Wolfram Computation Meets Knowledge

Wolfram Summer School

Alumni

Valeriu Ungureanu

Technology and Innovation

Class of 2018

Bio

Dr. Valeriu Ungureanu is an associate professor of mathematics and computer science at Moldova State University, the head of the Computer Science Department and the Moldova Wolfram Center. His research projects include game theory problems, optimization methods and Mathematica implementation in education and research. Some of his research papers are fully based on Mathematica applications. Valeriu is aiming to begin creation of a game theory package at the Wolfram Summer School.

Computational Essay

Method of Steepest Descent »

Project: A Game Theory Package for the Wolfram Language

Goal

Theory of games has had an impressive development during the last 70 years, both as a domain of applied mathematics and as a part of various important domains of human activity. It’s somewhat strange that Mathematica doesn’t include any functionality related to game theory. In this project, we intend to initiate a game theory Wolfram Language package. Its theoretical foundations are exposed in our recent monograph Pareto–Nash–Stackelberg Game and Control Theory, Springer International Publishing, 2018.

Main Results in Detail

We have designed a package structure and features that have to be applied to all its functions, their titles and their options. We have created algorithms and respective codes that solve problems of Nash equilibrium set finding as well as Maxmin solutions computing. We have also programmed the code that solves two-matrix, mixed-strategy games. The package includes, withal, a function that plots the Nash equilibrium set in 2×2 mixed-strategy games.

Future Work

We intend to develop the package in several successive stages and directions. At the first initiation stage, we plan to enlarge the number of strategic-form game theory problems solved by the package and to include more plotting possibilities. At the second stage, we intend to develop package functionality in order to solve extensive form games and to include their abundant plotting functionality. At the third stage, we are considering adding support for cooperative games. At the fourth stage, we plan to consider differential games and control. Later stages will include multi-criteria mixtures of simultaneous and sequential games as well as a lot of applied problems from all of the human activity.

Wolfram Summer School | Champaign, IL, USA | July 3 29–July 22, 2022

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