We spent part of May 2025 reading Ken Binmore's Game Theory: A Very Short Introduction (Oxford, 2007). It is a 176-page book that has no business covering as much ground as it does. It is also the book that gave us the excuse to work out a Nash equilibrium calculation for a Shadowrun run, which we have been wanting to do for a while.

Full notes on the wiki: Game Theory - A Very Short Introduction.

Why This Book

Game theory has a reputation for being either trivial (rock-paper- scissors and Prisoner's Dilemma) or impenetrable (Von Neumann's Theory of Games and Economic Behavior is 700+ pages). Binmore threads a needle: real coverage of the mathematical structure of Nash equilibrium, mixed strategies, backward induction, mechanism design, and evolutionary game theory - all in fewer pages than most introductory textbooks devote to a single chapter.

The 10 chapters:

1. The name of the game (Nash equilibrium, utility, revealed preference)
2. Chance (mixed strategies, indifference, Von Neumann's minimax)
3. Time (backward induction, subgame-perfect equilibrium, common knowledge)
4. Conventions (focal points, coordination games, tragedy of the commons)
5. Reciprocity (repeated games, folk theorem, TIT-FOR-TAT)
6. Information (imperfect information, Harsanyi types, costly signals)
7. Auctions (mechanism design, revenue equivalence, winner's curse)
8. Evolutionary biology (evolutionarily stable strategies, Hawk-Dove, Hamilton's rule)
9. Bargaining and coalitions (Nash bargaining, Rubinstein alternating offers, Shapley value)
10. Puzzles and paradoxes (Newcomb, surprise test, common knowledge)

Any one of those chapters is a legitimate subject for a graduate course. Binmore covers each in 15-20 pages by ruthlessly cutting the formalism where the intuition suffices, and using clear worked examples where the formalism doesn't.

The Idea That Kept Us Up

The chapter that stuck with us was Chapter 2: Chance. Specifically, the indifference principle for mixed-strategy Nash equilibria.

The setup: some games (Matching Pennies is the canonical example) have no equilibrium in pure strategies. There is no stable choice of "always play Heads" or "always play Tails" - whatever you commit to, your opponent can exploit. The way out is a mixed strategy: randomize between Heads and Tails with some probability.

The question is: with what probability?

The answer Binmore gives - and this is a genuinely counterintuitive result the first time you see it - is that you pick your randomization probabilities to make your opponent indifferent between their pure strategies.

Read that again. You choose your randomization to make your opponent indifferent, not to maximize your own payoff directly. Your opponent does the same. The equilibrium is the pair of randomizations where each player's mix leaves the other player unable to prefer any pure strategy over any other.

The reason this works is that if your opponent had a strictly preferred pure strategy against your mix, they would just play that pure strategy - and then you would want to deviate from your mix to exploit them. The only stable point is where neither of you can improve by deviating, which requires both of you to be indifferent.

Applying It to Shadowrun

Shadowrun is a cyberpunk tabletop RPG where players run "shadowruns" - illegal jobs for corporate clients. Teams are usually a mix of specialists: a decker who fights in cyberspace, a street samurai who solves problems with cybernetically enhanced violence, a mage who solves problems with spells, and so on.

There is a classic Shadowrun tension between the decker's preferred approach (subtle, quiet, undetected) and the street samurai's preferred approach (loud, fast, overwhelming firepower). Both can succeed if the team commits to one plan and executes it. Neither works if half the team is trying to be stealthy while the other half is blowing walls down.

We wrote up a specific scenario:

The setup. A teammate, "Glitch," has been kidnapped and is being held in a Redmond Barrens residential block. The team has two lead operators: "Zero" the decker (prefers Ghost Op) and "Raze" the street samurai (prefers Hard Target Extraction). They are in different parts of the city, prepping their gear, and comms are spotty - each has to commit to their approach before knowing what the other has committed to.

The payoffs (in "Success Points"):

Miscoordination is disaster (0, 0) - alarms blare, Glitch gets moved or killed, the team walks into a meatgrinder. Successful coordination succeeds, but each operator strictly prefers their own style.

This is the pure Battle of the Sexes structure from Binmore's book, with the payoffs adjusted for the setting.

The Math

For Zero to mix, Raze's strategy must make Zero indifferent between Ghost and Hard Target:

Setting these equal: \(2 q_G = 1 - q_G\), so \(q_G = 1/3\).

Raze should choose Ghost with probability 1/3 and Hard Target with probability 2/3.

By symmetric argument, Zero should choose Ghost with probability 2/3 and Hard Target with probability 1/3.

What This Means at the Table

With those probabilities, the outcomes distribute as:

• Both Ghost: (2/3)(1/3) = 2/9 ≈ 22.2%
• Both Hard Target: (1/3)(2/3) = 2/9 ≈ 22.2%
• Zero Ghost, Raze Hard: (2/3)(2/3) = 4/9 ≈ 44.4%
• Zero Hard, Raze Ghost: (1/3)(1/3) = 1/9 ≈ 11.1%

Total probability of miscoordination: 5/9 ≈ 55.6%.

Expected payoff for each operator: 2/3 SP.

That is not a good outcome. Both players are worse off in expectation than they would be under either pure-strategy coordination (which would give at least 1 SP, and possibly 2). But it is the equilibrium outcome. Given that they cannot communicate and cannot know what the other has committed to, the mixed strategy is the only strategy pair where neither player wants to deviate.

At the table, this maps neatly onto the Shadowrun mechanics. If you have a d6:

• Zero rolls: on 5-6, assist Raze and go Hard Target. On 1-4, hack it alone with Ghost.
• Raze rolls: on 5-6, assist Zero and go Ghost. On 1-4, go in guns blazing.

If both rolls "succeed," both plans conflict and the run implodes. If both rolls "fail," each does their own thing and the run also implodes. The only good outcomes are the mixed cases where one assists the other.

The Deeper Lesson

The reason we like this example is that it makes very concrete a lesson that Binmore hammers throughout the book:

Comms are worth more than combat rolls.

The mixed equilibrium gives each operator 2/3 SP in expectation. Successful pure coordination would give at least 1 SP, and possibly 2. The gap between 2/3 and 2 is entirely the cost of not being able to talk to each other before committing.

Every Shadowrun campaign should have a moment where the players learn this the hard way. If you are a GM, staging a scenario where comms are down and the team has to commit independently is one of the most effective ways to teach the value of a comm channel your players will spend Karma on for the rest of the campaign.

A Wider Recommendation

The Shadowrun example is a toy application. The real reason to read Binmore's book is that it gives you the vocabulary to notice strategic structure in situations that don't look like games - salary negotiations, whether to attend an optional meeting, whether to vote in an election where you know your vote won't be decisive.

The Chapter 2 material on the Good Samaritan game - where the probability of anyone helping decreases as the population increases, because rational individuals wait for someone else to help - is the kind of thing that changes how you read the news.

If you are reading one game theory book this year, read this one. If you are reading one book on Nash equilibrium ever, still read this one.

References

• Our wiki notes: Game Theory - A Very Short Introduction
• Binmore, K. (2007). Game Theory: A Very Short Introduction. Oxford University Press.
• Shadowrun: any edition works, but we run 5E.

We read (parts of) Thomas Hobbes's Leviathan (1651) in April and early May 2025. It is one of the founding texts of modern political philosophy, and reading it is about as enjoyable as drinking five cement milkshakes in a row.

Hobbes's arguments have all the subtlety of a boiling pot of water thrown in your face. And they're written in 17th-century English prose that seems to simultaneously look down its nose at you, treats you like you have the intelligence of a toddler, and is trapped in an age when people were much more close-minded and ignorant. The organization is not much better - massive 4-part books, with 47 chapters, and headers that are long run-on sentences - so the whole thing is a frustrating exercise. One might even use the phrase "interminable biblical exegesis," if one were reaching for ten dollar words.

Full notes on the wiki: Leviathan.

The Argument in One Paragraph

Hobbes says: if there were no government, life would be a war of everyone against everyone else, and would be "solitary, poor, nasty, brutish, and short." To escape this, rational individuals agree (hypothetically, via a "social contract") to give up nearly all their natural rights and submit to an absolute sovereign - a person or an assembly - whose job is to keep the peace by force.

Equally important is Hobbes' proposition that any sovereign, no matter how bad, is preferable to no sovereign at all, because anarchy is worse than tyranny.

That is the whole book. Everything else is Hobbes methodically building the argument up from first principles, then defending it against every objection he can think of - including all the biblical objections that mattered in 1651 England.

Why This Book Was Written When It Was

Hobbes was writing during and immediately after the English Civil War (1642-1651). Charles I had been executed. The country had spent almost a decade in a chaotic three-way war between royalists, parliamentarians, and various religious factions. Hobbes's family had fled to France. When he wrote Leviathan, "war of all against all" was not a thought experiment - it was recent memory.

This context matters because modern readers instinctively resist Hobbes's absolutism. Absolute sovereignty sounds like tyranny. But Hobbes had watched what happens when there is no sovereign, and he thought tyranny was clearly the lesser evil.

The book is aimed at people who lived through the same collapse he did. Reading it in a functioning democracy in 2025 is a very different experience than reading it in 1651.

The Four Parts

Leviathan has four parts, roughly:

Part I: Of Man (16 chapters). Hobbes builds up an account of human nature from mechanistic first principles - all thought comes from sensory experience, all action is motion, all motivation is appetite or aversion. He argues that humans are roughly equal in capability, driven by "a perpetual and restless desire of power after power, that ceaseth only in death," and so in the absence of a common power, they will inevitably fight each other for competition, safety, and glory.

Personal opinion: this is dreadfully boring - it has all the action-packed excitement of (insert the most boring Old Testament passage imaginable here) - and is cringe-inducing.

Part II: Of Commonwealth (15 chapters). Given the argument in Part I, Hobbes derives the necessity of an absolute sovereign, lays out the sovereign's rights (which are essentially unlimited), and describes the three types of commonwealth (monarchy, aristocracy, democracy). He argues monarchy is best because the monarch's private interest is most closely aligned with the public interest.

Personal opinion: the only portion of this book actually worth anything.

Part III: Of a Christian Commonwealth (11 chapters). Hobbes argues that religious authority must be subordinate to civil authority in a Christian society. This part is a lot of biblical interpretation, most of which is only interesting if you care about the 17th-century debate over church-state relations.

Personal opinion: worthless, skip.

Part IV: Of the Kingdom of Darkness (4 chapters). A polemic against the Catholic Church and Aristotelian philosophy, both of which Hobbes blames for confusing people about the proper relationship between religious and civil authority.

Personal opinion: if reading a 17th-century philosopher score some hits on the Pope is your idea of "fun" reading, then (a) Part IV is definitely for you, and (b) you should check yourself into a mental hospital, because you are not okay.

The Passages Worth Underlining

A few of the passages that stopped us:

On the desire for power (Chapter 11):

So that in the first place, I put for a general inclination of all mankind, a perpetual and restless desire of power after power, that ceaseth only in death.

This is the anthropological premise of the whole book. Hobbes is not saying humans are evil - he is saying humans are driven, and a world of driven people without a common referee is a world at war.

On the state of nature (Chapter 13):

In such condition there is no place for industry, because the fruit thereof is uncertain... no arts; no letters; no society; and which is worst of all, continual fear, and danger of violent death; and the life of man, solitary, poor, nasty, brutish, and short.

The most famous sentence in the book. Worth reading in context - the argument is that everything worthwhile in human life (industry, arts, letters, society) requires predictability, and predictability requires an enforcer.

On the social contract (Chapter 17):

This is the generation of that great LEVIATHAN, or rather (to speak more reverently) of that mortal god to which we owe, under the immortal God, our peace and defence.

The image the whole book takes its name from. The famous frontispiece of the 1651 edition shows a giant crowned king whose body is made of hundreds of tiny individual people - the sovereign as the literal composite of all his subjects.

On liberty (Chapter 21):

The liberty of a subject lieth therefore only in those things which, in regulating their actions, the sovereign hath praetermitted [omitted]: such as is the liberty to buy and sell and otherwise contract with one another; to choose their own abode, their own diet, their own trade of life, and institute their children as they themselves think fit; and the like.

Freedom is whatever the sovereign has not made a law about. This is the definition of liberty that makes modern readers most uncomfortable, and probably the one that is most philosophically distant from what we mean by liberty today.

The One Exception: Self-Preservation

Hobbes "gives" the sovereign nearly unlimited power. But there is one right the sovereign cannot take away, because it is the entire reason people submit to the sovereign in the first place - the right of self-preservation.

From Chapter 21:

If the sovereign command a man (though justly condemned) to kill, wound, or maim himself; or not to resist those that assault him; or to abstain from the use of food, air, medicine, or any other thing without which he cannot live, yet hath that man the liberty to disobey.

This is the entire modern human-rights tradition in embryo. It is also a very narrow exception. You can refuse to kill yourself. You cannot refuse to be taxed, censored, drafted, or otherwise regulated.

Why Read This In 2025

Reading Hobbes today is uncomfortable because his framing is almost the exact opposite of modern political intuition.

We tend to worry about state overreach - the risk that the sovereign will have too much power. Hobbes worried about state collapse - the risk that the sovereign will have too little.

In a country that has been at war with itself, Hobbes's worry is the more urgent one.

The reason to read the book anyway is that it clarifies what liberal democracy is for. Liberal democracy is a very particular set of institutions that try to prevent both failure modes - both state overreach and state collapse - by dividing sovereignty across branches, making the sovereign accountable to elections, and constraining the sovereign with a bill of rights. When you understand Hobbes, you understand what all those institutional constraints are working against. They are working against the pull toward either total sovereignty or none.

You can disagree with Hobbes's conclusions (we do, almost universally) and still find his framing of the problem useful. Political institutions have to solve the problem Hobbes identified: how do we get out of the state of nature without ending up with a tyrant? The modern answer is elaborate and multi-layered, and it mostly works. But it is worth remembering that the alternative Hobbes was writing about - a country tearing itself apart - is not a thought experiment. It happens, in living memory of some readers of this blog, in several countries.

References

• Our wiki notes: Leviathan
• Hobbes, Thomas. Leviathan. 1651. The Penguin Classics edition edited by C. B. Macpherson is our standard recommendation.
• Companion post on political theory: Reading Rick Perlstein's Nixonland

We wrote about Peter Golenbock's Bums back in November 2022. That book is an oral history of the Brooklyn Dodgers, and one of its central characters is Walter O'Malley, the owner who moved the team to Los Angeles after the 1957 season. In Golenbock's telling, O'Malley is the villain of the story - the guy who ripped the heart out of Brooklyn for money.

Michael D'Antonio's Forever Blue: The True Story of Walter O'Malley argues that story is incomplete, and in important ways just wrong. We read it in May 2025 and it changed our mind about several things. Full notes on our wiki: Forever Blue.

The Golenbock Version

The short version of the Bums narrative on O'Malley:

• O'Malley was a lawyer, not a baseball man - he came into the organization representing the Brooklyn Trust Company, which held the mortgage on Ebbets Field
• He maneuvered Branch Rickey out of the ownership structure in the early 1950s
• He decided he wanted a new stadium, didn't get exactly the deal he wanted from New York, and packed up and left for Los Angeles
• The move destroyed a piece of Brooklyn that has never come back

This is the version most Brooklynites believe. It is also the version that appears in almost every English-language baseball history book we have read. The move is treated as a betrayal, and O'Malley as the man who made it.

The D'Antonio Version

D'Antonio had access to O'Malley's personal papers, which is unusual - most O'Malley biographies rely on public records and the accounts of people who hated him. What he found argues for a different framing.

Ebbets Field was genuinely broken. By the mid-1950s, the ballpark was over 40 years old, seated only about 32,000 people, had almost no parking, and sat in a neighborhood where the demographics of the Dodgers' fanbase were rapidly leaving. The postwar suburban migration meant that fans who had walked to Ebbets Field in the 1930s were now driving in from Long Island, and there was nowhere to put the cars. Television revenue was starting to matter, and Ebbets Field was hard to broadcast from. The problem O'Malley was trying to solve was real.

He tried very hard to stay in Brooklyn. For years - the majority of the 1950s - O'Malley was pushing for a new, privately financed stadium in Brooklyn. His preferred site was the intersection of Atlantic and Flatbush Avenues, which is where the Barclays Center sits today. He wanted a domed stadium, which would have been the first domed stadium in the world if he had gotten to build it. He was not asking the city for money. He was asking the city to help him assemble the land, which required using the Title I condemnation mechanism that Robert Moses controlled.

Robert Moses said no. Repeatedly. Moses was the parks commissioner and the most powerful unelected official in New York. He controlled Title I. He would not use it for O'Malley's Atlantic and Flatbush site. What Moses offered instead was Flushing Meadows in Queens - the future site of Shea Stadium, home of the Mets. O'Malley did not want to be in Queens. He wanted to be in Brooklyn.

The negotiations dragged on. The Los Angeles Coliseum group started courting O'Malley, hard. The math for LA was overwhelming: enormous market, no existing team, willing to help with land, huge television territory. And still O'Malley tried to get the Brooklyn deal.

Eventually he ran out of patience and moved.

Robert Moses

The person who comes out worst in D'Antonio's telling is Robert Moses. If you have read Robert Caro's The Power Broker, this will not be surprising - Moses shaped and reshaped the physical form of New York City for decades, and a lot of his decisions were driven by personal aesthetics and personal vendettas rather than any coherent civic vision.

Moses had specific ideas about where major sports facilities belonged (in Flushing Meadows, near his beloved World's Fair site) and no interest in letting O'Malley build somewhere else. He had the power to block the Brooklyn deal, and he used it.

If Moses had said yes to Atlantic and Flatbush in 1955, the Brooklyn Dodgers might still be in Brooklyn. That is not a speculative claim - it is straightforwardly what the sequence of events shows.

What Changed Our Mind

Reading Bums in 2022, we came away with the standard Brooklyn grievance. O'Malley did it. He is the villain.

Reading Forever Blue in 2025, we came away with something messier. O'Malley made the final decision, yes, and he benefited enormously from moving to LA. But the choice was between "move to LA" and "keep losing money in a decaying ballpark I cannot replace because the city won't let me." Given those two options, the LA move looks less like villainy and more like the outcome of a specific political failure - a failure that Robert Moses owns as much as O'Malley does.

The historical villains of Brooklyn baseball, in something like descending order, are probably:

1. Robert Moses, for using his power to block the deal that would have kept the team
2. The New York political establishment, for letting Moses hold that much unaccountable power in the first place
3. Walter O'Malley, for taking the LA offer once Brooklyn was effectively closed
4. Horace Stoneham (owner of the New York Giants), whose move to San Francisco was more purely opportunistic and gets less attention because the Giants' fanbase never had the emotional grip on Manhattan that the Dodgers had on Brooklyn

D'Antonio is not making O'Malley a hero. He is making him a businessman in an impossible situation, which is a much more interesting portrait than either "villain" or "hero."

Two Books, One Story

The reason to read both books is that they are answering different questions. Golenbock is asking: what did it feel like to lose the Dodgers? D'Antonio is asking: how did that actually happen? Both questions have real answers, and neither answer is complete without the other.

If you can only read one, read Golenbock - the oral history format does something no biography can, which is put you in the room with the fans who lived it. But if you cared enough about that book to still be thinking about it three years later, Forever Blue is what you read next. It's the book that turns the tragedy into a particular kind of history: a decision that could have gone the other way, and didn't, because one specific person with too much power made it not go the other way.

References

• Our wiki notes: Forever Blue
• D'Antonio, Michael. Forever Blue: The True Story of Walter O'Malley, Baseball's Most Controversial Owner, and the Dodgers of Brooklyn and Los Angeles. Riverhead Books, 2009.
• Our earlier take: Reading Bums
• Robert Moses background: Caro, Robert A. The Power Broker. Alfred A. Knopf, 1974.