2.3 Decision-making under uncertainty

Decision-making under uncertainty is a crucial aspect of game theory. It involves making choices when the outcomes are unknown or uncertain, requiring strategies to navigate risk and ambiguity.

This topic explores various decision-making criteria, like maximin and maximax, and the use of subjective probabilities. It also examines the limitations of expected utility theory and alternative models that better capture real-world decision-making behavior.

Risk vs Uncertainty in Decisions

Distinguishing Between Risk and Uncertainty

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• Risk refers to situations where the probabilities of different outcomes are known or can be estimated, while uncertainty refers to situations where the probabilities are unknown or cannot be estimated
• Under risk, decision-makers can assign probabilities to different outcomes and make decisions based on expected values or other criteria that incorporate probabilities (expected utility theory)
• Under uncertainty, decision-makers lack information about the likelihood of different outcomes, making it more challenging to make informed decisions
• The distinction between risk and uncertainty is crucial for selecting appropriate decision-making strategies and tools in different situations

Implications for Decision-Making Strategies

• When facing risk, decision-makers can rely on probability-based methods such as expected value calculations or decision trees to guide their choices
• In situations of uncertainty, decision-makers may need to employ alternative decision criteria (maximin, maximax, minimax regret) or rely on subjective probabilities to make decisions
• Understanding the nature of the decision problem (risk vs uncertainty) helps decision-makers choose the most suitable approach and avoid applying inappropriate tools or assumptions
• Failing to distinguish between risk and uncertainty can lead to suboptimal decisions, as the strategies used for one may not be effective for the other

Maximin vs Maximax Criteria

Maximin Criterion

• The maximin criterion involves selecting the alternative with the best worst-case outcome, focusing on minimizing the potential loss in the most unfavorable scenario
• This conservative approach is suitable for decision-makers who prioritize avoiding the worst possible outcomes and minimizing downside risk
• To apply the maximin criterion, decision-makers identify the worst possible outcome for each alternative and then choose the alternative with the best worst-case outcome
• Example: When choosing between investment options, a risk-averse investor using the maximin criterion would select the option with the highest guaranteed minimum return

Maximax Criterion

• The maximax criterion involves choosing the alternative with the best best-case outcome, emphasizing the potential for the highest payoff without considering the worst-case scenario
• This optimistic approach appeals to decision-makers who are willing to take risks in pursuit of the highest possible rewards
• To apply the maximax criterion, decision-makers identify the best possible outcome for each alternative and then choose the alternative with the best best-case outcome
• Example: An entrepreneur deciding between business ventures using the maximax criterion would choose the venture with the highest potential profits, even if it also carries the greatest risk of failure

Subjective Probabilities in Decision-Making

Nature and Use of Subjective Probabilities

• Subjective probabilities are based on an individual's beliefs, experiences, and judgments about the likelihood of different outcomes, rather than on objective data or frequency-based probabilities
• Decision-makers can use subjective probabilities to assign weights to different states of nature when objective probabilities are unavailable, allowing them to make decisions based on their beliefs and expectations
• Subjective probabilities enable decision-makers to incorporate their unique insights, domain expertise, or situational knowledge into the decision-making process
• Example: A manager assigning subjective probabilities to different market scenarios based on their experience and understanding of the industry dynamics

Challenges and Biases in Subjective Probabilities

• Subjective probabilities are influenced by various cognitive biases, such as overconfidence (overestimating one's accuracy), anchoring (relying too heavily on initial information), and availability bias (overestimating the likelihood of easily recalled events), which can lead to systematic errors in judgment and decision-making
• The use of subjective probabilities can be controversial, as they may not accurately reflect the true underlying probabilities and can vary significantly among individuals
• Techniques such as the Delphi method (iterative, anonymous expert surveys) and expert elicitation (structured interviews with domain experts) can be used to aggregate and refine subjective probabilities from multiple sources to improve their accuracy and reliability
• Example: A group of analysts using the Delphi method to reach a consensus on the subjective probabilities of different economic scenarios

Limitations of Expected Utility Theory

Assumptions and Shortcomings

• Expected utility theory assumes that decision-makers have well-defined preferences, are fully informed, and always choose the alternative with the highest expected utility, calculated as the sum of the products of the utilities and probabilities of each outcome
• The theory does not account for the fact that individuals may have different attitudes towards risk, such as risk aversion (preferring certainty over risk) or risk-seeking behavior (preferring risk over certainty), which can lead to decisions that deviate from the predictions of expected utility theory
• The theory assumes that decision-makers have a complete and consistent set of preferences, which may not always be the case, particularly when dealing with complex or unfamiliar situations
• Expected utility theory does not consider the potential for ambiguity aversion, where decision-makers prefer options with known probabilities over those with unknown probabilities, even if the expected utilities are the same

Alternative Decision-Making Models

• Alternative decision-making models, such as prospect theory (which accounts for reference dependence and loss aversion) and regret theory (which incorporates anticipated regret into decision-making), have been developed to address some of the limitations of expected utility theory and better capture observed decision-making behavior under uncertainty
• These models often incorporate psychological factors and biases that influence decision-making, providing a more realistic representation of how people make choices in the face of risk and uncertainty
• Example: Prospect theory explains why people tend to be risk-averse when facing gains but risk-seeking when facing losses, a behavior that is inconsistent with expected utility theory
• Despite its limitations, expected utility theory remains a fundamental framework for analyzing decision-making under risk and has been widely applied in various fields, including economics, finance, and management