Saturday, June 25, 2005

group to space map and space to group map

initial run t=1 (t=0 is seeding agents)
1. group to space map :: CA-A 1
2. Synthetic Gestalt
3. space to group ie. agents know which edge permeable, which not :: CA-S 1
complete process of new bits (both birth agents and emerging spaces)
t=2, 3, ...n
1. group to space map :: CA-A 2
possible mapping: on top of existing y and on top of existing x
2. Synthetic Gestalt
3. space to group :: CA-S 2
new bits process as follows:
if on top of existing y, then insert new x that shares an edge to the y;
if on top of existing x,
first case (of the single permeable x to y), insert new x shares an edge to the x
second case (two adjoin x that share edges to y), no new x make the shared edge as permeable edge.

each new x means one agent birth, positioned randomly.

death rule: any unsupported mapping, will bring death to the existing space and its corresponding agent.


the problems:
1. the overall framework for agents' state changing and its impact to co-evolution
2. the same heading for spatial system, conjoin with the population state.
both done in a belief of CA as the procedure.

the essence of CA pull out: rules of state changing if surrounded by particular type of neighbours.

spatial system's CA conjoin with population state, where birth and death of agents interlink with each new emerging space.
in terms of mapping it, the grouping mapped onto either existing x or y.
a map onto y space seen as birth of agent, and thus a single permeable enclosure on space.
a map onto x space seen as possible birth and death, providing the rules abided. according to hillier's permeable space, only 2 types exists for this kind. new x that connects to an x which has connection to y, or new x with both connections to adjoin x and to y.

the birth rules as follows:
first type: new x (and thus new agent) allowed when a group map on a single permeable enclosure (ie. an x with connection to y only).
2n type: new x (new agent) allowed when a group map on each of single, adjoin cells which both have connection to y already.

death rules:
any occupational map not within above!

Thursday, June 09, 2005

some review on Schelling Micromotives


[Note to reader: This paper appeared in Constitutional Political Economy, 8, 319-335 (1997), pp. 91-106. Copyright Kluwer Academic Publishers, Boston. The present text matches the published 1997 version almost exactly, but has a different pagination and formatting.]

Convention, Social Order, and the Two Coordinations by Daniel B. Klein

"The central themes of Thomas Schelling's Micromotives and Macrobehavior (1978) are that a manifest, macro-level pattern may emerge, even though the process is without macro-level design, and that such an undesigned pattern is sometimes regarded as unsatisfactory by the very people who collectively generated it (19). "People can be trapped into self-enforcing rules that misdirect behavior" (120). One example is language: "in collective laziness we let inappropriate terminology into our language by default" (39).
Schelling is careful to distinguish the undesigned orders studied in Micromotives from the undesigned order of the free economy. He notes that the free-market order is not manifest: he writes of "the enormous complexity of the entire collective system of behavior, a system that the individuals who comprise the system needn't know anything about or even be aware of" (22). Schelling says that the free market "does remarkably well in coordinating or harmonizing or integrating the efforts of myriads of self-serving individuals and organizations" (23). His discussion of the free economy is brief, and ladened with reservations, but it projects a vision along the lines of Smith or Hayek. He explains that the market order consists chiefly of activities that do not have major or systematic effects on nonparticipants (28). In constrast, the activities studied in Micromotives do have such effects, and the mechanisms underlying those activities often do poorly in harmonizing or integrating individual efforts."

"While Schelling has been careful to distinguish between the market order and the manifest patterns that he studies, the new literature has sometimes conflated the two. In a magazine article on complexity and social order, Brian Arthur, a leading path-dependence theorist, is quoted as follows:
Right after we published our first findings, we started getting letters from all over the country saying, 'You know, all you guys have done is rediscovered Austrian economics ... I admit I wasn't familiar with Hayek and von Mises at the time. But now that I've read them, I can see that this is essentially true (as quoted in Tucker 1996: 38).
Hayek is cited in a similar way by Arthur DeVany (1996). In his computer simulation, agents choose between one of two technological standards, again like VHS versus Beta. The choice process is decentralized and agents have myopic knowledge, but random experimentation is injected into the process. Under certain parameter values the agents finally adopt the better technological standard, achieving higher network efficiency. DeVany writes: "Even though this is computer science, it is precisely the message of Smith, Hayek, and Alchian" (1996: 433). In describing the system's adoption of the better technological standard, DeVany uses the term "emergent order," a term that he seems to equate with Hayek's term "spontaneous order" (see p. 427).
Robert Sugden, again in a similar manner, writes in his article "Spontaneous Order" (1989) exclusively of the emergence of customs and conventions. Sugden describes a convention for the appropriation of driftwood as "an example of what Friedrich Hayek calls 'spontaneous order'" (85). The article makes no mention of the complex market system of myriad individual efforts."

"The term "spontaneous order" is found in the work of Auguste Comte (1896: Book VI, chap. V) and the word "spontaneous" is used in corresponding fashion by Herbert Spencer (1884/1892: 135, 196, 274, 301, 326) and by Emile Durkheim (1964: 360 and elsewhere).(6)
But it was Michael Polanyi (1951) who used the term "spontaneous order" in a consistent way to mean polycentric order, or an undesigned concatenation of affairs. Hayek uses it in the same way (Polanyi is quoted at Hayek 1960: 160). Hayek uses it primarily to mean the catallaxy and other undesigned concatenations of social activities. He generally did not mean by it undesigned conventions or rules; for that he generally used the word "rules," although he did occasionally use the term "spontaneous order" to mean undesigned conventions or rules (e.g., Hayek 1964: 5-6). On the whole, I would say the lately quoted words of Brian Arthur, Arthur DeVany, and Robert Sugden, who speak exclusively of undesigned conventions, are at least somewhat misguided in linking, without qualification, their own work to Hayek's work on spontaneous order."

"Ambiguity in the meaning of "spontaneous order" closely parallels ambiguity in usage of the word coordination. A fine example of Hayek's usage is the following: In the market economy we depend "on that division of knowledge between individuals whose separate efforts are co-ordinated by the impersonal mechanism for transmitting the relevant information known by us as the price system" (Hayek 1944: 49-50). Michael Polanyi writes in the same idiom in The Logic of Liberty (1951: 115): "[In] spontaneously ordered systems ... persons mutually adjust their full-time activities over a prolonged period, resulting in a complex and yet highly adaptable co-ordination of these actions." Ronald Coase (1937: 37) uses the word in the exact same way when he explains his central aim in his famous essay on the firm:
In view of the fact that, while economists treat the price mechanism as a co-ordinating instrument, they also admit the co-ordinating function of the "entrepreneur," it is surely important to enquire why co-ordination is the work of the price mechanism in one case and of the entrepreneur in another.
Also in his Nobel lecture, Coase (1992: 6) consistently refers to "the pricing mechanism" as a "method of co-ordination."

"Coordination is first and best understood as something we hope to achieve in our interaction with others. I hope to drive on the same side of the road as others, I hope to use the same semantics as do my listeners, I hope to go to the same place in Manhattan as the person I wish to meet. In these cases, we hope to coordinate our actions with the actions of others, by coordinating to some common principle or focal point.
The features of this type of coordination are explored by Thomas Schelling in The Strategy of Conflict (1960). I will sometimes refer to it here as Schelling coordination. Schelling coordination has been given more formal structure by the philosopher David K. Lewis in his book Convention: A Philosophical Study (1969). Lewis uses formal game models to characterize situations. Figure 1 shows a road game of whether to drive on the Right or the Left. (Suppose that cars are built in the American fashion, so Right is better than Left.) A set of strategies -- such as, for you: drive on the Left, and for me: drive on the Left -- constitutes a coordination equilibrium when two distinct kinds of requirements are satisfied. The first is the Nash requirement, namely, given that you are choosing Left, my choosing Left is best for me (and likewise for the statement that reverses you and me). The second goes beyond Nash; it requires that, given that I am choosing Left, your choosing Left is best for me (and likewise for the statement that reverses you and me). Coordination equilibrium is Nash equilibrium plus this second requirement (suitably generalized). Both of us driving on the Left is a coordination equilibrium, as is both of us driving on the Right. "

"In a situation with at least two coordination equilibria, we face, in Lewis's terminology, a coordination problem, because we may have difficulty coordinating with each other. We need a common principle or focal point to get us to a coordination equilibrium. Individuals make a conscious effort to coordinate with each other, or at least to coordinate to a focal point. They strive for and see a meshing of action in their own activities. Schelling coordination is manifest.
Now, is this what Hayek has in mind? When Hayek speaks of our separate efforts being coordinated by the impersonal mechanism known as the price system, can we reduce this to an issue of Schelling coordination? It is true that market participants are achieving face-to-face coordination, by sharing a common language, a common measure of time, and so on. Everyone at the office arrives by nine o'clock in the morning and this coordination enhances productivity. But Hayek has more in mind. He means that when the blacksmith forges a pair of clipping shears, that activity is well coordinated to the activities of the weaver, who some time later works with the wool that was clipped from sheep with those shears. There is a flavor of Schelling coordination here, but only a flavor. First of all, the blacksmith and the weaver do not even know of each other's existence, and have no manifest sense of coordinating their actions with the actions of the other. If one were to visualize a "game" which included all of their relevant strategy alternatives, it would have to be a game that also included the relevant strategies of hundreds or thousands or even millions of other players alike. One might venture to call it the "catallaxy game." Such an exercise would depart from noncooperative game theory, which draws up games with an understanding that that is how the game is understood by the players. This is the common-knowledge assumption of game theory.
Hayek emphasizes that the context understood by the individual is local and very limited. The weaver sees only the manufacturer, not the blacksmith. The individual uses common cultural focal points to carry out interaction with others, but this is like the baton pass between members of a relay team. The individual confronts problems that do not lie in achieving manifest coordination, but in activities analogous to running alone with baton in hand. He is responding to price signals and local opportunities; he is trying to gain lucrative insights; he is working hard to keep his promises, and to see that his trading partners keep theirs. He does not perceive himself to be playing a coordination game with myriad distant people. As Adam Smith (1776: 423) put it, each promotes "an end which was no part of his intention" -- nor even of his knowledge.
And there is another important point which suggests that Hayek coordination is not Schelling coordination. Hayek coordination must involve myriad individuals. Now, shall the "catallaxy game" include the retailer's competitors? If we include the competitors -- and doing so would seem essential to a Hayekian framework -- it becomes plain that market outcomes are not coordination outcomes. Whether we think of coordination equilibrium in formal games or of resolutions in Schelling's parables, the outcome in which the two retailers compete is not an instance of coordination. Retailer A, given his own action, is not best satisfied by the rivalrous actions taken by retailer B. Retailer A is not best satisfied when the distributor supplies articles not only to him, but also to retailer B. Most fundamentally, Retailer A is not best satisfied when the distributor raises his price, or when the customer departs without having made a purchase!"

coordination metacoordination

Interaction that is agreeable to the interactors

Manifest from the interactor's point of view

(From the intransitive verb)

Hayek, Polanyi, Coase

Arrangement of elements that is pleasing to an external

Abstract from the interactor's point of view
("invisible hand")

(From the transitive verb)

Figure 2. Two concepts of coordination