Three-Attribute Interrelationships for Industry-Level Demand Equations Developments in Business Simulation and Experiential Learning, Volume 33, 2006 THREE-ATTRIBUTE INTERRELATIONSHIPS FOR INDUSTRY-LEVEL DEMAND EQUATIONS Elizabeth J Tipton Murff Eastern Washington University ejtmurff@ewu.edu Richard D. Teach Georgia Institute of Technology, richard.teach@mgt.gatech.edu Robert G. Schwartz Eastern Washington University, robert.schwartz@ewu.edu ABSTRACT where P is price, M is marketing and promotion effort, and R is the research (and development) effort for the particular product. The latter variable is included as a proxy to reflect product quality. Equation 1 was recently recommended in Gold (2003) as part of his systems-dynamics based approach. However, the interrelationships among price, promotion and research are not explicitly addressed by this equation. Furthermore, in Perotti and Pray’s award winning paper (2000), they indicated that this model is unstable and does not exhibit desirable characteristics when using input variables in moderately extended ranges. This is clearly visible in Figure 1, which displays a surface map of this equation for two inputs (price and promotion): In business simulations, industry-level product demand is typically determined by a variety of factors. In the marketplace, these variables are not independent, yet many simulation algorithms in the literature assume that they are. The multiple-market-segment industry-level demand equation detailed in this paper allows for correlations among three attributes that form the domain of the demand equation. INTRODUCTION To prevent the simulation players from straying into the domain region where this problem occurs, the input options available must be bounded. Additionally, the Gold and Pray model does not control for relationships between the primary demand generating variables: A joint distribution Over twenty years ago, Gold and Pray (1983) presented the now frequently cited industry-level demand equation: (see equation 1) )()()( 765432),,( RggMggPgg RMPgRMPQ +++−= (1) 1 Figur fo 3 9 15 21 27 33 39 45 0 20000 40000 60000 80000 100000 Demand Promotion Price e 1: Surface map of Gold and Pray’s industry-level demand equation r price and promotion inputs (Price scale reversed for readability) 213 mailto:ejtmurff@ewu.edu mailto:richard.teach@mgt.gatech.edu mailto:robert.schwartz@ewu.edu Developments in Business Simulation and Experiential Learning, Volume 33, 2006 Fig fo 3 9 15 21 27 33 39 45 0 500 1000 1500 2000 2500 3000 3500 Demand Promotion Price Figure 3: Surface map of Murff et al.’s multi-segment industry-level demand equation for price and promotion inputs (Price scale reversed for readability) ) ) ( )( ) ( )( ) 1/1/ 11),,( −−−−− ++= MMPP MP eekRMPQ σµσµ (2 ))/)(()(sinh)/)((sinh(),( 11 gMgPkMPQ +−+−−= −− σµσµ (3 function has the form FX,Y(x,y the variables X and Y are Stirzaker, 1992, p99). Thus, p the same effect upon demand price or research effort. Supp fixed amount. If the product promotional expenditures we increase by a certain proporti priced at $30.00 and the p doubled, the demand would i proportion. BACKGR Carvalho (1991) led the w in industry-level demand equa the proportion of purchase cumulative distribution functio two input variables this approa problems inherent in Gold and require artificial constraint of interrelationship between pric 3 9 15 21 27 33 39 45 0 1000 2000 3000 4000 5000 6000 Demand Promotion Price ure 2: Surface map of Carvalho’s industry-level demand equation r price and promotion inputs (Price scale reversed for readability) MMMPPP ) = FX(x)FY(y) if and only if independent (Grimmett & romotional expenditures have regardless of the product’s ose research effort is set at a had a price of $10.00 and re doubled, demand would on. But, if the product was romotional expenditure was ncrease by exactly the same OUND ay for the use of probability tions by demonstrating that distribution is actually a n. As shown in Figure 2, for ch resolved the monotonicity Pray’s equation and does not the domain. However, the e and promotion was not explicitly included as Carvalho used independent logistic distributions: (See equation 2) In a working-paper, Teach and Schwartz (2001) attempted to include domain interrelationships in a cumulative distribution based equation. They began with appropriately shifted independent inverse hyperbolic sine functions: (See equation 3) They then applied non-orthogonal axes to introduce the dependencies in the domain variables. This distortion of the axes was quite cumbersome and extremely difficult to visualize. But, it is just a short step from equation 3 to one in which the correlation between two domain variables can be explicitly included without distorting the axes. First, consider Carvalho’s use of the logistic distribution in equation 2. This function differs from the normal distribution primarily in its larger kurtosis. Next, consider Teach and Schwartz’s use of the inverse hyperbolic sine function. Equation 3 is related to the inverse tangent function, which is the basis of the Cauchy cumulative distribution. The Cauchy distribution is a special case of a Student’s t distribution with one degree of freedom. Finally, Student’s t distribution with infinite degrees of 214 Developments in Business Simulation and Experiential Learning, Volume 33, 2006 dydxeQMPQ Px M y yxyx MP M M M P M M P P ∫ ∫ ∞ = −∞=                       −       − −      − +      − − − − = σ µ σ µ ρ σ µ σ µ ρ ρσπσ 2 )1(2 1 2max 22 2 12 1),( (4) ( ) ( ) ( )µµ π −Σ−− − Σ = xx RMP T exxxf 1 2 1 2/123 det)2( 1),,( (5) 222 PRPMMRPMMRPR ρρρρρρ 21+<++ (6) freedom is the normal distribution. This reasoning led Murff et al. (2005) to adapt the bivariate normal distribution to create an industry-level demand equation:(see equation 4) and Σii denotes the variance of variable i and Σij denotes the covariance between variables i and j. The difficulty in using equation 5 lies entirely in the development of an appropriate covariance matrix Σ as it must be positive definite to force the determinant of Σ to be positive (Watkins, 2002, p49). Price and promotion are now explicitly interrelated through the correlation (ρ). Furthermore, these authors suggested that the summation of several equations of this form would allow for multiple market segments. Different groups of buyers have different responses to product attributes (Rogers, 1962). For example, “innovators” are risk-takers driven by the thrill of discovery. They are a small segment (2.5%) willing to pay higher prices and are less responsive to large promotion efforts as they have multiple information sources. The “late majority” is a large segment (34%) preferring the tried-and-true, with lower prices and larger promotion efforts required. This equation allows for the presence of both groups simultaneously. As seen in Figure 3, this summation still displays the desired monotonicity characteristics, but equation 4 is limited to only two input variables. The correlation matrix is related to the covariance matrix Σ as follows (Johnson & Wichern, 1992, p59):                         =         ΣΣΣ ΣΣΣ ΣΣΣ =Σ R M P MRPR MRPM PRPM R M P RRMRPR MRMMPM PRPMPP σ σ σ ρρ ρρ ρρ σ σ σ 00 00 00 1 1 1 00 00 00 where σP, σM and σR are the standard deviations of price, promotion and research respectively and ρPM, ρPR and ρMR are the correlations between price and promotion, price and research, and promotion and research respectively. If the correlation matrix is known to be positive definite, Σ also must be positive definite (Watkins, 2002, p47). Thus, developing an appropriate correlation matrix will result in an appropriate covariance matrix. This may be done through the use of the Cholesky Decomposition Theorem (Watkins, 2002, p34) which states that a matrix is positive definite if and only if it can be decomposed into a unique upper triangular matrix R with positive main diagonal entries such that: THIS PAPER This paper extends the adapted bivariate normal model presented in Murff et al. (2005) to an adapted multivariate normal model to allow for interrelationships among three attributes. In the theoretical discussion, matrices were used for brevity. Inequality 6 is the key result as it defines the relationship required among the three correlations. In the practical discussion, one method for developing appropriate parameters is considered. In the algorithm section, a quick computational method for incorporating this model into the “black box” is provided. The discussion just before the conclusion explains the authors’ motivation for developing this model based on experiences in the administration of business simulations. RR r rr rrr rrr rr r T RR MRMM PRPMPP RRMRPR MMPM PP MRPR MRPM PRPM =                 =         00 00 00 1 1 1 ρρ ρρ ρρ As the main diagonal entries of R must be positive, a relationship for the three correlations results when the matrix multiplication is carried out: (see equation 6) If inequality 6 holds, the correlation matrix is positive definite which results in a positive definite covariance matrix which allows for an appropriate proportion of purchase function which yields an appropriate industry-level demand function. THEORETICAL DISCUSSION Unfortunately, no closed form exists for the multivariate normal cumulative distribution function, thus equation 5 must be integrated, remembering to reverse the direction of integration for price as demand falls as price increases (Gold and Pray, 1990). Let Qmax be the highest possible industry-level demand for the market segment defined by µ and Σ. Then the industry-level demand equation for this segment is: (see equation 7) The multivariate normal probability density function for a three-dimensional domain will be the probability of purchase function, defined by the equation (Johnson & Wichern, 1992, p128): (See equation 4) where:         = R M P x x x X , µ and Σ         = R M P µ µ µ         ΣΣΣ ΣΣΣ ΣΣΣ = RRMRPR MRMMPM PRPMPP 215 Developments in Business Simulation and Experiential Learning, Volume 33, 2006 promotion de m an d price m an d σM σM minM maxMµM deσP σP minP maxP µP Figure 4a: Demand as a function of price Figure 4b: Demand as a function of promotion I l i i e a F m a e ( p f t F D t r t L s i w i p c i w e ∫ ∫ ∫ ∞− ∞− ∞ =Σ p m p RMPRMP dxdxdxxxxfQQrmpQ ),,(),,|,,( maxmaxµ (7) n f n market segments are to be included in the simulation, et µi, Σi and Qmax,i be the set of constants used to define ndustry-level demand for market segment i. The overall ndustry-level demand function may be found by: (see quation 8) PRACTICAL DISCUSSION The constants may be easily adjusted by the game dministrator as they have practical interpretations. urthermore, the evolution of a particular market segment ay now be readily modeled by simply changing the ppropriate constants during the game play itself. For xample, µP, µM and µR are the points of diminishing returns that is, the inflection points of the demand curve) for price, romotion and research, respectively. σP is the distance rom µP where the marginal impact on demand with respect o changes in price inflects. σM and σR are defined similarly. igures 4a and 4b provide visualization for these constants. emand as a function of research has not been included as he function is identical to that of figure 4b with research eplacing promotion. Small values of σi result in a demand hat is highly sensitive to changes in variable i near µi. arge values of σi would result in a demand that is less ensitive near µi. One method for estimating these constants nvolves identifying the minimum and maximum values here a response to a change is seen. Then, and σ . 2/)min(max iii +=µ 6/)min(max iii −= Correlations near +1 indicate strong positive nterrelationships. For example, consider a situation where romotion and research are strongly and positively orrelated. This means that an increase in research will ncrease the impact in promotion, and vice versa. This ould represent a rapidly changing technology industry and xtensive R&D would be needed to keep up with the competition and high advertising expenditures would be needed to keep the potential customers informed about all the product changes taking place. Cell phones, computer games and digital organizers are products that might encounter this condition. A correlation near -1 indicates a strong negative interrelationship, that is, an increase in one of the variables will decrease the impact of the other, and vice versa. Variables not influencing the impacts of others will have correlations near 0. Appendix A provides valid ranges on a ∆=0.1 grid for the correlation between price and research given specific values for the correlation between price and promotion and the correlation between promotion and research. ),,|,,(),,( max,1 iiii QrmpQrmpQ Σ= ∑ = µ (8) To simplify this process as much as possible, the game developers should provide to the game administrator a selection of preset choices along with a verbal description of their practical meaning in the marketplace. This will place the complexity of the process in the “black box” and allow the game administrator to focus on the lesson to be taught. ALGORITHM For example, consider the two market segments defined by the constants in Table 1. Let the input values be XP = 25, XM = 1350, and XR = 210. Next, check that a valid set of correlations has been chosen by consulting Appendix A. If an invalid set has been chosen, an adjustment in one of the correlations will be needed before continuing. The calculation algorithm that follows is then applied to generate a value for overall industry-level demand. This procedure was adapted from the multivariate normal cumulative distribution function algorithm developed by Genz (1992). The notation normcdf(Z) refers to the left-tailed probability associated with the standard normal cumulative distribution function at Z. The notation norminv refers to the inverse of normcdf. The Excel 216 Developments in Business Simulation and Experiential Learning, Volume 33, 2006 workbook developed to perform the calculations shown below is available from the first author. DISCUSSION Many of the industry-level demand models used in simulations have a variety of flaws (Wolfe and Teach, 1987). Most of these flaws are not immediately detectable by participants or game administrators. However, these flaws cause subtle but important and detrimental changes in the nature of the competition, which affect game participant understanding of the results of each round of play. For example, some games create elasticities that are greater at the industry level than at the firm level. This causes participants to encounter unrealistic behavior in the game’s reaction to the changes in strategies and decisions. The algorithm described in this paper then was developed to correct flaws in existing industry-level demand algorithms. Further, many of the demand algorithms have very restrictive operating ranges. The algorithms work well if the game participants do not enter extreme values as decisions. While logic suggests that these extreme values do not make economic sense, they do occur, especially when teams make last ditch efforts to either break the game or win by making unconventional decisions. One of the authors of this paper had a simulation team submit a $1 million price on a product that had a normal price range of between $20 and $25. When confronted, the team members said they knew the game had a feature that would reduce demand as prices increased, but they hoped the algorithm would not allow demand to fall to zero. Therefore, they believed the sale of only a few products would generate a large profit. This use of illogical decisions generally occurs only in the last round of a game when a team’s firm is lagging behind in performance. These players are hoping for an error in mathematical or programming logic that will save their firm. The algorithm presented here allows for appropriate responses to unconventional decisions without restricting the domains of the input variables. When games have been used repeatedly in academic settings, institutional memory can develop. Students will often seek out those who used the simulation in prior semesters to obtain the way to “win the game.” This then detracts from the lesson being taught and reduces the simulation to a simple competition among the players. By simply altering the parameters defining the market segments involved in the simulation, the strategy of blindly following the choices of those who did well in previous semesters is no longer viable. The focus of the simulation can then return to the lesson to be learned. The algorithm developed in this paper handles these changes with ease. CONCLUSIONS In the actual marketplace, demand-generating decision variables are known to have interactions (Arora, 1979). The model presented in this paper incorporates these important interactions. As an example, a higher than average price may be offset by more aggressive advertising expenditures, whereas, at a lower than average price, the additional advertising expenditures might not generate the same effect on demand. Without the ability to model interactions that affect decisions and strategies, the understanding and learning that takes place during business simulations may be misleading and could potentially teach the wrong lessons. REFERENCES Arora, R. (1979) How promotion elasticities change. Journal of Advertising Research, 19(3), 57-62. Carvalho, G.F. (1991) Theoretical derivation of a market demand function for business simulators. Developments in Business Simulation and Experiential Exercises, 18, 11-14. Genz, A. (1992) Numerical Computation of Multivariate Normal Probabilities. Journal of Computational and Graphical Statistics, 2, 141-149. Gold, S.C. (2003) The design of a business simulation using a system-dynamics-based approach. Developments in Business Simulation and Experiential Learning, 30. Gold, S.C. and Pray, T.F. (1983) Simulating market and firm level demand – A robust demand system. Developments in Business Simulation & Experiential Exercises, 10, 101-106. Gold, S.C. and Pray, T.F. (1990) Chapter 8: Modeling demand in computerized business simulations. Guide to Business Gaming and Experiential Learning, 117- 138. Grimmett, G.R. and Stirzaker, D.R. (1992) Probability and Random Processes (2nd ed.) New York: Oxford University Press. Johnson, R.A. and Wichern, D.W. (1992) Applied Multivariate Statistical Analysis (3rd ed.). New Jersey: Prentice Hall. Murff, E.J.T., Teach, R.D. and Schwartz, R.G. (2005) Interrelationships in industry-level demand equations for Business Games. Proceedings of the 36th Annual Conference for the International Simulation and Gaming Association, June 2005 Perotti, V. and Pray, T. (2000) Visual Modeling of Business Simulations. Developments in Business Simulation & Experiential Exercises, 27, 34-41. Rogers, E.M. (1962) Diffusion of Innovations. New York: The Free Press. Teach, R.D. and Schwartz, R.G. (2001) Introducing interrelationship affects in demand algorithms. Working paper, 21 pages. Watkins, D.S. (2002) Fundamentals of Matrix Calculations (2nd ed.). New York: Wiley & Sons. Wolfe, J. and Teach, R.D. (1987) Three Downloaded Mainframe Games. The Academy of Management Review. (January), 181-192. 217 Developments in Business Simulation and Experiential Learning, Volume 33, 2006 218 Appendix A Valid ranges (min top, max bottom) on a ∆=0.1 grid for ρPR given specific values of ρPM and ρMR Correlation between price and promotion, ρPM -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 -0.9 0.7* 0.9 0.5 0.9 0.4 0.9 0.2 0.8 0.1 0.8 0.1 0.7 -0.1 0.6 -0.2 0.6 -0.3 0.5 -0.5 0.3 -0.6 0.2 -0.6 0.1 -0.7 -0.1 -0.8 -0.1 -0.8 -0.2 -0.9 -0.4 -0.9 -0.5 -0.9 -0.7 -0.8 0.5 0.9 0.3 0.9 0.2 0.9 0.1 0.9 -0.1 0.9 -0.2 0.8 -0.3 0.8 -0.4 0.7 -0.5 0.6 -0.6 0.5 -0.7 0.4 -0.8 0.3 -0.8 0.2 -0.9 0.1 -0.9 -0.1 -0.9 -0.2 -0.9 -0.3 -0.9 -0.5 -0.7 0.4 0.9 0.2 0.9 0.1 0.9 -0.1 0.9 -0.2 0.9 -0.3 0.9 -0.4 0.8 -0.5 0.8 -0.6 0.7 -0.7 0.6 -0.8 0.5 -0.8 0.4 -0.9 0.3 -0.9 0.2 -0.9 0.1 -0.9 -0.1 -0.9 -0.2 -0.9 -0.4 -0.6 0.2 0.8 0.1 0.9 -0.1 0.9 -0.2 0.9 -0.3 0.9 -0.4 0.9 -0.5 0.9 -0.6 0.9 -0.7 0.8 -0.8 0.7 -0.9 0.6 -0.9 0.5 -0.9 0.4 -0.9 0.3 -0.9 0.2 -0.9 0.1 -0.9 -0.1 -0.8 -0.2 -0.5 0.1 0.8 -0.1 0.9 -0.2 0.9 -0.3 0.9 -0.4 0.9 -0.5 0.9 -0.6 0.9 -0.7 0.9 -0.8 0.9 -0.9 0.8 -0.9 0.7 -0.9 0.6 -0.9 0.5 -0.9 0.4 -0.9 0.3 -0.9 0.2 -0.9 0.1 -0.8 -0.1 -0.4 0.1 0.7 -0.2 0.8 -0.3 0.9 -0.4 0.9 -0.5 0.9 -0.6 0.9 -0.7 0.9 -0.8 0.9 -0.8 0.9 -0.9 0.8 -0.9 0.8 -0.9 0.7 -0.9 0.6 -0.9 0.5 -0.9 0.4 -0.9 0.3 -0.8 0.2 -0.7 -0.1 -0.3 -0.1 0.6 -0.3 0.8 -0.4 0.8 -0.5 0.9 -0.6 0.9 -0.7 0.9 -0.8 0.9 -0.8 0.9 -0.9 0.9 -0.9 0.9 -0.9 0.8 -0.9 0.8 -0.9 0.7 -0.9 0.6 -0.9 0.5 -0.8 0.4 -0.8 0.3 -0.6 0.1 -0.2 -0.2 0.6 -0.4 0.7 -0.5 0.8 -0.6 0.9 -0.7 0.9 -0.8 0.9 -0.8 0.9 -0.9 0.9 -0.9 0.9 -0.9 0.9 -0.9 0.9 -0.9 0.8 -0.9 0.8 -0.9 0.7 -0.9 0.6 -0.8 0.5 -0.7 0.4 -0.6 0.2 -0.1 -0.3 0.5 -0.5 0.6 -0.6 0.7 -0.7 0.8 -0.8 0.9 -0.8 0.9 -0.9 0.9 -0.9 0.9 -0.9 0.9 -0.9 0.9 -0.9 0.9 -0.9 0.9 -0.9 0.8 -0.9 0.8 -0.8 0.7 -0.7 0.6 -0.6 0.5 -0.5 0.3 0.1 -0.5 0.3 -0.6 0.5 -0.7 0.6 -0.8 0.7 -0.9 0.8 -0.9 0.8 -0.9 0.9 -0.9 0.9 -0.9 0.9 -0.9 0.9 -0.9 0.9 -0.9 0.9 -0.8 0.9 -0.8 0.9 -0.7 0.8 -0.6 0.7 -0.5 0.6 -0.3 0.5 0.2 -0.6 0.2 -0.7 0.4 -0.8 0.5 -0.9 0.6 -0.9 0.7 -0.9 0.8 -0.9 0.8 -0.9 0.9 -0.9 0.9 -0.9 0.9 -0.9 0.9 -0.8 0.9 -0.8 0.9 -0.7 0.9 -0.6 0.9 -0.5 0.8 -0.4 0.7 -0.2 0.6 0.3 -0.6 0.1 -0.8 0.3 -0.8 0.4 -0.9 0.5 -0.9 0.6 -0.9 0.7 -0.9 0.8 -0.9 0.8 -0.9 0.9 -0.9 0.9 -0.8 0.9 -0.8 0.9 -0.7 0.9 -0.6 0.9 -0.5 0.9 -0.4 0.8 -0.3 0.8 -0.1 0.6 0.4 -0.7 - 0.1 -0.8 0.2 -0.9 0.3 -0.9 0.4 -0.9 0.5 -0.9 0.6 -0.9 0.7 -0.9 0.8 -0.9 0.8 -0.8 0.9 -0.8 0.9 -0.7 0.9 -0.6 0.9 -0.5 0.9 -0.4 0.9 -0.3 0.9 -0.2 0.8 0.1 0.7 0.5 -0.8 - 0.1 -0.9 0.1 -0.9 0.2 -0.9 0.3 -0.9 0.4 -0.9 0.5 -0.9 0.6 -0.9 0.7 -0.9 0.8 -0.8 0.9 -0.7 0.9 -0.6 0.9 -0.5 0.9 -0.4 0.9 -0.3 0.9 -0.2 0.9 -0.1 0.9 0.1 0.8 0.6 -0.8 - 0.2 -0.9 - 0.1 -0.9 0.1 -0.9 0.2 -0.9 0.3 -0.9 0.4 -0.9 0.5 -0.9 0.6 -0.8 0.7 -0.7 0.8 -0.6 0.9 -0.5 0.9 -0.4 0.9 -0.3 0.9 -0.2 0.9 -0.1 0.9 0.1 0.9 0.2 0.8 0.7 -0.9 - 0.4 -0.9 - 0.2 -0.9 - 0.1 -0.9 0.1 -0.9 0.2 -0.9 0.3 -0.8 0.4 -0.8 0.5 -0.7 0.6 -0.6 0.7 -0.5 0.8 -0.4 0.8 -0.3 0.9 -0.2 0.9 -0.1 0.9 0.1 0.9 0.2 0.9 0.4 0.9 0.8 -0.9 - 0.5 -0.9 - 0.3 -0.9 - 0.2 -0.9 - 0.1 -0.9 0.1 -0.8 0.2 -0.8 0.3 -0.7 0.4 -0.6 0.5 -0.5 0.6 -0.4 0.7 -0.3 0.8 -0.2 0.8 -0.1 0.9 0.1 0.9 0.2 0.9 0.3 0.9 0.5 0.9 C or re la tio n be tw ee n pr om ot io n an d re se ar ch , ρ M R 0.9 -0.9 - 0.7 -0.9 - 0.5 -0.9 - 0.4 -0.8 - 0.2 -0.8 - 0.1 -0.7 - 0.1 -0.6 0.1 -0.6 0.2 -0.5 0.3 -0.3 0.5 -0.2 0.6 -0.1 0.6 0.1 0.7 0.1 0.8 0.2 0.8 0.4 0.9 0.5 0.9 0.7 0.9 * This cell would read as “Correlations between price and research ranging between 0.7 and 0.9 are allowed when the correlation between price and promotion is -0.9 and the correlation between promotion and research is -0.9.” Table of Contents Volume 33, 2006 Learning Assurance Using Business Simulations Applications To Executive Management Education Team Teaching In An Integrated Business Course Using Critical Problem Based Learning Factors In An Integrated Undergraduate Business Curriculum: A Business Course Success Personality Type And Strategic Planning Business Games As Strategic Management Laboratories The Relationship Between Students' Success On A Simulation Exercise And Their Perception Of Its Effectiveness As A PBL Problem Forecasting Accuracy And Learning: The Key To Measuring Simulation Performance The Business Strategy Game: A Performance Review Of The New Online Edition Using The Socratic Method And Bloom's Taxonomy Of The Cognitive Domain To Enhance Online Discussion, Critical Thinking, And Student Learning Using Negotiation Exercises To Promote Critical Thinking Skills Effective Leadership Experiences For Management Majors In A Futures Class The Role Of Learning Versus Performance Orientations When Reacting To Negative Outcomes In Simulation Games Is Pay Inversion Ethical? A Three-Part Exercise Simulations And Experiential Exercises - Do They Result In Learning? Have We Figured It Out Yet? Examining Program Management In Business Simulations: Student And Faculty Views Validating Business Simulations: Do Simulations Exhibit Natural Market Structures? Characterizing Business Games Used In Distance Education Utilizing Games In A Graduate Level Instructional Game Course Employment Interview Preparation: Assessing The Writing-To-Learn Approach Simulations - Bridging From Thwarted Innovation To Disruptive Technology Creating An Authentic Cultural Lens Using Case Dialogue Learning By Fire: Reflections Of A First Time Online Instructor An International Internship With A Service-Learning Focus Learner Participation In The Online Learning Experience: Help Or Hindrance? Any Given Sunday: Intervention In Pursuit Of Simulation Team Parity Beginning With The End: Creating An Experiential Exercise From Assessment Criteria Simulating Life Cycles: Life Span As The Measure Of Performance In Business Gaming Simulations It's Puzzling: Communications, Competition, And Cooperation Balanced Scorecard Implementation For Strategy Management: Variation Of Manager Opinion In Real And Simulated Companies Cases And Business Games: The Perfect Match! Three-Attribute Interrelationships For Industry-Level Demand Equations Using A Web-Based Module To Teach Information Literacy Decision Support System For Demand Forecasting In Business Games The Invalidity Of Profit=F(Market Share) PIMS Validation Of Marketing Games Online Market Test Laboratory With The MINSIM* Program The Gas Mileage Game - A Policy Simulation Delivered Cost And Differentiation Applied To Threshold 3rd Ed. The Effect Of Team-Leadership Modes On Team Performance: A Preliminary Study The Design And Use Of A Macroeconomics Simulation Using Maple Software: A Pilot Study The Instructor's Toolbox: A Meaning-Centered Framework For The Social Construction Of Experiential Learning Incorporating Strategic Product-Mix Decisions Into Simulation Games: Modeling The 'Profitable-Product Death Spiral' Group Composition And Groupthink In A Business Game A Direct Approach To Teaching Business Ethics A Decision Support System For Planning Sales, Production, And Plant Addition With Manager: A Computer Simulation Polish - American Entrepreneurial Business Cooperation Workshop Utilizing The Income/Outcome Simulation Student Leader Training Exercise Student Preference To Mode Of Learning In Hong Kong Experiential Learning For Technology-Based And Management Programme In Hong Kong: A China Study Tour A Price Game With Product Differentiation In The Classroom Discrete Event Modeling In A New Transportation Simulation Supply-Side Modeling In A Total Enterprise Simulation The Quality Game Towards A Massive Multiplayer Online Business Simulation Making The Connection: Improving Virtual Team Performance Through Behavioral Assessment Profiling And Behavioral Cues Individual Learning Producing A Learning Organization: 'Playing Dice With Polar Bears' Narratology and Ludology: Competing Paradigms or Complementary Theories in Simulation Framework For Evaluating Internet Research Using Children's Games To Illustrate Strategy Concepts: Is Less Better?