The Significance of Ordinal Payoffs in Strategic Modeling
Two economists are modeling the same strategic policy interaction between two countries. Economist A uses the following numerical payoffs for one country's possible outcomes: {Best: 4, Good: 3, Bad: 2, Worst: 1}. Economist B, modeling the identical situation, uses a different set of payoffs for the same country: {Best: 100, Good: 50, Bad: -10, Worst: -200}. Analyze the two sets of payoffs. Explain why both economists, despite using vastly different numbers, should arrive at the exact same conclusion about the country's strategic choices. What is the fundamental principle about the payoffs that this demonstrates?
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Figure 4.23b: Two Different Climate Policy Games
Consider a strategic interaction between two countries deciding on environmental policy. For each country, the four possible outcomes are ranked in order of preference: 'Best', 'Good', 'Bad', and 'Worst'. An analyst then revises the model, doubling the numerical value associated with every outcome for both countries. However, the ranking of the outcomes (from 'Best' to 'Worst') remains identical for each country. How does this change in numerical values affect the strategic situation?
Consider a strategic game modeling the policy choices of two countries. For one of the countries, the four possible outcomes are assigned numerical values that correspond to a preference ranking from 'Best' to 'Worst'. Which of the following modifications to these numerical values would fundamentally alter the strategic choices predicted by the model for that country?
Evaluating Strategic Models of Climate Policy
Consider a strategic game modeling the policy choices of two countries. An analyst assigns numerical values to the four possible outcomes for each country, corresponding to a preference ranking from 'Best' to 'Worst'. If the analyst then adds 5 points to every single numerical payoff for both countries, the fundamental strategic nature and the predicted outcome of the game will be altered.
Interpreting Payoff Structures in Strategic Games
The Significance of Ordinal Payoffs in Strategic Modeling
Evaluating Methodologies in Strategic Modeling
Two different strategic games, Game A and Game B, are defined by a country's preference ordering for four possible outcomes. Match each of the following numerical payoff sets to the game it represents.
- Game A Preference Order: Outcome 1 (Best) > Outcome 2 (Good) > Outcome 4 (Bad) > Outcome 3 (Worst)
- Game B Preference Order: Outcome 1 (Best) > Outcome 3 (Good) > Outcome 2 (Bad) > Outcome 4 (Worst)
Two analysts are modeling a strategic interaction between Country A and Country B. Each country can choose one of two actions. The analysts create two different models, shown below, with different numerical payoffs. The first number in each pair is the payoff for Country A, and the second is for Country B.
Model 1 Payoffs:
Country B: Action 1 Country B: Action 2 Country A: Action 1 (10, 10) (0, 15) Country A: Action 2 (15, 0) (5, 5) Model 2 Payoffs:
Country B: Action 1 Country B: Action 2 Country A: Action 1 (100, 100) (20, 120) Country A: Action 2 (120, 20) (60, 60) Based on a comparison of these two models, which of the following statements is correct?
Advising on Strategic Model Interpretation