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There is a hint of a connection to game theory in Adam Smith's Wealth of Nations. For example, he says:

It is not from the benevolence of the butcher, the brewer, or the baker that we expect our dinner, but from their regard to their own interest.

We can put his general argument into a payoff matrix, like shown below:

enter image description here

There are two Nash Equilibria here: {DS,DS} and {S,S}.

Obviously, if they both specialize, they are both much better off. However, each of them not specializing is also an equilibrium.

Is there any way that Game Theory predicts the emergence of specialization in a population of such players?

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  • $\begingroup$ What's the argument here for why I lose out if I specialize but the other guy doesn't? $\endgroup$
    – user18
    Nov 12 '17 at 7:57
  • $\begingroup$ That's a good question. I didn't really consider it a problem when I drew up the matrix. But now that I think of it, perhaps the one who unilaterally specialises is at the mercy of the one who is self-sufficient. Does that make sense? There is an asymmetry in bargaining power in that situation. That's the only answer I can think of. $\endgroup$
    – Joebevo
    Nov 12 '17 at 12:21
  • $\begingroup$ I'd think of it as a repeated game, where at each stage it is a dominant strategy for each player to specialize a little more (so different from your payoff matrix here). Over time the division of labor deepens. $\endgroup$
    – user18
    Nov 13 '17 at 0:48
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I think you're over-analyzing here. Game theory is not just about maximizing your own pay-off, but about doing the best you can given the behavior of others. What Smith describes is just that people do what they're good at to make a living. That is, the way I read it, Smith claims that people specialize independent of what others do.

That being said if the emergence of specialization was to be predicted with game theory I'd look into evolutionary game theory. I'm not sure if you'll find anything though.

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    $\begingroup$ Both (DS,DS) and (S,S) are evolutionary stable strategies here. $\endgroup$
    – Giskard
    Nov 10 '17 at 12:19
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The matrix table show is just a part of Game theory tool set. The matrix only can be proven with granular heuristic rules.

Adams Smith claim of specialization is describing a generic context.
Because technology advancement can bring specialization beyond any imagination, that even bring diversification. For example, vacuum cleaner is something "specialize" before 20th century, today it is a household commodity. In addition, example like bakers/brewers doesn't guarantee efficiency, i.e. overproduction , recycling and many issues are beyond Adam Smith imagination.

I don't think it is possible to construct a reliable matrix to validate specialization.

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