no monopoly on game theory
Some years ago, when they were little kids, my children developed a hybrid game.They’d taken their Monopoly board over to a friend’s house. They’d remembered to bring back the board, but they’d forgotten the houses and hotels. What to do? So, they started to use Lego building blocks in place of the houses and hotels. But, with the Lego pieces offering more affordances, they immediately began to construct ever more elaborate structures. Even when the Monopoly pieces were returned, the Legos were much preferred and they played it again and again that year while they were first-graders in Budapest. Was it Monopoly? Was it Legos? It was “Legopoly.” Over time the rules evolved away from bankrupting one’s opponents and toward attracting customers to the plastic skyscrapers that towered over the Monopoly plain.
The story of my kids’ recombinant game was relegated to a footnote in my book, The Sense of Dissonance. The context is a story about a friend who had played Monopoly as a kid back in the communist era by turning over the officially sanctioned game “Economize Wisely” and drawing out the Monopoly real estate from memory. But because they then made their moves on the capitalist game with the communist pieces, the game evolved in interesting directions. It seemed like an apt metaphor for the postsocialist transformations: not playing on the ruins of communism but playing with the ruins. In Eastern Europe at that time (and still in some parts of the former Soviet Union) actors were not playing by just one set of rules but within several.
But the two stories are not just metaphors. Although they are quite literally “toy versions” of a model, they can be taken as actual cases of rules co-evolving and new games emerging as agents play in simultaneous multiple games. In social life, such multiple games are not that uncommon, as we frequently encounter situations in which there are multiple rules operating according to heterogeneous principles of valuation. How will game theory tackle these questions?
In sociology, Norton Long made the first significant contribution in his 1958 classic, “The Local Community as an Ecology of Games” AJS 64(3), and John Padgett and his co-authors have since developed that notion in a series of important articles.
At a conference some years ago, I told game theorist Adam Brandenburger that I hadn’t paid much attention to game theory but that I would when it gave serious treatment to the problem of strategic action in multiple games. Although game theory might have many agents and strategies, there was always only one game (or pay-off function). Adam sent me a copy of paper, “The power of paradox: Some recent developments in interactive epistemology” and I saw that these issues were starting to be addressed.
Two recent articles show that it is indeed time to pay attention because game theory is now grappling with this problem head-on. In “Co-creating Games: A Co-evolutionary Analysis” (available here), Jason Potts and John Banks do important conceptual work with a model that includes an analysis of a massively multiplayer game. Santa Fe Institute colleague, Scott Page and co-author Jenna Bednar offer similar insights but from a more technical perspective. See their “Can Game(s) Theory Explain Culture?: The emergence of Cultural Behavior Within Multiple Games.”
In my reading, each paper still lacks a sociologically robust concept of identity. But these are important papers. There is no reason that economics should have a monopoly on game theory any more than that sociology should have a monopoly on multiple games. Our work as sociologists and theirs as economists will be improved when more of us are making simultaneous moves in each of the others’ games.
Current issue of Rationality & Society has a piece by Herbert Gintis in which he critically reviews epistemic game theory (pieces by Aumann mainly) and tackles the problems related to the assumption of common knowledge in mainstream game theory.
I’m a sociologist and regard myself as a “consumer” of game theory I definitely agree with what you wrote. Majority of game-theoretic models assume single payoff structure that is known to all players and all players know that others know that etc (common knowledge). In reality people usually have to learn by themselves the rules of the game first. A good theory about these processes is still underdeveloped. Gintis gives nice example of such situation of a visitor in a foreign country; the foreigner does not know all the conventions and cultural “signals” that allow the “natives” to recognize what are the rules of the game in a particular interaction.
I also recall a chapter in one of the Raymond Boudon’s books, not sure which one now, where he analyzed a simple game in which both players had different ideas about the actual payoffs.
Although Gintis’ paper is quite technical at places it is a very interesting read.
michal
July 20, 2010 at 10:36 pm
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July 21, 2010 at 1:10 pm
David – Thanks for drawing our attention to those papers. I’ve been reading game theory and agent-based modeling for the last two hours now. It’s addictive stuff.
brayden
July 21, 2010 at 4:48 pm
David, I appreciate your comments and myself have tried to relax the common knowledge assumptions in various ways. Many game theorists I talk to are well aware of the idea that real people are effectively laying many games simultaneoulsy and link them through their strategies. I, too, am a bit skeptical of the epistemic game theory approach, and I suspect that the evol GT work on this will make the best headway first.
There is an unmentioned issue. It can be said that people play in multiple games simultaneously, yet mathematically this is can be restated as them playing one much larger game. In other words, there is nothing wrong with the game form; it is more a matter of identifying the actual game. This is separate from the issue of common knowledge.
Mike M.
July 21, 2010 at 6:15 pm
Richard Swedberg. 2001.Sociology and Game Theory: Contemporary and Historical Perspectives, Theory and Society.
Edy
July 21, 2010 at 7:38 pm
“Our work as sociologists and theirs as economists will be improved when more of us are making simultaneous moves in each of the others’ games.”
I firmly agree… I hope we can find more ways of encouraging such innovation.
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July 22, 2010 at 1:47 am
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