This post is a result of William Spaniel (@gametheory101) tweeting about pigs and game theory.

I have no idea what this illustration is supposed to be, so we're gonna call it a pigoner's dilemma. pic.twitter.com/LGKEhoOV36 — William Spaniel (@gametheory101) August 11, 2016

Dr. Vincent Knight tweeted back the image depicts an experiment where pigs played game theory.

William Spaniel found the image is a book cover (clearer image here: https://img1.doubanio.com/lpic/s6972287.jpg). The book’s title translates to “Game Theory In Our Daily Life” (博弈论的诡计全集) and the author is Wang Chun Yong. I found the book is listed on Amazon.ca and also several copies listed on Taobao.

So what do pigs have to do with game theory? I found an English reference in the book Games, Strategies, and Managers by John McMillan.

The game: pigs in a box

A pair of pigs, one dominant and one subordinate, are in a box and have a chance to be rewarded with food. At one end of the box is a lever which releases food when pressed. The twist is the food is released at the other end of the box. The pig that presses the lever is at a disadvantage as the other pig can get to the food first.

We can model the game using some numbers. If the dominant pig presses the lever, the subordinate pig can eat 80 percent of the food before the dominant pig can arrive and take the rest. If the subordinate pig presses the lever, then the dominant pig can take all the food as the subordinate pig races across the box. If neither pig presses the lever, then neither pig gets any food. And if both are adjacent when the lever is pressed, the dominant pig can eat 70 percent of the food.

Suppose the food is worth 10 units, it takes 1 unit of energy to press the lever and rush to the other side of the box to fight for the food. The game then has the following payouts.

How should the two pigs act if they reason like game theorists? Let’s solve this game and then see how pigs actually behave in an experiment.

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"All will be well if you use your mind for your decisions, and mind only your decisions." Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon. .

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Solving for the Nash equilibrium

Consider the choice of the subordinate pig. If the dominant pig presses the lever, then the subordinate pig is better off not pressing the lever and raiding the food to get 8. If the dominant pig does not press the lever, then the subordinate pig is better not pressing, because it is better to get 0 than to get -1 from getting no food and expending energy.

Notice the subordinate pig has a dominant strategy of not pressing the lever. These best responses are depicted by overlines in the appropriate cells of not pressing the lever.

What should the dominant pig do? For completeness, let us consider each choice of the subordinate pig. If the subordinate pig presses the lever, the dominant pig would rather not press the lever and get all 10 units of food. If the subordinate pig does not press the lever, then the dominant pig should press the lever to get a payoff of 1 versus a payoff of 0 for not pressing.

These best responses are depicted by underlines in the appropriate cells.

The unique Nash equilibrium of this game is the cell with both an overline and an underline, in which both pigs are playing a best response. This corresponds to the dominant pig pressing the lever, the subordinate pig not pressing the lever.

The subordinate pig gets 8 while the dominant pig gets only 1.

How pigs actually played

Baldwin and Messe did this experiment and published about it in 1979. While pigs do not actually write the matrix game and solve it, they can learn optimal behavior. The researchers found the dominant pigs did almost all of the pressing. In other words, the pigs acted just as game theory predicted they would! While pigs do not know game theory, there is a role of game theory to predicting animal behavior (read how dung flies optimally exit a war of attrition, for example).

The lesson: strength can be a weakness!

The game is also interesting from a business perspective. Typically we think dominance translates into strategic strength: the stronger animal should beat the weaker one. But in this game, strength is a weakness! The dominant pig ends up with almost no food compared to the subordinate pig.

Why is this happening? The strategic problem is the dominant pig is too dominant. If there is a fight for food, the subordinate pig knows that it will get nothing. So the subordinate pig never wants to waste time pressing the lever and fighting for the food.

As a consequence, the dominant pig settles for pressing the lever to get a little bit of food.

The subordinate pig’s “protest” to not press the lever steals the power and overwhelms the physical strength of the dominant pig.

Sources for this experiment at at the end of this post; I want to mention a couple items from the news first.

Game Theory News 1: Nash’s Nobel Up For Auction

John Nash’s Nobel Prize is set to be auctioned by October 17 and expected to sell between $2 to $4 million. It appears to be a standard open outcry bidding. Time to apply your game theory knowledge: it’s a weakly dominant strategy to bid up to your valuation!

NY Times

http://www.nytimes.com/2016/08/31/arts/john-nash-nobel-medal-to-be-auctioned-at-sothebys.html?_r=0

Sotheby’s

http://www.sothebys.com/en/news-video/blogs/all-blogs/Bibliofile/2016/08/john-f-nash-jr-nobel-prize-economic-studies.html

Game Theory News 2: Reinhard Selten Dies At 85

Selten shared the 1994 Nobel Prize with John Nash, who passed away last year. Selten proposed the idea of subgame perfect Nash equilibria–a refinement to the Nash equilibrium that excludes non-credible threats. Selten is also known for his work on “bounded rationality”–a more realistic assumption than the standard infinite reasoning capability–and he is considered a founding father in experimental economics.

Bloomberg

http://www.bloomberg.com/news/articles/2016-09-01/reinhard-selten-game-theorist-who-won-nobel-prize-dies-at-85

New York Times

http://www.nytimes.com/2016/09/04/business/economy/reinhard-selten-whose-strides-in-game-theory-led-to-a-nobel-dies-at-85.html?_r=0

A Fine Theorem (more details of work)

https://afinetheorem.wordpress.com/2016/09/01/reinhard-selten-and-the-making-of-modern-game-theory/?utm_source=twitterfeed&utm_medium=twitter

Sources For Pigs Experiment Game Theory

Baldwin, B. A., and G. B. Meese. “Social Behaviour in Pigs Studied by Means of Operant Conditioning.” Animal Behaviour 27 (1979): 947-957. https://www.researchgate.net/publication/256111949_Social_behaviour_in_pigs_studied_by_means_of_operant_conditioning

Games, Strategies, and Managers. John McMillan

Rational Pigs

http://www2.owen.vanderbilt.edu/lukefroeb/2003/mgt722/topics/game/game.html#3

GameTheory101 Tweet

https://twitter.com/gametheory101/status/763842095933190144

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Brian M. Mooney

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