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  # Game Theory - PowerPoint PPT Presentation
  
  Game Theory. Formalizing the Hobbesian Dilemma. A. Assumptions. Assumptions Rational choice – People act according to their preferences (desires, for Hobbes) Strategic interaction – What one person does affects what others should do Elements Players – Two or more
  
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  ## PowerPoint Slideshow about ' Game Theory' - rowa
  
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  ### Game Theory
  
  Formalizing the Hobbesian Dilemma
  
  • Assumptions
  
  • Rational choice – People act according to their preferences (desires, for Hobbes)
  
  • Strategic interaction – What one person does affects what others should do
  
  • Elements
  
  • Players – Two or more
  
  • Strategies – The choices players have (Means)
  
  • Outcomes – The results of the players’ choices (Ends)
  
  • Payoffs – How much each player values each Outcome (Desires)
  
  • Nash Equilibrium  Neither player could do any better by unilaterally changing its strategy choice
  
  • To Solve: Examine each cell to see if either player could do better by unilaterally choosing a different Strategy, given that its opponent does nothing different.
  
  Example:
  
  c. Not every game has a Nash Equilibrium
  
  • Example:
  
  d. Some games have multiple Nash Equilibria
  
  • Example:
  
  • Players – Limit to two for simplicity (result holds with more than two)
  
  • Strategies (Means) – We can be nice (help others or at least not harm them) or nasty (use violence to get what we want). Usual termnology is Cooperate vs Defect.
  
  • Outcomes – What might come about from the combination of our choices?
  
  • I cooperate but you defect – I’m dead. May not be able to defect later if I cooperate now (“there is no way for any man to secure himself so reasonable as anticipation”)
  
  • You cooperate but I defect – You’re dead (same logic as above)
  
  • We both defect – Life is nasty, brutish, and short – but since we each know the other is prepared, death is less likely
  
  • We both cooperate – We get along fine, but this means we have to each give up some things we desire. “Diffidence” = we both want the same thing.
  
  • Preferences (Desires) – Which outcome is best for each of us?
  
  • Prisoner’s Dilemma
  
  • Both players end up worse, even though each plays rationally!  Hobbesian Dilemma
  
  • Used to model the “Security Dilemma” by Realists (Efforts to increase own security make others less secure)
  
  • Chicken – Another Possibility
  
  • Equilibria: Someone swerves – but who?
  
  • Used to model nuclear crises
  
  • Could this be the state of nature?
  
  • “Stag Hunt”, aka the Assurance Game, aka Mixed-Motive PD
  
  • Used to model non-predatory security dilemma, driven by fear instead of aggression (Rousseau)
  
  • Equilibria: depends on trust – Nobody wants to be the only one looking for a stag!
  
  • Hobbes assumes life is zero-sum in state of nature, because we want the same things
  
  • Liberals assume we have different tastes AND that we have different talents/interests
  
  • If you and I are each better at making/gathering something, we can both do better by trade than predation!
  
  Given a day, what can each person produce?
  
  Fruit
  
  • Production possibilities without trade
  
  • Cain will buy Rabbits for < 2.5 fruit. Abel will buy Fruit for < 10/7 Rabbits.
  
  • Exchange rate must be between 2.5 fruit/rabbit and .7 fruit/rabbit
  
  • Example: Abel hunts 10 rabbits, trades 3 to Cain for 5 fruits. (1.67 fruits/rabbit = good deal for Cain, .6 rabbits/fruit = good deal for Abel!).
  
  • Result: Both sides achieve consumption beyond original production possibilities!
  
  10
  
  5
  
  5
  
  10
  
  Rabbits
  
  Given a day, what can each person produce?
  
  • Lisa has absolute advantage in both goods!
  
  • Lisa has comparative advantage in…
  
  • 2 to 1 in turkey, 1.2 to 1 in taters  turkey
  
  • Bart has comparative advantage in taters (5/6 as productive rather than only 1/2)
  
  • Bart buys turkey at < 2 taters, Lisa buys taters at < 5/6 turkey. Exchange rate must be between 2 and 1.2 taters/turkey
  
  • Example: Bart grows 10 taters, Lisa catches 10 turkeys. Bart trades 6 taters for 4 turkeys (1.5 taters/turkey)
  
  Taters
  
  20
  
  10
  
  5
  
  10
  
  Turkeys
  
  • Is trade possible in the state of nature?
  
  • Does it matter whether there are two people or thousands? Does this change incentives for predation vs. trade?
  
  • Could some type of money evolve in a state of nature? Locke argues yes…
  
  • Hobbesian tournament: Each player must play each other player in a series of Prisoners’ Dilemma (Hobbesian Dilemma) games.
  
  • Best strategy in a single-shot game is always Defect, but…
  
  • Which strategies produce the highest total payoff over many games against different players?
  
  • Best strategy is almost always Tit-for-Tat
  
  • Start by cooperating
  
  • Then do what opponent did last time
  
  • Matches some of Hobbes’s advice:
  
  • Cooperate at first, but retain ability to defect (Law of Complacence)
  
  • Match cooperation with cooperation (Law of Gratitude)
  
  • Respond to renewed good behavior (Law of Pardon)
  
  • Implication: People playing the best strategy will get along. If poor strategy = earlier death, only TFT players will survive.
  
  • Did Hobbes miss this implication? Is the state of Nature a repeated game? What happens if I fail to defect when I should have defected?
explanation: The provided text is a PowerPoint presentation on Game Theory, specifically focusing on the Hobbesian Dilemma and various game theory concepts such as Nash Equilibrium, Prisoner's Dilemma, and comparative advantage. The text does not contain a single, direct math question or a question-and-answer pair. Instead, it presents several examples and scenarios that involve mathematical reasoning and economic principles, but these are part of the broader discussion rather than standalone questions.
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  # Game Theory - PowerPoint PPT Presentation
  
  Game Theory. Formalizing the Hobbesian Dilemma. A. Assumptions. Assumptions Rational choice – People act according to their preferences (desires, for Hobbes) Strategic interaction – What one person does affects what others should do Elements Players – Two or more
  
  I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
  Download Presentation
  
  ## PowerPoint Slideshow about ' Game Theory' - rowa
  
  An Image/Link below is provided (as is) to download presentation
  
  Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
  
  - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
  Presentation Transcript
  
  ### Game Theory
  
  Formalizing the Hobbesian Dilemma
  
  • Assumptions
  
  • Rational choice – People act according to their preferences (desires, for Hobbes)
  
  • Strategic interaction – What one person does affects what others should do
  
  • Elements
  
  • Players – Two or more
  
  • Strategies – The choices players have (Means)
  
  • Outcomes – The results of the players’ choices (Ends)
  
  • Payoffs – How much each player values each Outcome (Desires)
  
  • Nash Equilibrium  Neither player could do any better by unilaterally changing its strategy choice
  
  • To Solve: Examine each cell to see if either player could do better by unilaterally choosing a different Strategy, given that its opponent does nothing different.
  
  Example:
  
  c. Not every game has a Nash Equilibrium
  
  • Example:
  
  d. Some games have multiple Nash Equilibria
  
  • Example:
  
  • Players – Limit to two for simplicity (result holds with more than two)
  
  • Strategies (Means) – We can be nice (help others or at least not harm them) or nasty (use violence to get what we want). Usual termnology is Cooperate vs Defect.
  
  • Outcomes – What might come about from the combination of our choices?
  
  • I cooperate but you defect – I’m dead. May not be able to defect later if I cooperate now (“there is no way for any man to secure himself so reasonable as anticipation”)
  
  • You cooperate but I defect – You’re dead (same logic as above)
  
  • We both defect – Life is nasty, brutish, and short – but since we each know the other is prepared, death is less likely
  
  • We both cooperate – We get along fine, but this means we have to each give up some things we desire. “Diffidence” = we both want the same thing.
  
  • Preferences (Desires) – Which outcome is best for each of us?
  
  • Prisoner’s Dilemma
  
  • Both players end up worse, even though each plays rationally!  Hobbesian Dilemma
  
  • Used to model the “Security Dilemma” by Realists (Efforts to increase own security make others less secure)
  
  • Chicken – Another Possibility
  
  • Equilibria: Someone swerves – but who?
  
  • Used to model nuclear crises
  
  • Could this be the state of nature?
  
  • “Stag Hunt”, aka the Assurance Game, aka Mixed-Motive PD
  
  • Used to model non-predatory security dilemma, driven by fear instead of aggression (Rousseau)
  
  • Equilibria: depends on trust – Nobody wants to be the only one looking for a stag!
  
  • Hobbes assumes life is zero-sum in state of nature, because we want the same things
  
  • Liberals assume we have different tastes AND that we have different talents/interests
  
  • If you and I are each better at making/gathering something, we can both do better by trade than predation!
  
  Given a day, what can each person produce?
  
  Fruit
  
  • Production possibilities without trade
  
  • Cain will buy Rabbits for < 2.5 fruit. Abel will buy Fruit for < 10/7 Rabbits.
  
  • Exchange rate must be between 2.5 fruit/rabbit and .7 fruit/rabbit
  
  • Example: Abel hunts 10 rabbits, trades 3 to Cain for 5 fruits. (1.67 fruits/rabbit = good deal for Cain, .6 rabbits/fruit = good deal for Abel!).
  
  • Result: Both sides achieve consumption beyond original production possibilities!
  
  10
  
  5
  
  5
  
  10
  
  Rabbits
  
  Given a day, what can each person produce?
  
  • Lisa has absolute advantage in both goods!
  
  • Lisa has comparative advantage in…
  
  • 2 to 1 in turkey, 1.2 to 1 in taters  turkey
  
  • Bart has comparative advantage in taters (5/6 as productive rather than only 1/2)
  
  • Bart buys turkey at < 2 taters, Lisa buys taters at < 5/6 turkey. Exchange rate must be between 2 and 1.2 taters/turkey
  
  • Example: Bart grows 10 taters, Lisa catches 10 turkeys. Bart trades 6 taters for 4 turkeys (1.5 taters/turkey)
  
  Taters
  
  20
  
  10
  
  5
  
  10
  
  Turkeys
  
  • Is trade possible in the state of nature?
  
  • Does it matter whether there are two people or thousands? Does this change incentives for predation vs. trade?
  
  • Could some type of money evolve in a state of nature? Locke argues yes…
  
  • Hobbesian tournament: Each player must play each other player in a series of Prisoners’ Dilemma (Hobbesian Dilemma) games.
  
  • Best strategy in a single-shot game is always Defect, but…
  
  • Which strategies produce the highest total payoff over many games against different players?
  
  • Best strategy is almost always Tit-for-Tat
  
  • Start by cooperating
  
  • Then do what opponent did last time
  
  • Matches some of Hobbes’s advice:
  
  • Cooperate at first, but retain ability to defect (Law of Complacence)
  
  • Match cooperation with cooperation (Law of Gratitude)
  
  • Respond to renewed good behavior (Law of Pardon)
  
  • Implication: People playing the best strategy will get along. If poor strategy = earlier death, only TFT players will survive.
  
  • Did Hobbes miss this implication? Is the state of Nature a repeated game? What happens if I fail to defect when I should have defected?
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is a PowerPoint presentation on Game Theory, specifically focusing on the Hobbesian Dilemma and various game theory concepts such as Nash Equilibrium, Prisoner's Dilemma, and comparative advantage. The text does not contain a single, direct math question or a question-and-answer pair. Instead, it presents several examples and scenarios that involve mathematical reasoning and economic principles, but these are part of the broader discussion rather than standalone questions.
  
  Label: no-question