John Kemp: Spontaneous Change, Unpredictability and Consumption Externalities: Appendix

Simulation using an Excel spreadsheet.

To keep the Excel file small for downloading only 50 iterations are performed. However, after loading it into Excel the last row can be copied down for as many further rows as the user wishes. To do this, it is first necessary to turn the protection off (Excel Tools menu, Protection). The charts displayed in the JASSS article were based upon the iteration of 500 rows.

The selection of A or B depends upon the generation of a random number 0 or 1 with prob0 = prob1 = 1/2.

If random number = 0 then a type J agent gets to make the choice:

If [Aj +j*Sin(Pi/20*Na)] > [Bj + j*Sin(Pi/20*Nb)]
then the J agent chooses A otherwise B.

If random number = 1 then a type K agent gets to make the choice:

If [Ak +k*Sin(Pi/20*Na)] > [Bk + k*Sin(Pi/20*Nb)]
then the K agent chooses A otherwise B.

Cells in blue: B9, B10, D9, D10, F9 and F10 can be set to values chosen by the user.

Placing any character in cell A12 and pressing "Enter" reactivates the spreadsheet, generates new series and displays a new chart. The previous simulation and chart are lost and can never be recovered or replicated.

Column A: N Shows total number of selections N = 1 to n.

Column B: RAND Generates random number 0 or 1.

Column C: J test Shows the selection A or B when a J agent selects.

Column D: Na Shows cumulative number of selections of good A by both types of agent and is displayed on Chart1 in dark blue.

Column E: Nb Shows cumulative number of selections of good B by both types of agent and is displayed on Chart1 in yellow.

Column F: K test Shows the selection A or B when a K agent selects.

Column G: Ja Shows 1 if J selects A otherwise 0.

Column H: Jb Shows 1 if J selects B otherwise 0.

Column I: Ka Shows 1 if K selects A otherwise 0.

Column J: Kb Shows 1 if K selects B otherwise 0.

Column K: (Na - Nb) Shows difference between the cumulative selections of A and B and is displayed on Chart1 in purple.

Chart1
Shows the series Na, Nb and (Na - Nb) as generated in columns D, E and K.

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Column A:	N	Shows total number of selections N = 1 to n.

Column B:	RAND	Generates random number 0 or 1.

Column C:	J test	Shows the selection A or B when a J agent selects.

Column D:	Na	Shows cumulative number of selections of good A by both types of agent and is displayed on Chart1 in dark blue.

Column E:	Nb	Shows cumulative number of selections of good B by both types of agent and is displayed on Chart1 in yellow.

Column F:	K test	Shows the selection A or B when a K agent selects.

Column G:	Ja	Shows 1 if J selects A otherwise 0.

Column H:	Jb	Shows 1 if J selects B otherwise 0.

Column I:	Ka	Shows 1 if K selects A otherwise 0.

Column J:	Kb	Shows 1 if K selects B otherwise 0.

Column K:	(Na - Nb)	Shows difference between the cumulative selections of A and B and is displayed on Chart1 in purple.

Chart1		Shows the series Na, Nb and (Na - Nb) as generated in columns D, E and K.