The Complete Idiot’s Guide to Game Theory - by Edward Rosenthal Ph.D.

ISBN: 161564055X
Date read: 2024-12-21
How strongly I recommend it: 6/10
(See my list of 360+ books, for more.)

Go to the Amazon page for details and reviews.

Great introduction to the subject.

my notes

Game theory is all about choosing what to do in the face of uncertain outcomes and scheming adversaries.

Game theory is about anticipating how others will act.
Anticipate the decisions that others are making.

The solutions are called equilibria because the players arrive at a point where their outcomes can’t be improved by any different choice of strategy.

A game is in strategic form when a table is used to enumerate the strategies for the two players as rows and columns, and the entries in the table indicate the outcomes.

A pair of numbers in each cell: each pair consists of a
1 to represent victory and a
-1 to represent defeat.
Notice how adding together 1 and -1 equals zero, as in “zero sum.”

An extensive form game is represented by a branching diagram in which the branches represent alternatives available to the players.

They begin with a single point, or node.
Each node, represented by a circle in the diagram, indicates when a player has a decision to make.
Different moves, or actions, are represented by branching lines that fan out (from left to right) from the starting node.
Each branch leads to another node, at which point either another decision takes place, or else the game ends with a certain payoff.

Chess (and checkers, Go, and tic-tac-toe), every information set is a single node.
In other words, nothing is hidden, so every time one player makes a move, they both know the resulting configuration.
Such games are called games of perfect information.

With games of incomplete information the solution involves trying to gauge the other players’ utilities.
In other words, the monetary outcomes or, at least, the relative preferences, of the other players.

These unknown evaluations are called types (as in, what type of folks we are up against).

Cooperative games: situations in which players are better off when they join up with others.
People benefit by forming subsets called coalitions.
List all of the possible coalitions that can be formed, together with what each coalition is able to accomplish by way of costs or profits, when cooperation is limited to just that coalition.
Each coalition’s value is determined solely by what they are able to accomplish on their own, without the participation of the remaining players.

The single most important idea in game theory: always put yourself in the other player’s position.
Ask what they would do.

People are often irrational in certain, often predictable, ways.

Events that directly impact us are completely out of our control.
Game theorists call these events states of nature.

The first step is to deal with averages.
A simple average is an average that counts each figure in the set exactly once.
A weighted average takes into account how frequent, or likely, the figures are.
Computing the weighted average revenue is a relatively simple matter: for each entrée you multiply its price by the number of times the dish has been ordered. You then add these terms up over all of the entrées and divide by the total number sold.
When probabilities of the outcomes are available, the weighted average, or expected value, is found by multiplying each outcome by its associated probability and adding up all the terms.

Performing a maximin analysis:
1. Identify all possible choices that you can make.
2. For each choice, find out what all the possible outcomes are and locate the worst possible choice (the one with the minimum gain).

Decision theory refers to a set of methodologies based on expected values, maximin, and related criteria that are used to select the best alternative when a decision maker is faced with uncertainty.

The most important solution concept in game theory: the notion of an equilibrium.
An equilibrium in a zero sum game is a pair of strategies such that neither player will improve their payoff by (unilaterally) deviating from his or her strategy.

In zero sum games, the most that one player can guarantee winning is equal to the least that the other player can guarantee losing.
The maximin outcome for the row player is always equal to the minimax outcome for the column player.
Every zero sum game has an equilibrium that is determined by these strategies.

When solving for equilibria in zero sum games you don’t worry about the opponent’s payoffs, just their strategies.
The reason is that the opponent’s payoffs are implicitly known—they are always diametrically opposed to yours.
But in nonzero sum games, when computing the equilibrium strategies, you have to consider what the opponent’s payoffs are.

A Nash equilibrium in a two-person, nonzero sum game is when both players are employing their best reply strategies.
Every nonzero sum game has at least one (Nash) equilibrium, possibly in mixed strategies.
Many nonzero sum games have more than one Nash equilibrium.

The advertising game is a form of an arms race where both parties would be better off agreeing not to spend!

When the U.S. government put an end to cigarette advertising on TV, they did the tobacco companies a favor.
The firms were forced into playing their cooperative strategies, and the bottom line was that all of them came out significantly better than before.

Stag Hunt is more benign than Prisoner’s Dilemma because the cooperative outcome (stag, stag) is a Nash equilibrium that yields the absolute best payoffs for them both.
You can imagine the players promising beforehand not to go chasing after rabbits, and actually keeping that promise.

One game can be changed into another.
It is a matter of the players generating additional incentives—carrots or sticks—that serve to modify the payoffs in one or more of the outcomes.
Adding conditions that make a particular outcome either more or less enticing can change the nature of the game and ultimately steer the players toward a mutually satisfying encounter.

People feel pressure to defect (in Prisoner’s Dilemma) for two reasons: greed and fear.

Each company to hold some of the other company’s assets until the joint venture has been completed to everyone’s satisfaction.
Firm A’s product had great potential but needed B’s complementary technology or expertise to succeed.
Perhaps A worries that B will steal its technology and market a similar product in the near future.
To make the joint venture work, they might enter into a contract in which B is required to purchase a certain amount of the resulting output.

Both parties to determine in advance what actions or consequences would constitute cheating, and to jointly create a binding agreement as to how the cheating, when detected, would be punished.
For players stuck in a Prisoner’s Dilemma, they provide some welcome get-out-of-jail-free.

A game of incomplete information is a game in which at least one player does not know the payoffs to the other players.

It costs more for an unproductive person to obtain a credential than for a productive person.
The naturally unproductive person requires more effort to reach the same goal.