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Game Theory (Part 19)
Okay, we’re almost done! We’ve been studying Nash equilibria for zero-sum 2-player normal form games. We proved a lot of things about them, but now we’ll wrap up the story by proving this: Grand...
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Game Theory (Part 20)
Last time we tackled von Neumann’s minimax theorem: Theorem. For every zero-sum 2-player normal form game, where ranges over player A’s mixed strategies and ranges over player B’s mixed strategies. We...
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Relative Entropy in Evolutionary Dynamics
guest post by Marc Harper In John’s information geometry series, he mentioned some of my work in evolutionary dynamics. Today I’m going to tell you about some exciting extensions! The replicator...
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The Game of Googol
Here’s a puzzle from a recent issue of Quanta, an online science magazine: Puzzle 1: I write down two different numbers that are completely unknown to you, and hold one in my left hand and one in my...
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Biology as Information Dynamics (Part 1)
This is my talk for the workshop Biological Complexity: Can It Be Quantified? • John Baez, Biology as information dynamics, 2 February 2017. Abstract. If biology is the study of self-replicating...
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Information Geometry (Part 16)
This week I’m giving a talk on biology and information: • John Baez, Biology as information dynamics, talk for Biological Complexity: Can it be Quantified?, a workshop at the Beyond Center, 2 February...
View ArticleCorrelated Equilibria in Game Theory
Erica Klarreich is one of the few science journalists who explains interesting things I don’t already know clearly enough so I can understand them. I recommend her latest article: • Erica Klarreich, In...
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Open Games: the Long Road to Practical Applications
In the third talk of the ACT@UCR seminar, Jules Hedges spoke about open games! He gave his talk on Wednesday April 15th. Afterwards we discussed it at the Category Theory Community Server, here:...
View ArticleCompositional Game Theory and Climate Microeconomics
guest post by Jules Hedges Hi all This is a post I’ve been putting off for a long time until I was sure I was ready. I am the “lead developer” of a thing called compositional game theory (CGT). It’s an...
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Exponential Discounting
Most of us seem to agree that the promise of a dollar in the future is worth less to us than a dollar today, even if the promise is certain to be fulfilled. Economists often assume ‘exponential...
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Game Theory (Part 10)
Last time we solved some probability puzzles involving coin flips. This time we’ll look at puzzles involving cards. Permutations Example 1. How many ways are there to order 3 cards: a jack (J), a queen...
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Game Theory (Part 11)
Here’s a game. I flip a fair coin. If it lands heads up, I give you $1. If it lands tails up, I give you nothing. How much should you pay to play this game? This is not a mathematics question, because...
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Game Theory (Part 12)
Suppose we have a 2-player normal form game. As usual, we assume: • Player A has some set of choices • Player B has some set of choices • If player A makes choice and player B makes choice the payoff...
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Game Theory (Part 13)
Last time we introduced mixed strategies, and generalized the idea of Nash equilibrium to mixed strategies. Now let’s look at an example. Matching pennies In the game of matching pennies, each player...
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Nash Equilibria
As you know if you’ve been reading this blog lately, I’m teaching game theory. I could use some help. Is there a nice elementary proof of the existence of Nash equilibria for 2-person games? Here’s the...
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Game Theory (Part 14)
Here is the first test in our game theory course. If you’re following along on this blog, you can do it and then look at the answers below. Definitions 1. Define a Nash equilibrium for a 2-player...
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Game Theory (Part 15)
In Part 13 we saw an example of a Nash equilibrium where both players use a mixed strategy: that is, make their choice randomly, using a certain probability distribution on their set of mixed...
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Game Theory (Part 16)
Last time we looked at a zero-sum game and noticed that when both players use their maximin strategy, we get a Nash equilibrium. This isn’t a coincidence—it always works this way for zero-sum games!...
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Game Theory (Part 17)
Last time we saw the official definition of maximin strategy. Now we’ll prove something really important. In a Nash equilibrium for a zero-sum game, both players must be using a maximin strategy! To...
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Game Theory (Part 18)
We’re talking about zero-sum 2-player normal form games. Last time we saw that in a Nash equilibrium for a game like this, both players must use a maximin strategy. Now let’s try to prove the converse!...
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