Supporting Pages:

• Bayesian Analysis in Geography
• Flexibility Strategies
• Multi-Locational Flexibilities
• Early Warning Systems
• Conceptualizing the Decision Process: Spatial Decision Process Models

1. Uncertainty: Definition

• Uncertainty: reference to the lack of knowledge (ignorance) about the state of the environment or other decision variables.
• Uncertainty about the future vs. uncertainty about other places, events, structures and other phenomena
• Risk: reference to the consequences of uncertainty, such as regret often expressed in terms of probabilities of such consequences uncertainty then reduced to uncertainty about actual occurrence and, possibly, about the reliability of probabilities.

2. complex patterns and lack of visibility and control
   • diversity of environments (with its impact on the amount of required information)
   • distance to environments (and its impact on the visibility and cost of collecting information)
   • directness or indirectness of links to relevant environments (and its impact on visibility and cost of collecting information, as well as the likelihood that different actors have different (and not easily known) access to intermittent nodes thereby creating difficult to understand differences in competitiveness...
   • interconnectedness (and hostility) of environments. Interdependence and its associated redundancies and multi-causalities makes the tracing of causal structures and processes difficult. Of particular interest might be the possibilities of coalitions and collusive structures forming in the environment which may become hostile ("talks behind one's back"; "ganging up" etc. as frequently found as part of unstable oligopolies.
   Extreme uncertainties have often been associated with the term "turbulence" which in turn has been most extensively conceptualized by Emery & Trist (1965) and subsequently by Terreberry (1968). In their systems-theoretical view, complexity and dynamic change together tend to create "turbulent fields" which may become unpredictable due to pervasive and significant "relevant uncertainties". Often, such situations are described as environments where "the ground is in motion", where there are few if any stable structures which could potentially be the basis for understanding and projections of consequences of actions. (See also discussion in this online paper)

1. quality and clarity of information
2. lack of understanding of causal relationships between variables
3. time required to receive clear information about consequences of actions (leads and lags): gestation periods, environmental feedback.

4. Uncertainty and the classical location model

1. price uncertainty: (see Day & Tinney)
2. locational uncertainty in duopoly: Hotelling model
3. climatic uncertainty: "Man against Environment" (Gould, 1963);
4. more complex uncertainty situations

5. Uncertainty and the Nature of Spatial "Decisions"

1. "decision" without uncertainty is "empty" (Shackle)
2. y = f(x; z); Payoff = f(controllable and uncontrollable variables)

1. What is Game Theory? [Some References]
2. The History of Game Theory [Timeline] [http://william-king.www.drexel.edu/top/class/histf.html]
3. Minimax/ Maximin: "Wald Criterion"
   • In the Wald model, the decision-maker selects that strategy which is associated with the best possible worst outcome regardless of whether probabilities are available or not. It is a conservative strategy which alternatively assumes that either there are no bases for likelihoods (of states of nature), that the decision-maker is (cognitively and intellectually) not capable of using probabilities or that she could not use any available probabilities because of her short-run need to survive unfavorable outcomes (no reserves needed to "risk" unfavorable outcomes).
     The decision-maker following the Wald criterion can thus be alternatively characterized as
     1. a 100% pessimist [assigns a 100% probabilty that the worst possible state of nature will prevail]
     2. conservative [who is willing to consider only "sure things" (even if she has the probabilities]
     3. not having access to probabilities (for whatever reasons)
     4. not having the capacity to use probabilities (know-how)
     5. not having the resources to use probabilities (i.e. unable to survive in the short-run) ["survival strategist who is locomoting along rock bottom"]
     6. a competitor who is convinced that other competitor(s) is/are as smart or smarter
   • Exercise [5-points exercise: 2 companies, one large, one small]
   • Prisoners' Dilemma: Locational applications?

4. Minimizing maximum regret strategy (Savage)
   • Savage's regret-based decision-model avoids the extreme conservatism of the Wald model. Based on a "regret matrix" which compares (subtracts) the highest outcomes of each strategy from other outcomes. The new matrix shows the extent to which a decision-maker could have (ex-post, i.e. based on hindsight) done better (opportunity loss). The Wald solution rule (maximin/minimax) is applied to this new matrix to gain the minimax regret solution.

5. Equal likelihood principle (LaPlace)
   • the Laplace model can be interpreted as a transition model between the probability/risk model of decision theory and game theory in that it suggests that in the absence of any probabilities which could potentially differentiate the payoffs, equal probabilities should be assigned. "If one is 'completely ignorant' as to the state of nature which will occur, he should behave as if all states are equally likely." (Walker et al, p.170)
   
   
6. Optimism (Hurwicz criterion)
   • This decision criterion involves the identification of the worst and best outcomes for each strategy. An optimism coefficient (a) and a pessimism coefficient (1-a) are then determined (a represents a given individual's optimism that a positive outcome will occur) and multiplied by the (best+worst) outcomes. The sum of the resulting coefficients is the optimism index. The strategy with the highest index will be followed. One should not interpret as the likelyhood of states of nature. Instead, it is the decision-maker's optimism index relating to the occurrence of an outcome. "When a=0, the Hurwicz solution is the same as the pure Wald solution." (Walker et al., p.171)

7. Probabilistic Approaches

1. Probability: quantitative expression for the likelihood of an event
2. Hotelling model with discrete locations and probabilities: "expected value maximization" The "expected" is applied here in the usual statistical sense. Expected values are weighted averages found by multiplying the value (payoff) associated with each environmental/competitive state (location of the other duopolist) by the probability of incurring it and then adding these products. The weights (probabilities) sum to 1.
3. Decision trees for decision making (John Magee)
4. Subjective probabilities
5. Improving probabilities through learning (gathering additional evidence)
   • Bayesian Statistical Sciences
   • Morris: "Management Science: A Bayesian Introduction"
   • Expected value of perfect information: Upper limit of costs expended for additional information. Expected cost associated with acting under uncertainty = Value of perfect information - (minus) Payoff of best present action under uncertainty
6. Limitations of expected value/utility maximization model (How (in)appropriate is the model for the locational discourse?)

1. Passive vs. active approaches
   • Passive: accepting the uncertainty and e.g. select a maximin strategy or do nothing
   • Active: reducing the uncertainty through information searches and learning activities
2. Building responsiveness into a project, policy or strategy
   • Diversification Strategy (no additional action needed, responsiveness occurs automatically or by default, e.g. "having many eggs in one's basket")
   • Adaptability strategies (adjustment through simple alterations, no additional investments needed)
     • "so long as the environment of the firm is unstable (and predictably unstable) the heart of the theory [of firm behavior] must be the process of short-run adaptive reactions." [Cyert & March, p.100]
   • Flexibility strategies (adjustment possibilities are created through initial planning of (optional) subsequent adjustment investments in response to new information (e.g. keeping real estate in reserve for subsequent expansions after successful marketing campaign.
   • Locational Flexibility: the ease of adjustment of the "locational setting" of an organization to changing location conditions.
     1. In-situ flexibility: a flexibility which can envoked without changing the location of the facility: adjustments are accomplished at the same location
     2. Interlocational flexibility: A multi-locational organization is often able to to accomplish locational adjustments by shifting activities between existing location, i.e. without creating new or abandoning obsolete locations.
     3. New Location Flexibility/ Plant Closure Flexibility: The relative ease of opening new or closing old locations: The cost and time delays associated with such relatively long-run projects can be reduced by a variety of embedded preparations.
3. Taking out insurance
   • Example I: Weather Insurance
4. Collecting more information
   • Hiring consultants
   • Opening a research department
   • etc.
5. Procrastinating, waiting for the future to arrive, waiting for better weather, riding out periods of particularly high levels of relevant uncertainty

Brian Goodall, Dictionary of Human Geography (key words): Behavioral environment; Behavioral matrix; Game Theory (incl. minimax; pay-off matrix; saddle point); Information field; Probabilistic; probability; Activity space; Subjective probability;

Internet Sites:

• Strategy and Conflict: An Introductory Sketch of Game Theory
• Game Theory: General Resources [http://econlinks.com/gametheory.shtml]
• Game Theory: Chronology [http://www.econ.canterbury.ac.nz/hist.htm]
• Institute for Hazards Mitigation Planning and Research [UW College of Architecture and Urban Planning]

Newspaper Clippings:

• Vulnerable companies bet billions on weather; Seattle Times, Sunday, July 12, 1998 by Sharon Walsh, The Washington Post

  "Global warming, greenhouse gases and the most extreme El Nino since the 1800s are contributing to severe swings in climate... companies scurrying to find ways to protect themselves against the vagaries of Mother Nature. For years, businesses have hedged against economic losses with financial products based on interest rates, currencies, commodities... These products ... are called derivatives because they are derived from different bets on the future movement of just about anything that can't be predicted with certainty. And, what's more unpredictable than the weather? So some companies are sheltering themselves with something new: weather derivatives..."

Literature:

Lists:

• Uncertainty in Economics and Finance; Dr. Richard MacMinn [Fall 1998]

G. A. Bradshaw and Jeffrey G. Borchers Uncertainty as Information: Narrowing the Science-policy Gap [National Center for Ecological Analysis and Synthesis (NCEAS) and USDA Forest Service; 2Department of Forest Science, Oregon State University]

Chichilnisky. Graciela, Economics of Uncertainty. August 1997 (online)

Downs, George W. and David M. Rocke, Optimal Imperfection? Domestic Uncertainty and Institutions in International Relations. Princeton Univ.Press 1995. [JX1395. D69]

Duncan, Robert B., "Characteristics of Organizational Environments and Perceived Environmental Uncertainty," Administrative Science Quarterly September 1972, 313-27.

Ekinsmyth, C. Hallsworth, A. Leonard, S. Taylor, M., Stability and instability: The uncertainty of economic geography. AREA. Vol. 27, no. 4, DEC 1995, p.289-299.

F.E.Emery & E.L.Trist (1965)

Hardaker, J. Brian, Coping with Risk in Agriculture. CAB International/ Oxford UP, 1997. (288pp.)

Forges, F. and J-F. Thisse, Game Theory and Industrial Economics, in: Norman, George and M. La Manna, in: The New Industrial Economics. 1992 pp. 12-47. [pp.33ff. The Location-Price Model] [HD 2326.N42, 1992]

Goodchild, Michael F., UNCERTAINTY IN GEOSPATIAL INFORMATION REPRESENTATION, ANALYSIS AND DECISION SUPPORT [FY97 NURI RESEARCH PROPOSAL; SUBMITTED BY THE NATIONAL CENTER FOR GEOGRAPHIC INFORMATION AND ANALYSIS AT THE UNIVERSITY OF CALIFORNIA, SANTA BARBARA AND THE UNIVERSITY OF MAINE]

Gould, Peter, Man against his Environment: A Game-Theoretic Framework, Annals (AAG), 53(3), 1963, 290-7.

David F. Hendry and Neil R. Ericsson, eds., Understanding Economic Forecasts (MIT Press, 2001) [HB3730.U49.2001/Suzz] [ PDF files (pre-publication) "Forecasting Uncertainty in Economic Modeling"]

Hey, John D., Uncertainty in Microeconomics. New York: NYU Press, 1979.

Kahneman, Daniel; Paul Slovic and Amos Tversky, eds., Judgment under Uncertainty: Heuristics and Biases. Cambridge: Cambridge University Press, 1982.

King, L.J. and R.G.Golledge, "Bayesian Analysis and Models in Geographic Research," in Univ. of Iowa Geography Dept. Discussion Papers No.12, 1969, pp.15-45 [Geographical Essays Commemorating the Retirement of Harold H. McCarty]

Rabin, Matthew. "Psychology and Economics," Journ. of Econ.Lit. 36(1) March 1998, 11-46 (Review Paper)

Sandmo, Agnar, "On the Theory of the Competitive Firm under Price Uncertainty," American Economic Review Vol. 61, No. 1, Mar., 1971,

Savage, L.J., The Foundations of Statistics, New York, 1954.

Thrift, Nigel. The Geography of International Economic Disorder. In: Johnston & Taylor, eds., A World in Crisis? 2nd ed., Oxford: Blackwell, 1989, 16-78.

Thrift, Nigel. A Hyperactive World. In: Johnston, Taylor and Watts, eds., Geographies of Global Change: Remapping the World in the Late 20th Century. Oxford: Blackwell, 1995.

Wald, A., Statistical Decision Functions, New York, 1950.

Walker, Warren E., Uncertainty : the challenge for policy analysis in the 21st century. Santa Monica, Calif. : RAND, [2001] [H97 W3395 2001]

Webber, Michael. Impact of Uncertainty on Location. Cambridge: M.I.T.Press, 1972.

Winberg, Alan R., Managing Risk and Uncertainty in International Trade: Canada's Natural Gas Exports. Boulder: Westview, 1987, Ch.6, pp.113ff. ("Uncertainty") [HD61.W56 1987, Suz]

Zhang, Jingxiong & Michael Goodchild, Uncertainty in Geographical Information Taylor & Francis (Routledge) 2002 [ISBN: 0415243343]

• Twelfth Conference on Uncertainty in Artificial Intelligence, August 1-3, 1996
• Papers from 1997 UAI Conference
• Fourteenth Conference on Uncertainty in Artificial Intelligence, July 24-26, 1998
• Uncertainty'99