests that the motivations and attitudes of respondents regarding altruism, inequality aversion, reciprocity and aversion to lying are important for determining economic choices as well as self-interest. Econometric analysis of the choice to share indicates that ethical and self-interested motives are more important for determining choices than personal characteristics

Are people ethical? An experimental approach

Individual decision making, ethics, experimental economics

Algebraic structures of tropical mathematics

Tropical mathematics often is defined over an ordered cancellative monoid \tM, usually taken to be (\RR, +) or (\QQ, +). Although a rich theory has arisen from this viewpoint, cf. [L1], idempotent semirings possess a restricted algebraic structure theory, and also do not reflect certain valuation-theoretic properties, thereby forcing researchers to rely often on combinatoric techniques. In this paper we describe an alternative structure, more compatible with valuation theory, studied by the authors over the past few years, that permits fuller use of algebraic theory especially in understanding the underlying tropical geometry. The idempotent max-plus algebra $A$ of an ordered monoid \tM is replaced by R: = L\times \tM, where $L$ is a given indexing semiring (not necessarily with 0). In this case we say $R$ layered by $L$. When $L$ is trivial, i.e, $L=\{1\}$, $R$ is the usual bipotent max-plus algebra. When $L=\{1,\infty\}$ we recover the "standard" supertropical structure with its "ghost" layer. When L = \NN we can describe multiple roots of polynomials via a "layering function" $s: R \to L$. Likewise, one can define the layering $s: R^{(n)} \to L^{(n)}$ componentwise; vectors $v_1, \dots, v_m$ are called tropically dependent if each component of some nontrivial linear combination \sum \a_i v_i is a ghost, for "tangible" \a_i \in R. Then an $n\times n$ matrix has tropically dependent rows iff its permanent is a ghost. We explain how supertropical algebras, and more generally layered algebras, provide a robust algebraic foundation for tropical linear algebra, in which many classical tools are available. In the process, we provide some new results concerning the rank of d-independent sets (such as the fact that they are semi-additive),put them in the context of supertropical bilinear forms, and lay the matrix theory in the framework of identities of semirings.Comment: 19 page