3.3 — The Evolution of Coooperation

# 3.3 — The Evolution of Coooperation
## ECON 316 • Game Theory • Fall 2021
### Ryan Safner<br> Assistant Professor of Economics <br> <a href="mailto:safner@hood.edu"><i class="fa fa-paper-plane fa-fw"></i>safner@hood.edu</a> <br> <a href="https://github.com/ryansafner/gameF21"><i class="fa fa-github fa-fw"></i>ryansafner/gameF21</a><br> <a href="https://gameF21.classes.ryansafner.com"> <i class="fa fa-globe fa-fw"></i>gameF21.classes.ryansafner.com</a><br>

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# Outline

### [The Evolution of Cooperation](#3)
### [The Folk Theorem](#6)
### [Interpreting Repeated Games](#12)
### [Application I: Reputation](#67)
### [Application II: Law Merchant & Medieval Trade Fairs](#67)

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# The Evolution of Cooperation

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# *The Evolution of Cooperation*

1943—
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- Research in explaining the **evolution of cooperation**
- Use prisoners' dilemma to describe human societies and evolutionary biology of animal behaviors
- Hosted a series of famous tournaments for experts to submit a strategy to play in an infinitely<sup>.magenta[1]</sup> repeated prisoners' dilemma

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> “The contestants ranged from a 10-year-old computer hobbyist to professors of computer science, economics, psychology, mathematics, sociology, political science, and evolutionary biology.”

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- *The Evolution of Cooperation* (1984)
- Among the most cited works in all of political science 
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.source[<sup>.magenta[1]</sup> Each round had a 0.00346 probability of ending the game, ensuring on average 200 rounds of play

Axelrod, Robert, 1984, *The Evolutioon of Cooperation]

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# *The Evolution of Cooperation*

1943—
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- Axelrod's discussion of successful strategies based on four properties:
  1. **Niceness**: cooperate, never be the first to defect
  2. **Be Provocable**: don't be suckered by being too nice, return defection with defection
  3. **Don't be envious**: focus on maximizing your own score, rather than ensuring your score is higher than your "partner's"
  4. **Don't be too clever**: clarity is essential for others to cooperate with you

- The winning strategy was, famously, **TIT FOR TAT**, submitted by Anatol Rapoport

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.source[Axelrod, Robert, 1984, *The Evolutioon of Cooperation]
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# The Folk Theorem

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# The Folk Theorem

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- Consider the **average payoff** to each player each round, depending on the strategies chosen
    - e.g. if both Cooperate forever, average payoff is (3,3) — both earn 3 every round

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<img src="3.3-slides_files/figure-html/unnamed-chunk-1-1.png" width="504" style="display: block; margin: auto;" />

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# The Folk Theorem

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- Consider the **average payoff** to each player each round, depending on the strategies chosen
    - e.g. if both Cooperate forever, average payoff is (3,3) — both earn 3 every round
- Consider the .red[set of feasible average payoff]
    - e.g. no way to produce average payoff of (6,6)
    - average payoff of (2.5, 2.5) is possible (players alternate between C and D each round)

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<img src="3.3-slides_files/figure-html/unnamed-chunk-2-1.png" width="504" style="display: block; margin: auto;" />

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# The Folk Theorem

- .hi[Folk theorem]: any .hi-purple[individually rational] and feasible average payoff can be sustained with sufficiently high `\(\delta\)` (or `\(\theta)\)`

- An average payoff is .hi-purple[individually rational] if it is at least as good as the one-shot Nash equilibrium (Defect, Defect), i.e. (2,2) outcome

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<img src="3.3-slides_files/figure-html/unnamed-chunk-3-1.png" width="504" style="display: block; margin: auto;" />

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# Folk Theorem: Simply Put

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- .hi[Folk theorem (simplified)]: Many strategies can sustain long-run cooperation if:
    - Each player can observe history
    - The value of future interactions must be sufficiently important to players
        - sufficiently high discount rate `\(\delta\)`
        - sufficiently high probability of game continuing `\(\theta\)`
- If this is true, *many* strategies can sustain long-run cooperation
    - Any in the teal set in the diagram before
    - *Grim trigger* is simply the bare minimum/worst case scenario (and, importantly, easiest to model!)
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# Assessing the Folk Theorem

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- **The Good**: cooperation is possible, rational, and efficient!
  - Any improvement above (D,D) is a Pareto improvement for all players
    
- **The Bad**: lack of predictive power
  - Anything goes! Almost *any* outcome can be a sustainable equilibrium
  - This is why game theorists use the grim trigger strategy results as the *bare minimum* sufficient strategy for cooperation
    
- As temptation payoff increases relative to Nash equilibrium, need higher `\(\delta\)` or `\(\theta\)` to sustain cooperation
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# Interpreting Repeated Games

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# Interpreting Repeated Games

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- One-shot game between rational players leads to the predicted result (in PD: mutual defection)

- (Infinitely) repeated games allow us to consider:
  - cooperation
  - altruism
  - trust
  - loyalty and betrayal
  - revenge and vindication
  - promises and threats
  
- These are things that look "irrational" to utility-maximizing *homo economicus*

- People have evolved norms and institutions to enable optimal behavior
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# Role of Institutions (and Biology?) I

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- (The bad side of the) Folk theorem shows us that nearly any set of strategies sustains cooperation

- Main role of institutions is to .hi-turquoise[select an equilibrium] for us to coordinate around
  - Importance of fairness and efficiency
  - .hi-purple[Reciprocal altruism]: agent acts against its interest temporarily, in the interest of another, with expectation that other will do the same in the future
  - “You scratch my back, I'll scratch yours”
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![](../images/socialgrooming.jpg)
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# Role of Institutions (and Biology?) I

- In long-run, non Nash-behavior will be eliminated
  - Later, we'll see such behavior is not “evolutionarily stable”

- .hi-purple[Cultural selection theory]: societies whose institutions select fair and efficient outcomes thrive, while others perish
    - Akin to biological natural selection
  
- We'll see more evolutionary biology applications of game theory shortly
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![](../images/socialgrooming.jpg)
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# Biological Cooperation: Stickelback Fish

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- When a potential predator appears, one or more sticklebacks approach to check it out

- Costly (dangerous) but provides useful information:
  - If hungry predator: flee
  - Otherwise, stay
    
- Milinski (1987) found these fish use Tit-for-Tat:
  - Two fish swim together towards potential predator
  - "**Cooperate**": move forward
  - "**Defect**": hang back
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.source[Milinski, M., 1987 "TIT FOR TAT in sticklebacks and the evolution of cooperation," *Nature* 4(325): 433-435]
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# Biological Cooperation: Vampire Bats

- Feed each other by regurgitating blood

- Sharing food is great benefit to recipient, great cost to giver

- Wilkinson (1984) provides evidence that bats that receive food are more likely to give food in future

- Bats share beyond simple kin-groups
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.source[Wilkinson, G, 1984 "Reciprocal Altruism in Bats and Other Mammals," *Ethology and Social Biology* 9(2-4): 85-100]

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# *Human* Social Cooperation

1711—1776
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> “Men being naturally selfish, or endowed only with a confined generosity, they are not easily induced to perform any action for the interest of strangers, except with a view to some reciprocal advantage, which they had no hope of obtaining but by such a performance.”

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# *Human* Social Cooperation

Adam Smith

1723-1790
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> "In civilized society [man] stands at all times in need of the cooperation and assistance of great multitudes, while his whole life is scarce sufficient to gain the friendship of a few persons...man has almost constant occasion for the help of his brethren, and .hi[it is in vain for him to expect it from their benevolence only]."

> "Whoever offers to another a bargain of any kind, proposes to do this. .hi[Give me that which I want, and you shall have this which you want]...and it is in this manner that we obtain from one another the far greater part of those good offices which we stand in need of. .hi[It is not from the benevolence of the butcher, the brewer, or the baker, that we expect our dinner, but from their regard to their own interest.] (Book I, Chapter 2).

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.source[Smith, Adam, 1776, [*An Enquiry into the Nature and Causes of the Wealth of Nations*](https://www.econlib.org/library/Smith/smWN.html)]

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# Cooperation, Even in Extreme Circumstances

- .hi-green[Examples]:
  - The hour of 8:00-9:00am was regarded as consecrated to "private business"
  - No shooting during meals
  - No firing artillery at enemy's supply lines

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> “After shooting, a German soldier shouted out 'We are very sorry about that; we hope no one was hurt. It is not our fault, it is that damned Prussian artillery.”

> “A key factor was the realization that if one side would exercise a particular kind of restraint, then the other might reciprocate,” (Axelrod 1984: 78-79)

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.source[Axelrod, Robert, 1984, *The Evolutioon of Cooperation*, Ch. 4, The Live-and-Let-Live System in Trench Warfare in World War I]
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# Application I: Reputation

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# (In)complete Contracts

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- In economics & contract theory, a .hi[complete contract] specifies all actions or transfers that parties must take under every possible contingency

- In the real world of .hi-purplw[uncertainty], complete contracts are *impossible*

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# Consequences of Incomplete Contracts

- Agreements are always incomplete contracts, actions for many (unforeseen) contingencies are unspecified

- Even for specified actions and contingencies, outcomes are indeterminate due to .hi-purple[enforcement costs]
  - argument about interpretation
  - slow litigation process, legal fees

- Gives rise to .hi[post-contractual opportunism] (shirking, fraud, renegotiation, hold-up, etc)

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# I Am Altering The Deal...

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# ...Pray I Don't Alter it Any Futher

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<iframe width="980" height="550" src="https://www.youtube.com/embed/OXyH1XkQo44" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
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# Asides: I/O & Theory of Firm

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[ECON 326 — Industrial Organization](https://ios20.classes.ryansafner.com)
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![:scale 75%](../images/law_hex.png)
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[ECON 315 — Economics of the Law](https://laws21.classes.ryansafner.com)
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- Research in industrial organization about how .hi-purple[firms solve these problems of transaction costs]
  - **vertical integration** to prevent post-contractual opportunism
  - **contractual restraints** (that look like they create market power but are actually efficient)

- In general .hi-purple[firms are a solution to high transaction cost situations]; .hi-purple[the law] is another
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