From Santa Fe Institute Events Wiki

Revision as of 20:02, 29 July 2008 by Cmefferson (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Last Tree Project


This is a group project of the SFI, lead by Juan Camilo Cardenas, Charles Efferson, and John H. Miller. Please do not cite or use any of the material contained herein, without the express written permission of the authors. Thanks.

Next Steps

  • JCC will look at his current data and identify (near) extinction events, and see if there are any insights to be had for this project.

The project site where the data will come is at: There are at least two sources of such data from human behavior: -Field experiments with villagers in colombia and thailand using the "forest game" (see a first papr reporting data from these games at: )

-Lab experiments using the "pacman" game of forest extraction with students forraging over a space of trees with regrowth

  • All three will continue to refine and expand this wiki with the near term goals of
    • Having a good sense of the basic problems and likely classes of explanation
    • Creating a set of simple experiments to explore the above
    • Figuring out a simple pilot experiment
    • Funding (we will need some $ for running the experiments---probably not that much money in the end)
      • Home institutions?
      • SFI International Program?


Throughout history we see humans driving various systems to extinction (trees on Easter Island [Diamond, Collapse], essentially American Bison, etc., etc.). Can a set of clever experiments illuminate the causes of such behavior?

Suggested Hypotheses for Why Things Get Driven to Extinction

Don't anticipate it (Diamond, ch 14)

We should look at the work by Erling Moxnes on how much do humans can anticipate it:

  1. Moxnes, E. (2004). "Misperceptions of basic dynamics, the case of renewable resource management." System Dynamics Review 20 (2) 139-162. Experiment T1, Instruction T1, Experiment T2, Instruction T2
  2. Moxnes, E. (2000). “Not only the tragedy of the commons: misperceptions of feedback and policies for sustainable development.” System Dynamics Review 16(4).
  3. Moxnes, E. (1998). “Not only the tragedy of the commons, misperceptions of bioeconomics.” Management Science 44(9):1234-1248.
  4. Moxnes, E. (1998). “Overexploitation of renewable resources: The role of misperceptions.” Journal of Economic Behavior and Organization 37(1):107-127.

Don't perceive it once it occurs (Diamond, Ch 14)

Fail to solve it once it is perceived (Diamond, ch 14)

Social dilemmas

Group think failure


  1. Overconfidence on the system's capacity to recover.
  2. A lack of economic (value) importance of the resource in period t or any t+n.


The general experimental framework will be the harvesting of a renewable resource in a very simple framework. For example, there are X trees in the world, at each round you can harvest some of the trees for experimental earnings, and at the end of each round we add some trees as a function of how many trees remain. We should probably have a fixed probability of the experiment ending at the conclusion of each round, so that we can impute a discount rate. The experiment ends when the system goes extinct.

The main observables will be total harvest and time to extinction.

Experimental Conditions

  1. Individual versus group decision making
    What happens when one individual is in charge of all of the decisions versus a group of individuals? Note that by "group" we could mean a group of individuals a'la the usual public goods experiments or a "governmental" group where the individuals have to agree with one another prior to making a decision. It would be interesting if we found conditions under which an individual drives the system to extinction, as that would imply that social dilemmas are not necessary for such events
    This treatment could cover the question of group size, i.e. as more players access the resource, is it more likely that someone will over exploit the resource.
  2. Underlying growth processes
    How does the structure of the underlying growth process impact extinction? Are there some forms that are much harder for decision makers? The experimental literature has largely ignored dynamical decision-making in a CPR setting. Nonetheless, harvesting is an intrinsically dynamical process. Treating them as such in experiments would be one important way into the problem. There is some literature, though. Here's a paper:
    1. Types of growth processes. We need to figure out a few, simple, prototypical growth processes from ecology. At the moment we have three characteristic processes discussed here:
    2. Are these the full set of prototypical growth processes? Answer: Probably not the full set, but they represent three very different and widely discussed postulates.
    3. What if we put lags in the growth process? Answer: Discrete-time models/experiments involve an implicit lag. Or is something else meant here?
  3. Abstract versus real objects
    Are people better at dealing with these process when they are abstract (e.g. tokens) or real (e.g. trees or some other resource with which they have some actual experience)?
  4. Change in scale
    Can we induce a sense of "false abundance" by simply changing the scale of the problem (let every tree become 10 shrubs), and does this have any implication for behavior?
  5. Information and uncertainty impact this system?
    1. Does noise in the growth process make this easier or harder? (Similar to lags)
    2. Does noise or uncertainty in the actions of others in a group make extinction more likely?
    3. Can we induce "moral wiggle room" by, for example, having some probability that at any time, harvesting trees will help the ecosystem and increase growth, or that the growth is not tied to the existing number of trees? (This latter option is also known as the "bad and inconclusive science" approach a'la Bush---there is a chance that we have no impact on global warming...) The wiggle room would be more interesting if they could, for free, know what kind of world they are operating in. Presumably, under such a condition, you would want to know as it would help you maximize payoffs, but if you wanted the wiggle room, you might not want it revealed and just act as if it was the more favorable world.
  6. Discount rates
    Presumably, under high discount rates, extinction is the preferred option. Does the discount rate matter to the participants? Can we make them stay in the game too long?
  7. Price - scarcity effects
    As the stock approaches zero, and the resource units are still highly valued (i'd assume the social value of that last tree in Easter Island could be pretty high), one question emerges: would that drive those extracting it to more rapidly grab those units? or would they value the capacity of regeneration and maintain a longer stream of income for more rounds? (they would still need to figure out the collective action and free-riding problem).
    In an experiment, we could have the group amount extracted create a typical supply function that drives prices based on scarcity and see the reaction of those extracting. For instance, we could update the price paid per tree/token extracted based on supply and demand and as the stock goes down to zero the price would increase. Would that push them to grab even more and accelerate extinction? or would that bring incentives to stop extinction and value those highly priced delicacies?
    The value of rare delicacies as a source of data and thought: Highly priced delicacies that come from nature could provide some more insights. Here is a list of examples (skip gold, just stupid for my taste):
  8. Starting conditions and path dependence: do starting conditions change the system convergence? Is it the same to start with a healthy ecosystem vs a depleted one?

Choosing among treatments

We have 8 treatments overall

  1. Juan Camilo's ranking:
  7. Price - scarcity effects, 5. Information and uncertainty impact this system?, 1. Individual versus group decision making
  1. Juan Milleroso's ranking (based on factors below):
  1. Group Size (1), 2. Ending Condition (3), 3. Reporting (4)
  1. Carlos Effersonio's ranking (conditional on holding some kind of ecologically motivated growth process fixed):
  (1) Group size, (2) Price, (3) Initial conditions, (4) Ending conditions

Next Set of Experiments? (And their relevant questions behind)


  1. Group Size (N= 1, 2, 10)
        1. Q/ Even 1 player might not be able to optimize the path of extraction
        2. Q/ As more players access the resource, it is more likely someone will grab resource units 
  2. Growth Process (exponential with a cap) 10% vs 25% (cap of 1000)
        1. choosing logistic vs exponential growth has trade-offs regarding modeling
        2. both models behave similarly at the near-exhaustion region of the resource stock 
  3. Ending Condition (10 rounds vs 10% chance of ending each round)
        1. Q/ "last round" effects could be important 
  4. Reporting (each round, two round lag)
        1. Q/ Available information and timing of the information might affect how players anticipate the consequences of their actions 
  5. Discount (0% vs 10% decrease in value each round)
  6. Starting conditions (100 vs 1000)
        1. Q/ path dependence: do starting conditions change the system convergence? 
  7. Institutional conditions: rules
        1. Q/ Do certain agreements by players (rotation vs quotas vs incentives) change chances of exhaustion? 
  8.  ??? what else, what can we eliminate ??? 


Spring, 2008, Pilot

Miller added the following question to a CMU experiment on altruism (and other topics):

Assume you live on an isolated island that has some trees with 9 other people. Every time you harvest a tree you will be paid $1. This payment will go only to you, and be made in private.

For every two trees that are not harvested, one new tree will grow next period. Thus, if 200 trees remain after the harvest, then next period there will be 300 trees (the 200 original trees plus the 100 trees that arise from the 200); if there are 50 trees remaining, then the next period there will be 75 trees (the original 50 plus 25 new trees). Suppose that at the end of the harvest, there are 100 trees remaining. How many trees will be around at the start of the next period?

There will be twenty harvest periods in this task. In every period, every individual on the island will decide (in private) how many trees to harvest in that period (and then be paid, in private, $1 for every tree that he or she harvested). At the end of each harvest period, the total number of trees that remain will be announced to everyone, but you will never be told (nor will anyone else) the number of trees harvested by any particular person. Assume that you are one of ten people on the island and that there are 100 trees. It is the first period of the task, how many trees do you want to individually harvest?

This question was given to three groups of eight subjects each. Two of the subjects failed to give the correct response to the first question (indicating a misunderstanding about the growth process involved), and they were eliminated from the data. Of the remaining 22 subjects, their answers to the second question were:

100 100 100 75 50 45 30 20 17 15 12 10 10 10 10 8 5 5 5 4 3 3

28.95 avg, 11 median, 10 mode.

Note that 17/22 (68%) of the subjects named an amount that, if copied by all other participants, would lead to extinction after the first period. Also, note that the optimal strategy here would be to not harvest anything (assuming that the twenty periods happen quickly), and this would leave around $221,684 to be split among the participants (versus the $100 available in period 1).


Some papers:

Some Further Economics of Easter Island: Adding Subsistence and Resource Conservation

John C. V. Pezzey ( and John M. Anderies ( Additional contact information John C. V. Pezzey: Centre for Resource and Environmental Studies, Australian National University John M. Anderies: Sustainable Ecosystems Division, CSIRO

Working Papers in Ecological Economics from Australian National University, Centre for Resource and Environmental Studies, Ecological Economics Program

Abstract: We extend Brander-Taylor's model of development on Easter Island by adding a resource subsistence requirement to people's preferences, and a conservation incentive in the form of a revenue-neutral, ad valorem tax on resource consumption. Adding subsistence improves plausibility; makes overshoot and collapse of population more extreme, and the steady state less stable; and allows for the possibility that statue building and erection will suddenly stop, in line with the archaeological evidence. We find a tax rate path which almost completely prevents overshoot, and conjecture that the overall strength of this path must rise when the subsistence level rises.

Easter Island: historical anecdote or warning for the future? Ecological Economics Rafael Reuveny, Christopher S. Decker Volume 35, Issue 2, November 2000, Pages 271-287

Abstract: Two standard solutions for the ‘Malthusian Trap’ involve institutional reforms and technological progress. Using Easter Island as an example, we investigate the hypothetical role that technological progress and population management reform might have played in preventing the collapse of the island's civilization. The model includes a composite manufactured good and a composite harvested renewable resource. Fertility is assumed to rise with per capita income. The resource's carrying capacity and intrinsic growth rate as well as labor's harvesting productivity are subject to technological progress. Fertility is subject to population management reform. The model yields a system of two simultaneous, nonlinear, non-autonomous differential equations. We first study the system's steady states. The system is then parameterized for Easter Island and its comparative dynamics are investigated in simulations. We find that technological progress can generate large fluctuations in population, renewable resources, and per capita utility, sometimes resulting in system collapse. With high fertility rates, the population and the resource vanish. None of the simulations investigated here exhibit a constantly growing per capita utility over time. Finally, we evaluate the applicability of these results to contemporary societies.