## Line Chart: EWF^CCE across Games ### Overview The chart compares the relationship between **Exploitability** (x-axis) and **Social Welfare** (y-axis) across four game-theoretic scenarios: Prisoner's Dilemma, Stag Hunt, Chicken Game, and Pigou's Network. Social Welfare is measured on a scale from 0.4 to 2.0, while Exploitability ranges from 0.0 to 1.0. Each game is represented by a distinct line with unique markers and colors. ### Components/Axes - **X-axis (Exploitability)**: Labeled "Exploitability," scaled from 0.0 to 1.0 in increments of 0.2. - **Y-axis (Social Welfare)**: Labeled "Social Welfare," scaled from 0.4 to 2.0 in increments of 0.2. - **Legend**: Located in the bottom-right corner, mapping colors to games: - **Blue (▼)**: Prisoner's Dilemma - **Green (●)**: Stag Hunt - **Yellow (◆)**: Chicken Game - **Red (■)**: Pigou's Network ### Detailed Analysis 1. **Prisoner's Dilemma (Blue Line)**: - Starts at approximately **0.4** Social Welfare when Exploitability = 0.0. - Increases sharply to ~**1.2** by Exploitability = 0.2. - Remains flat at ~**1.2** for Exploitability ≥ 0.4. - **Trend**: Initial steep rise followed by stabilization. 2. **Stag Hunt (Green Line)**: - Maintains a constant Social Welfare of **2.0** across all Exploitability values. - **Trend**: Perfectly flat line, indicating no sensitivity to Exploitability. 3. **Chicken Game (Yellow Line)**: - Stays consistently at ~**1.6** Social Welfare across all Exploitability values. - **Trend**: Flat line, similar to Stag Hunt but with lower welfare. 4. **Pigou's Network (Red Line)**: - Begins at ~**1.3** Social Welfare at Exploitability = 0.0. - Increases gradually to ~**1.5** by Exploitability = 1.0. - **Trend**: Linear upward slope, showing positive correlation with Exploitability. ### Key Observations - **Stag Hunt** achieves the highest Social Welfare (2.0) regardless of Exploitability, suggesting robustness. - **Prisoner's Dilemma** exhibits the lowest initial Social Welfare (0.4) but improves significantly with moderate Exploitability. - **Pigou's Network** demonstrates adaptive behavior, with Social Welfare increasing as Exploitability rises. - **Chicken Game** maintains mid-range Social Welfare (~1.6) but shows no improvement with higher Exploitability. ### Interpretation The data suggests that **Stag Hunt** is the most resilient game in terms of Social Welfare, maintaining optimal outcomes even under high Exploitability. **Pigou's Network** appears designed to mitigate exploitation, as its Social Welfare improves with increasing Exploitability. In contrast, **Prisoner's Dilemma** starts vulnerable but stabilizes at a moderate welfare level. The **Chicken Game**'s flat performance indicates limited adaptability. These trends highlight trade-offs between cooperation, exploitation, and welfare in game-theoretic systems, with implications for designing mechanisms that balance fairness and efficiency.