{"id":817,"date":"2021-04-18T16:06:26","date_gmt":"2021-04-18T16:06:26","guid":{"rendered":"https:\/\/math.hmc.edu\/su\/?page_id=817"},"modified":"2021-06-05T13:55:39","modified_gmt":"2021-06-05T13:55:39","slug":"math188","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/su\/math188\/","title":{"rendered":"Math 188: Social Choice and Decision Making"},"content":{"rendered":"\n

Term:<\/strong> Summer 2021, May 24 – June 11.<\/p>\n\n\n\n

Course meets: <\/strong>Virtually, Mon-Tue-Thu-Fri, 8:45-noon (Pacific time). The private Zoom link was sent by e-mail, and is also available on the course Sakai page<\/a>.<\/p>\n\n\n\n

Office Hours: <\/strong>By appointment, usually at 1:30pm.<\/p>\n\n\n\n

People make decisions everyday — small ones such as what to eat or wear, to large ones such as which job to take or whether to buy a house. Groups of people also make decisions, such as which president to elect, or what policies to adopt, what business strategies to pursue. Mathematics has much to offer the decision-maker — both in the analysis of strategies and suggestions for a course of action.<\/p>\n\n\n\n

In this course, we will focus on the modeling of individual and group decisions using mathematical techniques from “game theory”, the area of mathematics that was pioneered in the 1950’s by John Nash and others, but now has applications to a wide variety of disciplines: economics, biology, computer science.<\/p>\n\n\n\n

Topics will include: basic concepts of game theory and social choice theory, representations of games, Nash equilibria, utility theory, non-cooperative games, cooperative games, voting games, paradoxes, Arrow’s impossibility theorem, Shapley value, power indices, “fair division” problems, and applications. <\/p>\n\n\n\n

Prerequisites<\/h3>\n\n\n\n

Math 55 (or some experience with discrete math) is recommended, but not required.<\/p>\n\n\n\n

Texts<\/h3>\n\n\n\n