This is a summary of key points from the same title book of Ken Binmore

I. The name of the game

1. What is game theory about?

• Definition and Scope: Game theory analyzes situations of interaction where the outcome depends on the choices made by multiple individuals ("players"). Examples range from everyday scenarios like driving in traffic, bidding on eBay, wage negotiations, political campaigns, and economic pricing decisions to larger-scale interactions like courtship (Antony and Cleopatra), business strategy (Bill Gates), and geopolitical conflicts (Hitler and Stalin, Cuban Missile Crisis). Essentially, a game is played whenever humans interact.
• Rationality Assumption: Game theory primarily predicts the behavior of players who act rationally. It doesn't claim universal predictive power, as it cannot account for the actions of "love-sick teenagers" or "madmen." However, since people often try to act rationally (e.g., spending money sensibly), studying rational play is valuable. Economic theory relies on this approximate rationality.
• Even when players don't consciously strategize, game theory can be relevant. It has successfully explained the behavior of non-thinking entities like spiders and fish. This occurs because irrational behavior tends to be eliminated over time through evolutionary processes (natural selection) or market forces (companies going bankrupt). Entities that survive behave as though they were rational.

2. Does game theory work?

• Practical Applications: Initially dismissed by some practical business people, game theory gained significant credibility after its successful application in designing government auctions for radio frequencies (telecom auctions).
• Telecom Auctions Example: Game theorists advised on the rules for US and UK telecom auctions, leading to governments raising substantially more revenue than predicted by orthodox methods ($20 billion in the US, $35 billion in a single UK auction Binmore was involved in). This demonstrated the practical value and effectiveness of game theory when applied correctly. Binmore notes the media reaction, including being called a "ruthless, Poker-playing economist."
• Scope: Game theory works not just in economics but also in evolutionary biology and political science. Binmore mentions applying it even to ethics in his book Natural Justice.

3. Toy games

• Purpose of Simplification: Real-world applications like telecom auctions are complex and require tailoring designs to specific circumstances. Mathematical models cannot capture every detail. Therefore, game theory often uses simplified "toy games" that mimic the essential strategic features of a problem. This book focuses on such toy games, minimizing algebra and technical jargon, as even these provide significant insights.

4. Conflict and cooperation

• Most games in the book involve two players, conventionally named Alice and Bob.

• Matching Pennies (Pure Conflict): This is the first example game. Alice and Bob each show a coin (heads or tails). Alice wins if the faces match; Bob wins if they differ. Each player has two strategies: heads and tails. This game represents pure conflict, where one player's gain is the other's loss. (Similar situations: Sherlock Holmes vs. Moriarty choosing train stations, auditors vs. accountants).

  

  Alice and Bob’s decision problem in Matching Pennies

• Payoff Tables: Game information (players, strategies, payoffs) can be summarized in a payoff table. Alice typically chooses a row, Bob chooses a column. Payoffs are shown within the cells, usually Alice's in the southwest corner and Bob's in the northeast. Payoffs don't have to be monetary; icons (thumbs-up/down) can represent winning/losing.

• Driving Game (Pure Coordination): A contrasting game where Alice and Bob must choose to drive on the left or right. Their interests are perfectly aligned; both win if they coordinate (both left or both right) and effectively lose if they don't. This represents pure cooperation, a "win-win" situation.

Payoff tables. Alice chooses a row and Bob chooses a column

5. Von Neumann

• Minimax Theorem: John Von Neumann provided the first major result in game theory, the minimax theorem, which applies specifically to two-person games of pure conflict (zero-sum games) like Matching Pennies.