Introduction to Mathematical F Book

While the ideas on game theory contained herein are interesting, the presentation lacks the pizzazz of "Thinking Strategically" by Dixit and Nalebuff. Kreps's effort is a little more technical and, therefore, dry. He spends a lot of time introducing and defining terminology and somewhat less exploring and applying those terms. This book prepares you to speak intelligently about game theory, but doesn't itself speak much about it. For the intelligent layman looking to learn about the topic, select "Thinking Strategically" instead.

Here are some brief notes jotted down from this book:

Book focuses on basic concepts of non-cooperative game theory. Introduces terminology and concepts, which help analyze our strategic intuition and behavior.

Terminology
2 branches of game theory:
1. co-operative - unit of analysis is the group, aka coalition
2. non-cooperative - unit of analysis is the individual

2 forms of economic game theory models:
1. strategic form (aka normal form) is comprised of:
a. a list of participants, or players
b. for each player, a list of strategies
c. for each array of strategies, one for each player, a list of payoffs that players receive
2. extensive form - looks like a tree (arborescence), has nodes and arrows
Kreps says: "To every extensive form game there is a corresponding strategic form game, where we think of the players simultaneously choosing strategies that they will implement. But a given strategic form game can, in general, correspond to several different extensive form games."

Information set - what the players know

Solution techniques - methods of predicting player behavior. 2 types:
1. dominance arguments - logic of dominance tells you what won't happen (e.g., players won't knowingly choose lower payoff). 2 types of dominance:
a. simple dominance - first step
b. recursive or iterated or successive - chain of inferences
2. equilibrium analysis or Nash equilibrium - an array of strategies, one for each player, such that no player has an incentive (in terms of improving his own payoff) to deviate from his part of the strategy array. The criterion is that each player is maximizing on his own, given the supposed actions of the others.
a. Classic example is prisoner's dilemma

Incredible threats or promises - threats or promises where the ex ante incentives to make them do not match the ex post incentives to carry them out. Lots of examples:
1. Government promises oil developers that it won't hike taxes after production comes online
2. An artist promises to destroy a mold after only a few copies are made
3. A firm is considering entry into a market and threatens the monopolist that it will produce units at a loss unless monopolist cuts back on its production

Credible threats or promises - when threat/promise is accompanied by actions which make keeping the threat/promise more likely ex post

Folk theorem - shows that any payoffs for the 2 firms that give each more than zero (more than the worst payoff the other can inflict upon them) and sum to less than monopoly profits (per period) can be sustained in an equilibrium, if the future is weighted heavily enough by each.

Specific strategic suggestions:
Imagine 2 companies with identical products who must set prices simultaneously. Lower pricing wins bids. The strategy is to "compete in restrained fashion as long as your rival has a reputation for restrained competition, and slash prices otherwise."

A competition some years back asked economists to submit computer programs to negotiate. The winning program played a simple strategy of "tit-for-tat," wherein the program mimicked the opponent's prior move. Though it never beat an individual opponent, it had the highest return in the aggregate as it cooperated with cooperative opponents and responded to aggression with aggression.