Epistemic Game Theory: Reasoning and Choice (Perea, 2012)

Epistemic Game Theory: Reasoning and Choice (Perea, 2012)

Andres Perea

In everyday life we must often reach decisions while knowing that the outcome will not only depend on our own choice, but also on the choices of others. These situations are the focus of epistemic game theory. Unlike classical game theory, it explores how people may reason about their opponents before they make their final choice in a game.

Packed with examples and practical problems based on stories from everyday life, this is the first textbook to explain the principles of epistemic game theory. Each chapter is dedicated to one particular, natural way of reasoning. The book then shows how each of these ways of reasoning will affect the final choices that can rationally be made and how these choices can be found by iterative procedures. Moreover, it does so in a way that uses elementary mathematics and does not presuppose any previous knowledge of game theory.

A deep read about game theory By Taylor Ellwood VINE VOICE on May 16, 2013

This book is a deep read that will take you on a journey that explores the history of game theory before launching into a version that is based on an Epistemic perspective: how people make decisions using rationality and logic, and how these decisions can be anticipated using logic as well. You do need to have some knowledge of math in order to understand the proofs, otherwise you'll get lost. This book is for an academic audience, so you ideally have a real interest in the academic aspects of game theory. The author does discuss both static and dynamic games, which can be interesting because of what it presents in terms of the knowledge each player has about other players. This book is a dense read, so be prepared for a slog.

"epistemic game theory... attempts to bring game theory back to its basic elements - namely the reasoning by players about their opponents... to date there is no textbook on epistemic game theory, nor is there any other game theory textbook that focuses on the reasoning process of the players. The aim of this book is to fill this gap, by providing a text that concentrates on the way people can reason about their opponents before making a choice in a game... reasoning about your opponents is such an important and natural ingredient of the decision-making process in games."

JLJ - WHYY do the authors of every book I have read on game theory ignore the fact that games emerge, mostly, due the competence-difficulty gap that arises from to the limited brain powers of humans and the (possibly large) complexity of the (game) world? My second WHYY is why do these authors ALL formulate the problems precisely in terms that only they have the resources to solve? Most games go away as "games" when we face them repeated times. We develop heuristics to "solve" or untangle the complexity. We can get better at the games we need for survival, social, or academic purposes when we are able to perform game-based analysis using these heuristics - which might include trial and error learning.

It seems that 1) laying a foundation for untangling the complexity of the situation is the starting point for games, 2) developing heuristics the next point, and 3) developing a framework for analysis the 3rd point. Anything else is, well, just playing games.

p.1-2 In our lives we are continuously asked to make choices - small choices about daily issues, but also big choices with important consequences. Often, the final outcome of a choice does not only depend on our own decision, but also on decisions made by other people surrounding us... Such situations, in which the final outcome does not only depend on your own choice but also on the choices of others, are called games. The discipline that studies such situations is called game theory... The people whose choices directly influence the final outcome are called players... we usually refer to the other players as your opponents... In order to evaluate the possible consequences of your own choice, it is important to form some belief about the likely choices of your opponents, as these will affect the final result... you must reason about your opponents before you can form a reasonable belief about them.. And this reasoning process will precisely be the main topic of this book.

p.2 We have just seen that reasoning about your opponents is a crucial step towards making a good choice in a game. In fact, Oskar Morgenstern - one of the early founders of game theory - had stressed the importance of this reasoning process, in particular to form beliefs about the beliefs of others, in his paper Morgenstern (1935). but strangely enough it is exactly this reasoning step that has largely been overlooked by the game theory literature - including the game theory textbooks - during the last sixty years! This immediately raises the question; Why? [JLJ - interesting as well is the fact that the "internal conversation" does not appear to play a role either, or the forming of a stance or posture]

p.2 epistemic game theory... attempts to bring game theory back to its basic elements - namely the reasoning by players about their opponents... to date there is no textbook on epistemic game theory, nor is there any other game theory textbook that focuses on the reasoning process of the players. The aim of this book is to fill this gap, by providing a text that concentrates on the way people can reason about their opponents before making a choice in a game... reasoning about your opponents is such an important and natural ingredient of the decision-making process in games.

p.13 In everyday life we must often reach decisions while knowing that the outcome will not only depend on our own choice, but also on the choices of others.

p.65 A player in a game is a decision maker who faces uncertainty about the choices to be made by his opponents... Although it seems entirely natural to model a player in a game explicitly as a decision maker under uncertainty, it took game theory a surprisingly long time to do so.

p.65 We say that a player chooses rationally if he makes a choice that maximizes his expected utility, given the subjective probabilistic belief he holds about the opponents' choices... Rational just means that the choice is optimal for some belief, and does not put any restrictions on the belief.

p.146 there is nothing wrong with believing that some of your opponents may have incorrect beliefs about your own beliefs. After all, your opponents cannot look inside your head, so why should they be correct about your beliefs? ...All people think differently, so why should your opponents hold exactly the same beliefs as you do?

p.347 In this part of the book we will study dynamic games, which are situations where a player may have to make several choices over a period of time, and where he may learn about the opponents' previous choices during the game... a player in a dynamic game may have to revise his beliefs about the opponents duing the game... we have to take into account that his beliefs may change during the game.

p.358 a strategy for player i is a complete plan of his choices throughout the game.

p.358 In Part I on static games, we modeled the belief of a player about his opponents' choices by a single probability distribution over the opponents' choices... In a dynamic game things are more complicated. Suppose that a player must make a choice at one of his information sets. To see whether this choice is optimal for this player or not, we must consider the belief this player holds at the moment he must make this choice.

p.359 in a dynamic game, we must be careful to use the right beliefs in order to evaluate a choice by a player. Another difficulty is that in a dynamic game, a player typically chooses more than once, so we do not just evaluate the optimality of one choice, but usually of several choices.

p.379 In the last few sections we developed the idea of common belief in future rationality, which states that you always believe that your opponents will choose rationally now and in the future... An important question is whether common belief in future rationality is always possible. [JLJ - here is where I start to disagree with the authors. How sure are we in the "Painting Chris' house" example, that everything is as it seems? What if Chris was *gasp* running a social science experiment, or Barbara knew our calculating procedure, or something else was amok? We might want to have some margin, or a fallback position where we do not bid. In the real world there is always some degree of ambiguity. Chris might not pay or even have any money. Now you have painted a house and are out the cost of the materials plus a day's time lost. Barbara might retrieve your scrap papers you used to calculate your bid, and see what you are planning to bid. Etc. When I build engineering designs, I always include margin, because the real world does not EVER function exactly like you think it does.]