Tuesday, May 22, 2012

Let the Buyer Beware


"Modern societies are complex systems" may be the understatement of the year.

Obvious or not, however, it must be stated when attempting to model even some minuscule aspect of such a society. Take, for instance, the paper published today by T.P. Peixoto and S. Bornholdt from the Universitat Bremen in Germany, where the authors develop a model to simulate commodity buyers and sellers in an open, capitalist market. The model is based upon a "trust game," which, in a nutshell, assumes (as in real life) that each individual agent wants to choose what's in his or her best interest, but doesn't necessarily know which option is the most likely. Thus the decision must be made on the basis of trust: belief that the chosen option is the right option. Or, in the language of this particular model, "buyers must decide if a certain product is worth its cost, and sellers must decide which price they should assign for their products."
Add to this trust game a confounding factor: perhaps we don't have the option of choosing whether or not to buy, but only from where (or from whom) we buy. Think of gasoline or groceries. We may be able to shop at Safeway or Kroger or Fresh Market, but we can't realistically opt to not buy groceries. So we're looking at a system where sellers set their price, buyers choose their sellers, and hopefully (as capitalists would have us believe) the market works out to be maximally beneficial to all parties (more specifically, both buyers and sellers agree upon a fair price).

Here's where things get interesting.

Keep in mind that, in the model, all of the agents - the buyers and sellers - operate independently. The sellers' only goal is to maximize payoff, and the buyers' only goal is to minimize cost. The model doesn't assume that there's any difference in the actual quality of the commodity, only that each agent has some net (monetary) benefit from its interactions: an overall buyer's satisfaction and an overall seller's profit. In the modeling equations, each of these is related to the "value of money," which can be interpreted as a value of the goods/services purchased. With each iteration of the model (ie, the progression of time), the buyer's strategy is updated through comparison - "am I getting a fair price from this seller?" - and the seller's strategy is updated through repetition - "this seems to be a working market for me."
There's one final rule in the model which the authors can tweak: the sellers, essentially, react faster than the buyers. And when this is the case, the outcome is quite surprising.
The sellers are able to quickly opt for lower values of money, leaving fewer and fewer higher values available to the buyers (remember that your money "goes further" as a buyer when it's worth more). These values then remain low because the buyers are left with no other options, although there can still be substantial small-level fluctuation, brought about because the buyers are still forcing the sellers to compete. In plainer terms, the system has produced a cartel: a group of sellers who control the price of a commodity (the value of money) to their own benefit and to the detriment of buyers.
Now, it's very important to remember that the agents in this model are acting independently. There is no collusion between sellers, no implicit or explicit agreement as to setting the value of money. The behavior is what's known as emergent - it appears, simply and completely unforced, as an outcome of the rules of the game.

(a more appropriate caption: "just look at the value of money crash and burn!")

So the simple capitalistic trust game modeled by the authors leads us, surprisingly, to the behavior of a cartel; to unanticipated price-fixing (without collaboration among sellers) that is detrimental to all buyers. Sure, the model doesn't take everything into account, but the result is still shocking.

Like the authors themselves state, there's no need for conspiracy: it seems like simple, individualistic capitalism can lead directly to cartels. Caveat emptor.

Tiago P. Peixoto, & Stefan Bornholdt (2012). No Need for Conspiracy: Self-Organized Cartel Formation in a Modified Trust Game Physical Review Letters, 108 (21) : 10.1103/PhysRevLett.108.218702

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