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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?
The text passage 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. It includes several examples and scenarios to illustrate these concepts.
no_question

the passage does not contain any explicit mathematical questions or problems that require solving. it provides examples and scenarios to explain game theory concepts, but it does not ask the reader to solve any specific mathematical problems or provide answers to such questions.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
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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?
user
The text passage 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. It includes several examples and scenarios to illustrate these concepts.

TYPE: NO_QUESTION

The passage does not contain any explicit mathematical questions or problems that require solving. It provides examples and scenarios to explain game theory concepts, but it does not ask the reader to solve any specific mathematical problems or provide answers to such questions.