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Discovering Game Theory as An Infant(初学者版)

已有 517 次阅读 2024-10-29 15:00 |系统分类:论文交流

Discovering Game Theory as An Infant

Yucong Duan

International Standardization Committee of Networked DIKWfor Artificial Intelligence Evaluation(DIKWP-SC)

World Artificial Consciousness CIC(WAC)

World Conference on Artificial Consciousness(WCAC)

(Email: duanyucong@hotmail.com) 

Introduction

From the earliest days of my life, I have been immersed in a world of interactions—interactions with my parents, siblings, and the environment around me. These interactions often involve choices, responses, and outcomes that affect not only me but also those around me. Through observing and participating in these exchanges, I began to notice patterns and strategies that could influence the results of these interactions. Driven by curiosity and a desire to understand how my actions impact others and vice versa, I embarked on a journey to uncover the underlying principles governing strategic decision-making.

In this narrative, I will detail how, starting from infancy, I conceptualized and reasoned out the foundational concepts of Game Theory. This exploration is grounded in my direct experiences and logical reasoning, without relying on subjective definitions or prior knowledge. By building up from basic interactions, I aim to demonstrate how complex ideas about strategy, cooperation, and competition can emerge naturally.

Chapter 1: Early Interactions and Observations1.1 Understanding Cause and EffectObserving Reactions to My Actions
  • Crying for Attention:

    • Observation: When I cry, my parents come to comfort me.

    • Reflection: My action (crying) leads to a response (attention).

  • Smiling at People:

    • Observation: When I smile, others smile back and engage with me.

    • Reflection: Positive actions elicit positive responses.

Recognizing Patterns
  • Consistent Outcomes:

    • Certain actions consistently lead to specific reactions from others.

  • Influence Through Behavior:

    • I can influence others' actions by choosing how I behave.

1.2 Interacting with SiblingsSharing Toys
  • Scenario:

    • My sibling and I both want to play with the same toy.

  • Observation:

    • If I grab the toy aggressively, my sibling might grab it back or cry.

    • If I offer to share, we both can play and enjoy the experience.

  • Reflection:

    • Different approaches lead to different outcomes, affecting both of us.

Competing for Attention
  • Scenario:

    • Both of us try to get our parents' attention simultaneously.

  • Observation:

    • If we both shout, it creates chaos, and our parents become frustrated.

    • If we take turns, we both receive attention peacefully.

  • Reflection:

    • Cooperation can lead to better outcomes than competition.

Chapter 2: Understanding Choices and Outcomes2.1 Making Decisions Based on Expected ResponsesPredicting Reactions
  • Observation:

    • Certain behaviors lead to predictable reactions from others.

  • Example:

    • If I refuse to eat vegetables, my parents might offer dessert as an incentive.

  • Reflection:

    • Anticipating others' responses can guide my choices to achieve desired outcomes.

2.2 Exploring ConsequencesPositive Reinforcement
  • Observation:

    • Completing tasks or behaving well results in praise or rewards.

  • Reflection:

    • Positive actions increase the likelihood of receiving favorable outcomes.

Negative Reinforcement
  • Observation:

    • Misbehaving leads to time-outs or loss of privileges.

  • Reflection:

    • Negative actions result in unfavorable consequences.

Chapter 3: Recognizing Strategic Interactions3.1 Games and PlaySimple Games
  • Peekaboo:

    • Observation: The surprise element keeps the game engaging for both parties.

    • Strategy: Timing my actions to maximize enjoyment.

  • Hide and Seek:

    • Observation: Finding good hiding spots increases the challenge.

    • Strategy: Anticipating where others might look first.

Understanding Rules and Strategies
  • Board Games with Family:

    • Observation: Each player makes choices that affect the game's outcome.

    • Reflection: Success depends on strategy, not just chance.

3.2 The Concept of Mutual DependenceInterdependent Decisions
  • Scenario:

    • Deciding whether to share snacks with a friend.

  • Observation:

    • Sharing may lead the friend to share with me in the future.

  • Reflection:

    • My choices can influence others' future behavior toward me.

Trust and Cooperation
  • Observation:

    • Building trust through cooperative actions leads to stronger relationships.

  • Reflection:

    • Long-term benefits can outweigh immediate gains from selfish actions.

Chapter 4: Formulating the Basic Concepts of Game Theory4.1 Defining Players, Strategies, and PayoffsPlayers
  • Definition:

    • Individuals involved in a strategic interaction.

  • In My Context:

    • Myself, siblings, parents, friends.

Strategies
  • Definition:

    • The set of possible actions a player can take.

  • Examples:

    • Sharing or not sharing toys.

    • Cooperating or competing in games.

Payoffs
  • Definition:

    • The outcomes resulting from the combination of players' strategies.

  • Positive Payoffs:

    • Gaining a friend, receiving a reward, mutual enjoyment.

  • Negative Payoffs:

    • Conflicts, loss of privileges, mutual dissatisfaction.

4.2 Creating a Simple Game MatrixScenario: Sharing Toys with a Sibling
Sibling SharesSibling Doesn't Share
I ShareBoth enjoy playing together (+2, +2)Sibling plays alone (+0, +3)
I Don't ShareI play alone (+3, +0)Neither plays happily (+0, +0)
  • Understanding the Matrix:

    • Each cell represents the payoffs for both me and my sibling based on our choices.

    • The numbers represent the satisfaction or enjoyment levels.

Analyzing Strategies
  • Best Mutual Outcome:

    • Both share, leading to mutual enjoyment.

  • Temptation to Defect:

    • Not sharing might give me more immediate enjoyment, but harms the relationship.

Chapter 5: Exploring the Prisoner's Dilemma5.1 Conceptualizing the DilemmaHypothetical Scenario
  • Situation:

    • My friend and I are suspected of breaking a vase. Our parents question us separately.

  • Choices:

    • Confess or remain silent.

  • Outcomes:

    • If both remain silent, minimal punishment.

    • If one confesses and the other doesn't, the confessor gets leniency while the other receives a harsher punishment.

    • If both confess, both receive moderate punishment.

Creating the Payoff Matrix
Friend SilentFriend Confesses
I Remain SilentMinimal punishment (-1, -1)Harsh punishment (-3, 0)
I ConfessLenient punishment (0, -3)Moderate punishment (-2, -2)
5.2 Analyzing the DilemmaDominant Strategy
  • Definition:

    • A strategy that results in a better payoff regardless of the other player's action.

  • In This Scenario:

    • Confessing appears to be the dominant strategy to avoid the harshest punishment.

Nash Equilibrium
  • Definition:

    • A situation where no player can benefit by changing their strategy unilaterally.

  • In This Scenario:

    • Both confessing is the Nash Equilibrium, even though mutual silence would lead to a better collective outcome.

Reflection
  • Understanding the Conflict:

    • Individual incentives lead to a worse collective outcome.

  • Implications:

    • Highlights the challenges of cooperation when individual interests conflict with mutual benefits.

Chapter 6: Extending Concepts to Repeated Interactions6.1 The Importance of ReputationObservation
  • Long-Term Relationships:

    • Consistently cooperating builds trust.

    • Betraying trust leads to damaged relationships.

Strategies in Repeated Games
  • Tit-for-Tat Strategy:

    • Starting with cooperation and then mimicking the other player's previous action.

  • Reflection:

    • Encourages cooperation by rewarding positive behavior and discouraging negative actions.

6.2 Evolution of CooperationLearning from Experience
  • Observation:

    • Over time, cooperative strategies lead to better outcomes.

  • Adjusting Behavior:

    • Choosing strategies that promote mutual benefit based on past interactions.

Chapter 7: Incorporating Uncertainty and Risk7.1 Dealing with Incomplete InformationSituations with Uncertainty
  • Example:

    • Deciding whether to share my favorite toy with a new friend.

  • Uncertainty:

    • Not knowing if they will reciprocate or take advantage.

Strategies Under Uncertainty
  • Risk Assessment:

    • Weighing potential benefits against possible losses.

  • Maximin Strategy:

    • Choosing the action that maximizes the minimum payoff.

7.2 Mixed StrategiesRandomizing Choices
  • Example:

    • Sometimes sharing, sometimes not, to prevent predictability.

  • Purpose:

    • Keeps others uncertain, potentially improving my position.

Chapter 8: Advanced Concepts8.1 Bargaining and NegotiationDividing Resources
  • Scenario:

    • Splitting a limited amount of dessert with a sibling.

  • Negotiation:

    • Proposing a fair division to avoid conflict.

  • Strategies:

    • Making offers and counteroffers to reach an agreement.

8.2 Signaling and CommunicationExpressing Intentions
  • Observation:

    • Communicating willingness to cooperate can influence others.

  • Example:

    • Saying, "I'll share my toy if you share yours."

Building Trust Through Communication
  • Outcome:

    • Clear communication reduces uncertainty and promotes cooperation.

Chapter 9: Synthesizing My Understanding of Game Theory9.1 Defining Game Theory
  • Definition:

    • The study of mathematical models of strategic interaction among rational decision-makers.

  • In My Context:

    • Understanding how my choices affect others and how their choices affect me.

9.2 Fundamental Concepts
  • Players: Individuals involved in the interaction.

  • Strategies: Possible actions each player can take.

  • Payoffs: Outcomes resulting from the combination of strategies.

  • Equilibrium: A state where no player can benefit by changing their strategy unilaterally.

9.3 Applications in Daily Life
  • Conflict Resolution: Using strategic thinking to resolve disputes.

  • Cooperation: Recognizing mutual benefits in working together.

  • Decision-Making: Anticipating others' actions to make better choices.

Chapter 10: Reflecting on the Journey10.1 The Power of Observation and Reasoning
  • Realizing Patterns:

    • Through interactions, I observed consistent patterns in behavior and outcomes.

  • Logical Deduction:

    • Analyzing these patterns led me to understand the underlying principles of strategic decision-making.

10.2 Implications for Personal Growth
  • Enhanced Social Skills:

    • Understanding Game Theory improves my ability to interact effectively with others.

  • Ethical Considerations:

    • Recognizing the impact of my actions on others encourages me to make choices that benefit everyone involved.

10.3 Broader Significance
  • Universality of Game Theory:

    • These principles apply not only to my experiences but also to economics, politics, biology, and more.

  • Foundation for Further Exploration:

    • My understanding serves as a stepping stone to delve deeper into complex strategic analyses.

Conclusion

Starting from simple interactions as an infant, I have journeyed through the discovery of strategic thinking and the foundational concepts of Game Theory. By observing the consequences of my actions and others', I recognized the importance of choices, strategies, and outcomes. Through logical reasoning and reflection, I developed an understanding of how to navigate complex social situations, anticipate others' behavior, and make decisions that lead to favorable results.

This exploration demonstrates that even without prior knowledge or subjective definitions, one can arrive at sophisticated concepts through careful observation and reasoning. Game Theory, rooted in everyday experiences, provides valuable insights into human behavior and interactions, highlighting the interconnectedness of our choices and their impact on the world around us.

Note: This detailed narrative presents how, as an infant, I independently observed, experimented, and reasoned out the principles of Game Theory. Each concept is developed from direct experiences, emphasizing the natural progression from simple interactions to the understanding of complex strategic decision-making. This approach showcases the potential to grasp advanced ideas through logical reasoning grounded in real-world experiences.

References for Further Reading

  1. International Standardization Committee of Networked DIKWP for Artificial Intelligence Evaluation (DIKWP-SC),World Association of Artificial Consciousness(WAC),World Conference on Artificial Consciousness(WCAC)Standardization of DIKWP Semantic Mathematics of International Test and Evaluation Standards for Artificial Intelligence based on Networked Data-Information-Knowledge-Wisdom-Purpose (DIKWP ) Model. October 2024 DOI: 10.13140/RG.2.2.26233.89445 .  https://www.researchgate.net/publication/384637381_Standardization_of_DIKWP_Semantic_Mathematics_of_International_Test_and_Evaluation_Standards_for_Artificial_Intelligence_based_on_Networked_Data-Information-Knowledge-Wisdom-Purpose_DIKWP_Model

  2. Duan, Y. (2023). The Paradox of Mathematics in AI Semantics. Proposed by Prof. Yucong Duan:" As Prof. Yucong Duan proposed the Paradox of Mathematics as that current mathematics will not reach the goal of supporting real AI development since it goes with the routine of based on abstraction of real semantics but want to reach the reality of semantics. ".



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