[6] **viXra:1506.0213 [pdf]**
*replaced on 2015-07-03 08:34:55*

**Authors:** J. S. Markovitch

**Comments:** 13 Pages.

This article concerns the psychology of the paradoxical Two Envelope Problem. The goal is to find instructive variants of the envelope switching problem that are capable of clear-cut resolution, while still retaining paradoxical features. By relocating the original problem into different contexts involving commutes and playing cards the reader is presented with a succession of resolved paradoxes that reduce the confusion arising from the parent paradox. The goal is to reduce confusion by understanding how we sometimes misread mathematical statements; or, to completely avoid confusion, either by reforming language, or adopting an unambiguous notation for switching problems. This article also suggests that an illusion close in character to the figure/ground illusion hampers our understanding of switching problems in general and helps account for the intense confusion that switching problems sometimes generate.

**Category:** General Mathematics

[5] **viXra:1506.0167 [pdf]**
*submitted on 2015-06-23 10:54:52*

**Authors:** C. Coanda, Gh. Duta, Gh. Dragan, J. Ilie, I. Ivanescu, F. Smarandache, L. Tutescu, S. Draghici

**Comments:** 188 Pages.

Probleme de matematica rezolvate, din anii 1991-1997, pentru clasele V-VIII.

**Category:** General Mathematics

[4] **viXra:1506.0140 [pdf]**
*submitted on 2015-06-18 11:17:20*

**Authors:** Stephen I. Ternyik

**Comments:** 3 Pages.

Futuring the legacy of Paul Erdös

**Category:** General Mathematics

[3] **viXra:1506.0136 [pdf]**
*replaced on 2016-06-26 03:11:22*

**Authors:** Giuseppe Rauti

**Comments:** 3 Pages.

Studies in Mathematics.

**Category:** General Mathematics

[2] **viXra:1506.0114 [pdf]**
*submitted on 2015-06-14 16:49:09*

**Authors:** Harris V. Georgiou

**Comments:** 19 Pages. Copyright (c) Harris Georgiou, 2015 - Licensed under Creative Commons Attribution (BY) 3.0

In this paper, a gentle introduction to Game Theory is presented in the form of basic concepts and examples. Minimax and Nash's theorem are introduced as the formal definitions for optimal strategies and equilibria in zero-sum and nonzero-sum games. Several elements of cooperaive gaming, coalitions, voting ensembles, voting power and collective efficiency are described in brief. Analytical (matrix) and extended (tree-graph) forms of game representation is illustrated as the basic tools for identifying optimal strategies and “solutions” in games of any kind. Next, a typology of four standard nonzero-sum games is investigated, analyzing the Nash equilibria and the optimal strategies in each case. Signaling, stance and third-party intermediates are described as very important properties when analyzing strategic moves, while credibility and reputation is described as crucial factors when signaling promises or threats. Utility is introduced as a generalization of typical cost/gain functions and it is used to explain the incentives of irrational players under the scope of “rational irrationality”. Finally, a brief reference is presented for several other more advanced concepts of gaming, including emergence of cooperation, evolutionary stable strategies, two-level games, metagames, hypergames and the Harsanyi transformation.

**Category:** General Mathematics

[1] **viXra:1506.0012 [pdf]**
*submitted on 2015-06-02 10:51:16*

**Authors:** Irsen Virnoy

**Comments:** 1 Page.

A solution for the P versus NP problem.

**Category:** General Mathematics