Chapter 8 Discusses The Issue Of Decision Making Under Uncer

Chapter 8 Discusses The Issue Of Decision Making Under Uncertainty For

Chapter 8 discusses the issue of decision-making under uncertainty for firms, but the same principles can also be applied to individuals. Suppose there is a lottery that has the following possibilities: - 30% chance of winning 10$ - 35% of winning 20$ - 10% chance of winning 100$ - 25% chance of winning nothing. a) Calculate the expected gain from this lottery. b) If I gave you a choice between that lottery and flipping a coin with the following payoff; Head you make 40$ and tails you make nothing, which one would you take? Why?

Paper For Above instruction

Decision-making under uncertainty is a fundamental aspect of economics and behavioral psychology, influencing both firms and individuals in choosing among probabilistic options. This essay examines the principles of decision-making under uncertainty, exemplified through a specific lottery scenario and a comparison with a simple binary gamble. The analysis involves calculating expected values and assessing risk preferences, which are central to understanding rational and behavioral responses to uncertain prospects.

Expected Value Calculation

The first part of the problem involves calculating the expected gain from a given lottery with different probabilistic outcomes. The lottery outlines a set of possible winnings with associated probabilities:

- 30% chance of winning $10

- 35% chance of winning $20

- 10% chance of winning $100

- 25% chance of winning nothing ($0)

To compute the expected value (EV) of this lottery, each outcome’s payoff is multiplied by its probability, and these products are summed:

EV = (Probability of outcome 1 × Payoff of outcome 1) + (Probability of outcome 2 × Payoff of outcome 2) + ... + (Probability of outcome n × Payoff of outcome n)

Plugging in the values:

EV = (0.30 × $10) + (0.35 × $20) + (0.10 × $100) + (0.25 × $0)

Calculating each term:

- 0.30 × $10 = $3

- 0.35 × $20 = $7

- 0.10 × $100 = $10

- 0.25 × $0 = $0

Summing these yields:

EV = $3 + $7 + $10 + $0 = $20

Therefore, the expected monetary gain from the lottery is $20.

Decision-Making: Lottery vs. Coin Flip

The second part involves comparing this lottery to a coin-flip gamble. The coin flip has a 50% chance of winning $40 (heads) and a 50% chance of winning nothing (tails). The expected value of the coin flip is:

EV = 0.50 × $40 + 0.50 × $0 = $20 + $0 = $20

This equal expected value presents a choice between two risky options: the original lottery with an expected gain of $20 and the coin flip with the same expected value.

However, decision-making under uncertainty is influenced not just by expected value but also by risk preferences and psychological factors. Rational decision-makers might be indifferent between the two options since their expected values are equal. Yet, in practice, risk-averse individuals might prefer the certainty of the coin flip if they perceive the lottery as too unpredictable or if they value certainty more highly. Conversely, risk-seeking individuals might prefer the lottery considering its potential for a higher payoff, especially given the chance of winning $100 in the lottery.

Behavioral models such as Expected Utility Theory suggest that individuals do not always evaluate options purely based on expected monetary value. Instead, they use a utility function that reflects their risk preferences. Risk-averse individuals have concave utility functions and tend to favor guaranteed outcomes or less risky options, even if the expected monetary value is the same. Risk-seeking individuals have convex utility functions and might prefer the lottery due to potential higher payoffs, despite similar expected values.

Implications for Decision-Making Under Uncertainty

This comparison exemplifies core concepts in decision theory, emphasizing that human decision-making often involves subjective utility rather than pure expected value calculations. Prospect theory further explains that individuals overweight small probabilities and underweight large ones, influencing their choices in gambling scenarios. For example, the possibility of winning $100, though only a 10% chance, might disproportionately attract risk-tolerant individuals, while risk-averse persons might avoid such a gamble.

Furthermore, decision-making strategies can also be influenced by framing effects, where how choices are presented affects preferences. For instance, framing the coin flip as a guaranteed $20 versus risking $40 might lead to different decisions, despite identical expected values. Such behavioral findings challenge the traditional economic assumption of rationality and demonstrate the importance of psychological factors in real-world decision-making.

Conclusion

In summary, decision-making under uncertainty involves balancing expected values with individual risk preferences and psychological biases. The given lottery analysis shows that while the expected monetary gain from the lottery and the coin flip is identical ($20), the choice depends on subjective utility and attitude towards risk. Recognizing these factors is critical for understanding economic behavior, crafting effective policies, and designing investment strategies that align with individual and organizational preferences. Ultimately, a thorough comprehension of risk attitudes and behavioral biases enriches the theoretical and practical approaches to decision-making under uncertainty.

References

  • Kahneman, D., & Tversky, A. (1979). Prospect Theory: An Analysis of Decision under Risk. Econometrica, 47(2), 263-291.
  • von Neumann, J., & Morgenstern, O. (1944). The Theory of Games and Economic Behavior. Princeton University Press.
  • Arrow, K. J. (1971). Essays in the Theory of Risk Bearing. North-Holland Publishing Company.
  • Lopes, L. L. (1984). Risk and Uncertainty: An Evolutionary Perspective. In Handbook of Experimental Economics (pp. 418-451). Springer.
  • Savage, L. J. (1954). The Foundations of Statistics. Wiley.
  • Holt, C. A., & Laury, S. K. (2002). Risk Aversion and Incentive Effects. The American Economic Review, 92(5), 1644-1655.
  • Friedman, M., & Savage, L. J. (1948). The Utility Analysis of Choices Involving Risk. The Journal of Political Economy, 56(4), 279-304.
  • Gambling Behavior and Decision-Making, University of Western Ontario. (2020). Retrieved from https://www.uwo.ca
  • Barberis, N., & Thaler, R. (2003). A Survey of Prospect Theory. Forthcoming in Handbook of the Economics of Finance. Elsevier.
  • Camerer, C. F. (2000). Prospect Theory in Behavioral Economics. Revue économique, 51(4), 1073-1103.

Related Assignments