## Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

## Description

This class will focus on the foundations and philosophical applications of Bayesian decision theory, game theory, and the theory of collective choice. We will be interested in general questions about the nature of practical rationality, contrasting interpretations of probability and of utility, the status of the principle of expected utility, with the application of these concepts to the study of the interaction of different rational agents in competitive and cooperative situations, and with the relationship between individual values and the values of groups, institutions and societies. We will try to connect an examination of the basic concepts of Bayesian decision theory with philosophical questions about the nature of action, personal identity, deliberation and responsibility, and an examination of the basic concepts of game theory and social choice theory with philosophical questions about the interaction of epistemic and causal concepts, individual and group decision making, and the nature of meaning and communication.

## Prerequisites

There are no prerequisites for this course.

## Texts

The following book will provide the main framework for the class:

Resnik, Michael. *Choices: An Introduction to Decision Theory*. Minneapolis, MN: University of Minnesota Press, 1987. ISBN: 9780816614400.

This will be supplemented with material that will be made available, as we go, including readings from five other books:

Jeffrey, Richard. *The Logic of Decision*. 2nd ed. Chicago, IL: University of Chicago Press, 1990. ISBN: 9780226395821.

Schelling, Thomas. *The Strategy of Conflict*. Cambridge, MA: Harvard University Press, 2008. ISBN: 9780674840317.

Joyce, James M. *The Foundations of Causal Decision Theory*. Cambridge, UK: Cambridge University Press, 1999. ISBN: 9780521641647.

Leyton-Brown, Kevin, and Yoav Shoham. *Essentials of Game Theory: A Concise, Multidisciplinary Introduction*. San Rafael, CA: Morgan and Claypool Publishers, 2008. ISBN: 9781598295931.

Sen, Amartya K. *Choice, Welfare, and Measurement*. Cambridge, MA: MIT Press, 1982. ISBN: 9780262192149.

## Grading

ACTIVITIES | PERCENTAGES |
---|---|

Written assignment 1 | 25% |

Written assignment 2 | 25% |

Final exam | 50% |

The required work for the class will consist of a sequence of short writing assignments, some more like problem sets, some more like short papers. The problem sets are ungraded. There will also be a final exam during the exam period in May.

## Calendar

We will spend a little more than a third of the term on individual decision theory, a little more than a third on game theory, and the rest of the time on the theory of social choice. In each part, we will start with the basic technical apparatus, but we will try to keep it simple, developing only as much of the technical framework as we need to raise the conceptual and philosophical questions that will be our main concern.

SES # | TOPICS | KEY DATES |
---|---|---|

1 | Introduction: What is rationality? | |

I. Individual decision theory |
||

2-10 |
Preference, ignorance and risk Probability – subjective and objective Utility and value Causal decision theory |
Problem set 1 out 1 day after Ses #4 and due in Ses #6 Short paper 1 out 1 day after Ses #9 |

II. Game theory |
||

11-19 |
The basic framework Nash Equilibrium and other solution concepts Game theory and individual decision theory Coordination games, bargaining and negotiation |
Short paper 1 due in Ses #12 Short paper 2 out 1 day after Ses #16 and due 2 days after Ses #19 |

III. Theory of collective choice |
||

20-26 |
Defining social value in terms of individual value Arrow's theorem, and other impossibility results Interpersonal comparisons of utility |