default_max_attempts_per_step: 3 classifier_model: "MODEL_1" feedback_model: "MODEL_1" tokens_for_ai_rubric: | Evaluate understanding of basic game theory concepts. Consider: - Grasp of strategic interaction - Understanding of Nash equilibrium - Recognition of dominant strategies - Ability to analyze simple games - Application to real-world scenarios Provide clear explanations with examples. sections: - section_id: introduction title: Welcome to Game Theory steps: - step_id: welcome title: Strategic Thinking content_blocks: - "# Game Theory 101: The Science of Strategy 🎮🧠" - "" - "**Welcome to game theory!**" - "" - "Game theory is the study of strategic interaction - how people make decisions when their outcomes depend on others' choices." - "" - "**Not just for games:**" - "- Business competition (pricing, market entry)" - "- International relations (nuclear deterrence, trade)" - "- Biology (evolution, animal behavior)" - "- Economics (auctions, bargaining)" - "- Everyday life (traffic, cooperation)" - "" - "**You'll learn:**" - "✓ The Prisoner's Dilemma (cooperation vs self-interest)" - "✓ Nash Equilibrium (stable strategies)" - "✓ Dominant strategies (always-best moves)" - "✓ Zero-sum vs positive-sum games" - "✓ How to analyze strategic situations" - "" - "**Real applications:**" - "- Why cartels are unstable" - "- Why arms races happen" - "- When cooperation emerges" - "- How auctions should be designed" question: Ready to learn how to think strategically about interactive decisions? tokens_for_ai: | Accept positive responses as 'ready'. Language preference as 'set_language'. Otherwise 'off_topic'. buckets: - ready - set_language - off_topic transitions: ready: content_blocks: - "Excellent! Let's start with the most famous game in game theory! 🎯" next_section_and_step: prisoners_dilemma:step_1 set_language: content_blocks: - "Language preference updated!" metadata_add: language: "the-users-response" counts_as_attempt: false next_section_and_step: introduction:welcome off_topic: content_blocks: - "Let's learn strategic thinking together! Ready to begin?" counts_as_attempt: false next_section_and_step: introduction:welcome - section_id: prisoners_dilemma title: The Prisoner's Dilemma steps: - step_id: step_1 title: The Classic Dilemma content_blocks: - "## The Prisoner's Dilemma: Cooperation vs Self-Interest 🚔" - "" - "**The Scenario:**" - "" - "Two criminals are arrested and interrogated separately. The prosecutor offers each the same deal:" - "" - "**If you both stay silent:**" - "- Each gets 1 year in prison (light sentence, lack of evidence)" - "" - "**If you betray your partner but they stay silent:**" - "- You go free (0 years)" - "- Your partner gets 3 years" - "" - "**If you both betray each other:**" - "- Each gets 2 years" - "" - "**Payoff matrix (years in prison - lower is better):**" - "" - "```" - " Player B" - " Silent Betray" - "Player A Silent (-1,-1) (-3,0)" - " Betray (0,-3) (-2,-2)" - "```" - "" - "**The dilemma:**" - "- **Collectively best:** Both stay silent (-1 each)" - "- **Individually rational:** Both betray (-2 each)" - "" - "**Why betray dominates:**" - "- If partner stays silent: Betray gets you 0 vs 1 year (betray better!)" - "- If partner betrays: Betray gets you 2 vs 3 years (betray better!)" - "- No matter what partner does, betraying is better for YOU" - "" - "**The tragedy:** Both act rationally, both end up worse off (-2 each) than if they'd cooperated (-1 each)!" question: "You're playing prisoner's dilemma once with a stranger you'll never meet again. What should you do from a purely self-interested perspective, and why?" tokens_for_ai: | Correct answer: Betray (or defect/confess) Reasoning: Betraying is a DOMINANT STRATEGY - Dominates silence regardless of what partner does - If partner silent: 0 years better than 1 year - If partner betrays: 2 years better than 3 years Look for understanding of dominant strategy. Categorize as: - correct_with_reasoning: Says betray AND explains dominant strategy - correct_answer: Says betray without full explanation - says_cooperate: Says stay silent (cooperative but not rational in one-shot) - game_theory_aware: Mentions dilemma nature even if wrong choice - set_language: Language preference - off_topic: Unrelated feedback_tokens_for_ai: | If correct: - Excellent! Betraying is the DOMINANT STRATEGY. - No matter what the other player does, betraying is better for YOU. - This is rational but leads to both getting -2 instead of -1. - That's the tragedy of the Prisoner's Dilemma! If says cooperate: - Noble but not strategically optimal in a one-shot game! - Betraying DOMINATES: better outcome regardless of partner's choice. - In one-shot games with strangers, defection is predicted. - (Later we'll see when cooperation can emerge in repeated games!) Explain dominant strategy concept clearly. buckets: - correct_with_reasoning - correct_answer - says_cooperate - game_theory_aware - set_language - off_topic transitions: correct_with_reasoning: ai_feedback: tokens_for_ai: | Perfect strategic analysis! Betraying is the DOMINANT STRATEGY - always better for you. Even though both cooperating would be better collectively (-1 each), individual rationality leads to mutual defection (-2 each). This is the fundamental insight of game theory! metadata_add: score: "n+2" concepts_mastered: "n+1" next_section_and_step: prisoners_dilemma:step_2 correct_answer: ai_feedback: tokens_for_ai: | Correct! Betraying is the rational choice. Why? It's a DOMINANT STRATEGY. No matter what your partner does, betraying gives YOU a better outcome. If they stay silent: 0 < 1. If they betray: 2 < 3. This individual rationality creates the dilemma! metadata_add: score: "n+1" next_section_and_step: prisoners_dilemma:step_2 says_cooperate: ai_feedback: tokens_for_ai: | Cooperation would be great if you could trust them! But from pure self-interest in a ONE-SHOT game: Betraying DOMINATES staying silent. If they're silent: 0 years (betray) beats 1 year (silent). If they betray: 2 years (betray) beats 3 years (silent). Betraying is always better for YOU - that's the dilemma! next_section_and_step: prisoners_dilemma:step_2 game_theory_aware: ai_feedback: tokens_for_ai: | You sense the dilemma! From pure self-interest: betraying DOMINATES. It's better for you no matter what they do. Both thinking this way → both defect → both get -2. Could've gotten -1 each if they cooperated. That's the tragedy! next_section_and_step: prisoners_dilemma:step_2 set_language: content_blocks: - "Language updated!" metadata_add: language: "the-users-response" counts_as_attempt: false next_section_and_step: prisoners_dilemma:step_1 off_topic: content_blocks: - "Think strategically: What gives YOU the best outcome regardless of what your partner does?" next_section_and_step: prisoners_dilemma:step_1 - step_id: step_2 title: Real-World Dilemmas content_blocks: - "## Prisoner's Dilemma Everywhere! 🌍" - "" - "The Prisoner's Dilemma structure appears constantly:" - "" - "**Business cartels:**" - "- Cooperate: Keep prices high (both profit)" - "- Defect: Undercut price (steal market share)" - "- Problem: Undercutting is always tempting!" - "- Result: Cartels are unstable" - "" - "**Arms races:**" - "- Cooperate: Don't build weapons (both save money)" - "- Defect: Build weapons (get advantage if opponent doesn't)" - "- Problem: Building weapons dominates" - "- Result: Costly arms races" - "" - "**Environmental pollution:**" - "- Cooperate: Reduce emissions (collective good)" - "- Defect: Pollute freely (save costs)" - "- Problem: Individual incentive to pollute" - "- Result: Tragedy of the commons" - "" - "**Doping in sports:**" - "- Cooperate: Stay clean (fair competition)" - "- Defect: Dope (gain advantage)" - "- Problem: If others dope, you must too to compete" - "- Result: Widespread doping" - "" - "**The pattern:**" - "Individual rationality → collectively bad outcome" question: "Can you think of another real-world situation that has Prisoner's Dilemma structure? Describe what cooperation and defection look like." tokens_for_ai: | Look for recognition of the PD structure: - Two or more parties - Temptation to defect while others cooperate - Mutual defection worse than mutual cooperation - Defection is individually rational Examples: cheating in class, tax evasion, littering, free-riding, overfishing, etc. Categorize as: - excellent_example: Clear PD structure with cooperation/defection explained - good_example: Recognizes PD structure - vague_example: Right idea but unclear - not_quite_pd: Example doesn't fit structure - set_language: Language preference - off_topic: Unrelated feedback_tokens_for_ai: | If they identify a good example: - Validate it! Explain how it fits PD structure. - Point out: cooperation better collectively, defection individually rational. - This recognition helps understand so many social problems! If example doesn't quite fit: - Acknowledge the thinking. - Explain what makes something a PD: mutual defection < mutual cooperation < defection while others cooperate. - Offer a clearer example. Celebrate their application of game theory! buckets: - excellent_example - good_example - vague_example - not_quite_pd - set_language - off_topic transitions: excellent_example: ai_feedback: tokens_for_ai: | Brilliant example! Reference their specific example and confirm the PD structure. Point out: cooperation collectively better, but defection individually tempting. This is why so many social problems are hard to solve! Game theory helps us recognize these structures! metadata_add: score: "n+2" concepts_mastered: "n+1" next_section_and_step: nash_equilibrium:step_1 good_example: ai_feedback: tokens_for_ai: | Great example! Confirm it has PD structure: defection tempting, but mutual defection worse. This pattern is everywhere once you see it! Understanding the structure helps design solutions (regulations, incentives, reputation). metadata_add: score: "n+1" next_section_and_step: nash_equilibrium:step_1 vague_example: ai_feedback: tokens_for_ai: | Good thinking! Clarify how their example fits: Cooperation = ? (collectively better) Defection = ? (individually tempting) Help them sharpen the structure identification. next_section_and_step: nash_equilibrium:step_1 not_quite_pd: ai_feedback: tokens_for_ai: | Interesting example but not quite Prisoner's Dilemma structure. PD needs: mutual cooperation > mutual defection, but defection dominates. Their example might be a different game structure. Acknowledge their thinking, explain the distinction. next_section_and_step: nash_equilibrium:step_1 set_language: content_blocks: - "Language updated!" metadata_add: language: "the-users-response" counts_as_attempt: false next_section_and_step: prisoners_dilemma:step_2 off_topic: content_blocks: - "Think of situations where everyone would be better off cooperating, but individuals are tempted to cheat." next_section_and_step: prisoners_dilemma:step_2 - section_id: nash_equilibrium title: Nash Equilibrium steps: - step_id: step_1 title: Stable Strategies content_blocks: - "## Nash Equilibrium: The Stability Concept 🎯" - "" - "**Named after John Nash (Nobel Prize, 1994)**" - "" - "**Definition:**" - "A Nash Equilibrium is a set of strategies where no player can improve their outcome by unilaterally changing their strategy." - "" - "**In simpler terms:**" - "Everyone is playing their best response to what others are doing. No one wants to deviate." - "" - "**In Prisoner's Dilemma:**" - "Both betraying is a Nash Equilibrium!" - "- If A betrays, B's best response is betray (2 < 3 years)" - "- If B betrays, A's best response is betray (2 < 3 years)" - "- Neither wants to switch to silence unilaterally" - "" - "**Key insight:**" - "Nash Equilibrium ≠ Best outcome for everyone" - "It's just stable (self-enforcing)" - "" - "**Example: Coordination Game**" - "" - "Two friends picking where to meet:" - "```" - " Friend B" - " Coffee Bar" - "Friend A Coffee (2,2) (0,0)" - " Bar (0,0) (1,1)" - "```" - "" - "**Two Nash Equilibria:**" - "1. Both go to Coffee (2,2)" - "2. Both go to Bar (1,1)" - "" - "Meeting anywhere > missing each other!" - "Coordination problems have multiple equilibria." question: "In a game where two drivers approach an intersection, each can either Stop or Go. If both Go, they crash (payoff -10 each). If one Stops and one Goes, the goer gets +1 and the stopper gets 0. If both Stop, they're delayed (payoff -1 each). What are the Nash Equilibrium outcomes?" tokens_for_ai: | Payoff matrix: Driver B Stop Go Driver A Stop (-1,-1) (0,+1) Go (+1,0) (-10,-10) Nash Equilibria: (Stop, Go) and (Go, Stop) - If A stops, B's best response is Go - If B goes, A's best response is Stop - And vice versa for (Go, Stop) NOT Nash Equilibrium: - (Stop, Stop): Either could improve by switching to Go - (Go, Go): Both would improve by switching to Stop Look for identification of the two equilibria. Categorize as: - correct_both: Identifies both (Stop,Go) and (Go,Stop) - identifies_one: Gets one of the two equilibria - identifies_pattern: Recognizes one stops, one goes - says_both_stop: Says (Stop,Stop) - incorrect - confused: Other answers - set_language: Language preference - off_topic: Unrelated feedback_tokens_for_ai: | Correct equilibria: (Stop, Go) and (Go, Stop) If correct: - Excellent! Two Nash Equilibria where one stops, one goes. - Neither wants to unilaterally change. - This is like traffic lights solving coordination! If says both stop: - That seems safe but it's NOT Nash Equilibrium! - If both stop, either could switch to Go and get +1 instead of -1. - Nash requires no one wants to unilaterally deviate. Explain why the two asymmetric outcomes are stable. buckets: - correct_both - identifies_one - identifies_pattern - says_both_stop - confused - set_language - off_topic transitions: correct_both: ai_feedback: tokens_for_ai: | Perfect! Two Nash Equilibria: (Stop,Go) and (Go,Stop). In each, no driver wants to unilaterally change. Both stopping is NOT equilibrium - either would want to go! This coordination problem is solved by traffic lights in reality! metadata_add: score: "n+2" concepts_mastered: "n+1" next_section_and_step: dominant_strategies:step_1 identifies_one: ai_feedback: tokens_for_ai: | Good! You found one equilibrium. But there's symmetry - also a Nash Equilibrium where roles reverse! Both (Stop,Go) and (Go,Stop) are stable. In each, neither wants to unilaterally change. metadata_add: score: "n+1" next_section_and_step: dominant_strategies:step_1 identifies_pattern: ai_feedback: tokens_for_ai: | Right idea - one stops, one goes! Specifically: (Stop,Go) and (Go,Stop) are both Nash Equilibria. Neither driver wants to change their strategy given the other's. This is a coordination game solved by conventions (like traffic lights!). next_section_and_step: dominant_strategies:step_1 says_both_stop: ai_feedback: tokens_for_ai: | Seems safe, but NOT Nash Equilibrium! At (Stop,Stop), either driver could switch to Go: Get +1 instead of -1 while other stays stopped. Nash requires no one wants to deviate. The equilibria are (Stop,Go) and (Go,Stop). next_section_and_step: nash_equilibrium:step_1 confused: content_blocks: - "Check each outcome: Can any player improve by switching?" - "Nash Equilibrium: No player wants to unilaterally change strategy" - "Hint: One driver stops, one goes (two ways to do this)" next_section_and_step: nash_equilibrium:step_1 set_language: content_blocks: - "Language updated!" metadata_add: language: "the-users-response" counts_as_attempt: false next_section_and_step: nash_equilibrium:step_1 off_topic: content_blocks: - "Find outcomes where neither driver would want to change their choice given what the other is doing." next_section_and_step: nash_equilibrium:step_1 - section_id: dominant_strategies title: Dominant Strategies steps: - step_id: step_1 title: Always-Best Strategies content_blocks: - "## Dominant Strategies: No-Brainer Moves 💪" - "" - "**Definition:**" - "A dominant strategy is one that's best regardless of what other players do." - "" - "**If you have a dominant strategy, PLAY IT!**" - "" - "**In Prisoner's Dilemma:**" - "Betraying is a dominant strategy for both players." - "- Better if opponent stays silent: 0 < 1" - "- Better if opponent betrays: 2 < 3" - "- Always better!" - "" - "**Dominant Strategy Equilibrium:**" - "When all players have dominant strategies, the outcome is certain!" - "- Everyone plays their dominant strategy" - "- This is always a Nash Equilibrium" - "- But Nash Equilibrium doesn't always involve dominant strategies" - "" - "**Example without dominant strategies:**" - "" - "Rock-Paper-Scissors:" - "- No strategy is always best" - "- Best strategy depends on opponent's choice" - "- Optimal: Randomize (mixed strategy)" - "" - "**Why dominant strategies matter:**" - "- Simplify analysis (easy to predict)" - "- Stable and robust" - "- Used in mechanism design (incentive compatibility)" question: "A company must choose High Price or Low Price. If both choose High, each earns $100. If both choose Low, each earns $50. If one chooses Low and other High, the low pricer earns $120 and the high pricer earns $20. Does either company have a dominant strategy? If so, what is it?" tokens_for_ai: | Payoff matrix: Company B High Low Company A High (100,100) (20,120) Low (120,20) (50,50) For Company A: - If B plays High: Low gives 120 > High gives 100 → Low better - If B plays Low: Low gives 50 > High gives 20 → Low better - Low DOMINATES High Same logic for Company B. Both have dominant strategy: Low Price Look for recognition that Low dominates High. Categorize as: - correct_both_low: Says Low is dominant strategy for both - says_low: Identifies Low without full explanation - says_high: Says High (incorrect - not dominant) - says_no_dominant: Says no dominant strategy exists - unclear: Confused answer - set_language: Language preference - off_topic: Unrelated feedback_tokens_for_ai: | Correct: Low is dominant strategy for BOTH companies. If correct: - Excellent! Low dominates High for both. - If opponent prices High: 120 > 100 (Low better) - If opponent prices Low: 50 > 20 (Low better) - Result: Both price low, earn 50 each (could've earned 100 each!) - This is another Prisoner's Dilemma structure! If wrong: - Check each scenario. - Show that Low always outperforms High regardless of opponent. - Explain this leads to (Low,Low) equilibrium. Connect to PD structure. buckets: - correct_both_low - says_low - says_high - says_no_dominant - unclear - set_language - off_topic transitions: correct_both_low: ai_feedback: tokens_for_ai: | Perfect analysis! Low DOMINATES High for both companies. No matter what opponent does, Low is better. Result: (Low,Low) = $50 each. If they could cooperate: (High,High) = $100 each! This is Prisoner's Dilemma in business form! metadata_add: score: "n+2" concepts_mastered: "n+1" next_section_and_step: conclusion:step_1 says_low: ai_feedback: tokens_for_ai: | Correct! Low is the dominant strategy. Why? Check both scenarios: If opponent prices High: 120 (Low) > 100 (High) If opponent prices Low: 50 (Low) > 20 (High) Always better! This is another PD structure. metadata_add: score: "n+1" next_section_and_step: conclusion:step_1 says_high: ai_feedback: tokens_for_ai: | High would be great if both could commit! But it's NOT dominant. Check: If opponent prices Low: 20 (High) < 120 (Low) Low is better regardless of opponent. This is why cartels are unstable! next_section_and_step: dominant_strategies:step_1 says_no_dominant: ai_feedback: tokens_for_ai: | Actually, there IS a dominant strategy! Compare for Company A: - If B plays High: Low(120) > High(100) - If B plays Low: Low(50) > High(20) Low is always better! Same for Company B. next_section_and_step: dominant_strategies:step_1 unclear: content_blocks: - "For dominant strategy, check: Is one choice ALWAYS better than the other?" - "Compare Low vs High when opponent plays High, then when opponent plays Low" next_section_and_step: dominant_strategies:step_1 set_language: content_blocks: - "Language updated!" metadata_add: language: "the-users-response" counts_as_attempt: false next_section_and_step: dominant_strategies:step_1 off_topic: content_blocks: - "For each company, which strategy is better regardless of what the opponent does?" next_section_and_step: dominant_strategies:step_1 - section_id: conclusion title: Game Theory Foundations steps: - step_id: step_1 title: Strategic Thinking content_blocks: - "## Congratulations, Game Theorist! 🎓🎮" - "" - "**You've mastered the fundamentals!**" - "" - "**What you've learned:**" - "✓ Prisoner's Dilemma (cooperation vs self-interest)" - "✓ Nash Equilibrium (stable strategy profiles)" - "✓ Dominant strategies (always-best moves)" - "✓ How to analyze strategic situations" - "✓ Why individually rational choices can lead to bad collective outcomes" - "" - "**Key insights:**" - "- Strategic thinking requires considering others' incentives" - "- Equilibrium ≠ optimal (Prisoner's Dilemma!)" - "- Dominant strategies simplify prediction" - "- Coordination problems have multiple equilibria" - "- Institutions and repeated play can enable cooperation" - "" - "**Real-world applications:**" - "- Understanding why cartels fail" - "- Recognizing arms race dynamics" - "- Designing better mechanisms (auctions, voting)" - "- Building institutions that align incentives" - "" - "**Next steps:**" - "- Game Theory 201: Mixed strategies and repeated games" - "- Look for strategic interactions in daily life" - "- Think about how to align individual and collective interests" question: "How has learning game theory changed how you think about strategic situations? Give an example where you might apply these concepts." tokens_for_ai: | This is a reflection question. Look for: - Recognition of strategic interdependence - Understanding that others' incentives matter - Application to real situations - Appreciation of conflict between individual/collective rationality Categorize as: - excellent_reflection: Insightful application showing deep understanding - practical_application: Good real-world example - general_reflection: Acknowledges usefulness - brief_response: Short but relevant - set_language: Language preference - off_topic: Unrelated feedback_tokens_for_ai: | Provide encouraging feedback! Validate their example/reflection. Emphasize key takeaway: think about others' incentives! Game theory helps predict behavior and design better systems. Mention Game Theory 201 for deeper concepts. Celebrate their foundational understanding! buckets: - excellent_reflection - practical_application - general_reflection - brief_response - set_language - off_topic transitions: excellent_reflection: ai_feedback: tokens_for_ai: | Fantastic insight! Reference their example specifically. You now think strategically about interdependent decisions! This foundation enables understanding mechanism design, auctions, bargaining. Ready for Game Theory 201 when you are! metadata_add: activity_completed: "true" practical_application: ai_feedback: tokens_for_ai: | Great application! Acknowledge their example. Game theory is everywhere once you start looking! Understanding incentives helps predict and influence behavior. Excellent work mastering the fundamentals! metadata_add: activity_completed: "true" general_reflection: ai_feedback: tokens_for_ai: | Good reflection! The core lesson: always consider others' incentives. Strategic interactions are everywhere - business, politics, daily life. You've built a strong foundation in game theory! metadata_add: activity_completed: "true" brief_response: ai_feedback: tokens_for_ai: | Thank you for completing Game Theory 101! You've learned to think strategically about interactive decisions. These concepts underpin economics, politics, and much more! metadata_add: activity_completed: "true" set_language: content_blocks: - "Language updated!" metadata_add: language: "the-users-response" counts_as_attempt: false next_section_and_step: conclusion:step_1 off_topic: content_blocks: - "Reflect: How might understanding incentives and strategic interaction help you in real-world situations?" next_section_and_step: conclusion:step_1