Rationality-in-relations - Extensions and Criticisms

American Journal of Economics and Sociology, The,  Jan, 2003  by Hans Bernhard Schmid

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What is Rational about the "Principle of Coordination"?

COORDINATION PROBLEMS ARISE WHEN, TECHNICALLY SPEAKING, there are at least two approximately equally good proper coordination equilibria and no "salient" solution in a given situation. (17) As pedestrians on the sidewalk, it matters little to us whether we get by each other by both moving to the right or both moving to the left, as long as both choose the same strategy. Sometimes, however, we get in each other's way, not because we are lost in our thoughts and simply do not watch out for each other, but because our respective strategies to avoid collision do not match. In such cases, awareness of the situation (and our awareness of the awareness of the others) is per se of no help. It can even make things more complicated. For if I knew that you, being completely lost in your thoughts, will just walk straight on irrespective of what I do (and if there is enough space), I could easily get out of your way simply by moving to the other side of the sidewalk. But since I know that you are aware of the situation an d aware of my awareness of the situation (and so on), I know that this strategy will be successful only conditionally. My moving aside will help bringing about our getting by each other only if you don't simultaneously make the same decision. If you move out of my way, I should walk straight on. Thus if we restrict the analysis to pure strategies and if we take ourselves to be decent, not preferring "walking straight on" to "moving aside" (which would turn the situation into a "chicken game"), the two equally good equilibria are "move aside"/"walk straight" and "walk straight"/"move aside," both allowing us to get by each other hassle-free.

In the absence of any conventions, informal customs (such as the norm to keep to the right-hand side of the sidewalk), or any other form of "salience" that would make one of the equilibria the "obvious" solution (such as traffic signs saying "keep to your right"), we are at loss for an answer as to what is "rational" to do in such situations, and the economic standard theory simply gives us an explanation for why this is so. Here, it is generally assumed that the participants A and B are both rational individual utility maximizers having preferences (such as a desire not to get in each other's way), and making their choices over alternative strategies in accordance with the expected consequences of their individual choices. In game theory, it is further assumed that the participants have "common knowledge" of their rationality as well as of their respective preferences, that is, of their respective payoffs in the matrix that displays the possible outcomes of a given situation. In the standard model of rationa l choice, the term "common knowledge" (18) serves to describe a form of "knowing x" that all "participants" in a given situation have, and that is mediated by infinite hierarchic iterations of knowledge on the other participant's knowledge. Thus in the case of the pedestrians, A knows that B is rational and that B prefers "getting by" to "colliding," and he knows that B knows that A is rational and that A prefers "getting by" to "colliding," and he knows that B knows that A knows and so on and so forth. (19) The problem, however, is that they have no rational ground to decide over the alternatives "walk straight"/"move aside," not in spite but because of their rationality. They simply cannot form expectations concerning the outcome of their individual choices over the given alternatives. Having common knowledge of their rationality, both A and B know that the likeliness of the other's choices (which they somehow have to size up in order to form some expectation concerning the consequences of their own individ ual decision) is dependent on the other's expectation of her or his own decision, which leads to an infinite regress.