Yet another game theory article

Lately, I’ve been diving into books and articles on Game Theory, and I’ve found it surprisingly fascinating. One book that really stood out is The Art of Strategy. It’s a bit long (560+ pages) and occasionally technical, but it’s full of powerful insights and practical tools for making smarter decisions in everyday life.

Photo by Florian Klauer on Unsplash

In this post, I’ll break down the key ideas from the book in a clear, easy-to-digest way.

So, please grab a cup of coffee, and let’s get into it.

Quick Summary for those in a hurry

Ever wonder why some people seem to always make the right move in tricky situations?

The Art of Strategy breaks down the hidden rules behind smart decision-making using game theory (don’t worry, it’s way more practical than it sounds). From Survivor-style tactics to negotiation hacks and auction tricks, the book shows how strategy shapes everything from business to daily life.

You’ll learn how to think ahead, read others, and make your moves count, all without needing to be a math genius.

If you lead, negotiate, or just want to win more often, this is a great resource. Not quite ready to commit to 560+ pages? You might find the following summary a helpful place to start.

Introduction

There is one thing about the strategies discussed within the book: they are not based on philosophy or ethics. They are based on game theory. In fact, some of the tactics might not be very popular with opponents, as the authors Avinash Dixit and Barry Nalebuff highlight.

So, you can use the shown tactics to your benefit, but in some situations, you might want to choose not to (because of philosophical or ethical concerns).

Part I

In part I of the book, the authors start with the basics: definition of strategy (with examples) and introduce two core methods: backward reasoning and Nash equilibrium.

Ten Tales of Strategy

I really enjoyed this chapter as it shows ten different fields of life where strategy plays an influential role.

1. Guess a number between 1 and 100 (You’re told if your guess is too high or too low, and you get 5 tries): The authors use this to explain how game theory actually works. A logical way to guess is to keep cutting the range in half. But if your opponent knows you’re using that method, they might choose a number that makes this approach fail (by thinking ahead multiple times and picking, e.g., 12.5).
2. Winning by losing (Inspired by the TV show Survivor): Sometimes losing a round can help you win in the long run.
3. The “Hot Hand” Fallacy: People think that success leads to more success, but it’s often just chance.
4. To lead or not to lead: Sometimes it’s smarter to follow, even if you’re in front (like in sailing races).
5. Here I stand: Holding your position can be a strategic move.
6. Thinning your options: Sometimes, having fewer choices makes you stronger. Too many choices can numb our decision-making mechanisms.
7. Buffet’s Dilemma: A twist on the Prisoner’s Dilemma where cooperation is tricky, especially when food (or opportunity) is limited.
8. Mix your moves: Don’t be predictable. Randomizing can give you an edge.
9. Avoid one-sided bets: If only one side takes a risk, it’s probably not a good deal.
10. Game theory can be bad for your health: Overthinking strategy can be exhausting and even harmful.

Games Solvable by Backward Reasoning

Rule #1 of strategy: Look forward, reason backward. - Avinash Dixit and Barry Nalebuff

The authors suggest using “game trees”: they’re like decision trees, but include your opponents’ possible choices too.

Example: The Flag Game (for more details, see this article)

The game follows these rules:

• 21 flags
• 2 teams
• Each team must take exactly 1, 2, or 3 flags per turn (not 0 or 4)
• Whoever takes the last flag wins.

If you take the correct strategy, you can ensure that you win. If you leave your opponent with 4 flags, they’re doomed, as they cannot stop you winning anymore. If you apply backward reasoning, it gives you the sequence: 4, 8, 12, 16, 20. So, if you go first, take just 1 flag and you are guaranteed to win.

In this version, the first player can always win because there’s no uncertainty. But if there were only 20 flags, the second player would always win (if they knew the strategy). Unfortunately, this isn’t true in real life, as games often include uncertainty.

Example: The Ultimatum Game

• One person (the proposer) gets a sum of money and decides how to split it with another person (the receiver).
• The receiver can accept or reject the offer. If they reject it, no one gets anything.

In theory, the receiver should accept anything above zero. But in real life, people often reject unfair offers just to punish the proposer. Studies show offers average around a 50/50 split, → fairness and emotion do matter.

This shows that humans aren’t just rational. They care about fairness, too.

Prisoner’s Dilemmas and How to Solve Them

Real-world versions of the Prisoner’s Dilemma pop up all the time. In the book, the authors provide some case studies that discuss different versions of the Prisoner’s Dilemma. If you’ve never heard about it, check out the Wiki article.

Game theory tip: If you have a dominant strategy (a choice that’s better no matter what the other side does), use it.

A Beautiful Equilibrium

This chapter is all about the Nash Equilibrium, a cornerstone of game theory.

Especially in simultaneous games (where players act at the same time), the Nash Equilibrium helps predict outcomes. It answers the question: “What should I do, considering what you think I’ll do?”

But people who aren’t too much into strategy and game theory don’t think much ahead. There is a clever game that shows how people fall short of true strategic thinking:

• 2 players
• Choose a number between 0 and 100
• The goal: Pick a number that’s half of your opponent’s choice

Most people don’t think beyond 2-3 layers of reasoning, especially in the first round of the game. So many people pick 50 (or, if they are especially clever, they pick 25).

Sometimes, a game can have more than one Nash Equilibrium.

A key to cooperation in simultaneous games is the idea of a focal point: something both sides naturally focus on. For instance, many people can meet up in NYC without planning, simply because landmarks like Times Square or noon serve as natural focal points.

Part II

Part II is about how randomness can be beneficial and how important credibility is in the context of strategy.

Choice and Chance

In some games, adding randomness helps.

This is especially true in zero-sum games (where one side’s gain is the other’s loss). For example, during a penalty kick in soccer, it’s better if the kicker doesn’t always choose the same side, because if she did, the goalkeeper would already know (if he studied the statistics). Only if the kicker adds randomness to his passes does it become unpredictable for the goalkeeper.

Strategic Moves

Threats and promises can be powerful tools. Examples:

• “Meet or beat” pricing clauses: Why are they so powerful? Because they work automatically, you don’t need to constantly analyze what your competitors are doing. With a “meet the competition” clause, you don’t have to update catalogs or launch a pricing campaign every time a rival lowers its prices. The clause does the work for you, helping you retain customers without extra effort.
• The Cold War and nuclear deterrence: A similar principle played out on a much larger scale during the Cold War. The doctrine of mutually assured destruction acted as a strategic automatism: if one side launched a nuclear attack, the other would automatically respond in kind. This made the threat of retaliation so credible that it prevented either side from striking first. The power wasn’t in the action: it was in the certainty of the reaction.

Making Strategies Credible

As with the credibility of a retaliation during the Cold War, in every area, making your strategy believable is important. And it can be a science of its own. Here are some ways to do it:

• Third parties/contracts: For example, if a supplier signs a contract with penalties for late delivery, they’re more likely to deliver on time.
• Reputation: If people know you keep your word (or fear what happens if you don’t), they’re more likely to trust you.
• Automation: Set up systems that act on your behalf. (like automatic retaliation in war).
• Team pressure: Peer influence works, too. Think of the Roman army punishing soldiers who didn’t stop deserters (they’d face the same fate as the deserters: execution).

Part III

In part III, Avinash Dixit and Barry Nalebuff apply tactics and techniques from game theory in areas such as auctions, contests, bargaining, and voting.

Interpreting and Manipulating Information

Imagine a company hiring managers. A great hire boosts profits. However, a bad one could cost millions.

How can they tell who’s talented?

One way: require candidates to have an MBA. This helps not just because of the skills they learn during the MBA, but because of the high effort linked to an MBA: because it’s expensive and takes years to complete, it acts as a filter. For untalented candidates, the cost and effort for acquiring an MBA aren’t worth the risk, so they’re less likely to apply.

This idea shows how signals (like education) can help screening for quality.

Cooperation and Coordination

Coordination matters. It matters a lot. Without it, we can end up with bad outcomes for everyone.

Why?

Because even if one person improves their situation, it can hurt the group.

Examples are:

• Traffic routes: When people switch to faster routes, congestion balances things out.
• Keyboard layouts: We still use QWERTY instead of more efficient options like Dvorak. Why? Because the incentive to learn a different method is lower if there isn’t a critical mass. If suddenly > 10 % of people would use Dvorak, all the remaining people would transition to the more effective method.
• Neighborhoods: In the U.S., diverse neighborhoods often become segregated, even though most people prefer mixed areas. The reason is tipping points: once reached, they converge to an overall more imbalanced solution.
• Politics: Competing parties move closer together (from the extreme left/right sides), trying to win the same voters.

But there is hope. In such cases, policy changes (like tolls or incentives) can help to push the system toward better outcomes.

Auctions, Bidding, and Contests

There are several types of auctions, each requiring its own strategic approach:

• English Auction: Classic style, bids go up until no one bids more.
• Japanese Auction: Everyone keeps bidding (hands up) until the price passes their max.
• Vickrey Auction: Secret bids, the highest bid wins, but pays the second-highest price.
• Sealed Bid Auction: Everyone submits secret offers; the highest wins.
• Dutch Auction: Starts high and drops until someone bids.

A common pitfall in auctions is the winner’s curse. When you get caught up in the bidding and end up overpaying. To avoid it, use this simple check: If you win, will you still feel good about the price you paid? Keeping that question in mind helps you stay grounded and be clear.

Bargaining

BATNA (Best Alternative to a Negotiated Agreement) is key in negotiations. The “pie” being split is the difference between each side’s BATNA and the deal they agree on. But that only works when both sides aim to grow the pie, not just grab more of it.

Tactics include:

• Brinkmanship (pushing to the edge)
• Virtual strikes (symbolic threats)
• Look forward, reason backward (as discussed in part I)

Voting

This chapter explores different voting systems. The authors show that most systems allow for strategic voting, where people don’t vote for their favorite option, but the one most likely to win or block someone else.

Their conclusions are similar to this Veritasium Docu, which argues that a perfect democracy is mathematically impossible.

Incentives

The authors dig into reward systems. Briefly summarized, they conclude the following:

• Non-linear incentives are great near the goal (like a bonus for exceeding targets).
• Linear incentives are more stable and predictable.
• Best? Combine both.

But be careful: if the reward is too small, it might backfire. People may lose intrinsic motivation and only work for the money.