The Evolution of Cooperation
Robert Axelrod
1943—
- 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 infinitely1 repeated prisoners' dilemma
“The contestants ranged from a 10-year-old computer hobbyist to professors of computer science, economics, psychology, mathematics, sociology, political science, and evolutionary biology.”
- The Evolution of Cooperation (1984)
- Among the most cited works in all of political science
1 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
The Evolution of Cooperation
Robert Axelrod
1943—
Axelrod's discussion of successful strategies based on four properties:
- Niceness: cooperate, never be the first to defect
- Be Provocable: don't be suckered by being too nice, return defection with defection
- Don't be envious: focus on maximizing your own score, rather than ensuring your score is higher than your "partner's"
- 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
The Folk Theorem
- 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
The Folk Theorem
- 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 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)
The Folk Theorem
Folk theorem: any individually rational and feasible average payoff can be sustained with sufficiently high δ (or θ)
An average payoff is individually rational if it is at least as good as the one-shot Nash equilibrium (Defect, Defect), i.e. (2,2) outcome
Folk Theorem: Simply Put
- 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 δ
- sufficiently high probability of game continuing θ
- 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!)
Assessing the Folk Theorem
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 δ or θ to sustain cooperation
Interpreting Repeated Games
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
Role of Institutions (and Biology?) I
(The bad side of the) Folk theorem shows us that nearly any set of strategies sustains cooperation
Main role of institutions is to select an equilibrium for us to coordinate around
- Importance of fairness and efficiency
- 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”
Role of Institutions (and Biology?) I
Any institution must be a Nash equilibrium in the “game” of life
In long-run, non Nash-behavior will be eliminated
- Later, we'll see such behavior is not “evolutionarily stable”
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
Biological Cooperation: Stickelback Fish
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
Milinski, M., 1987 "TIT FOR TAT in sticklebacks and the evolution of cooperation," Nature 4(325): 433-435
Biological Cooperation: Vampire Bats
Vampire bats starve after 60 hours
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
Wilkinson, G, 1984 "Reciprocal Altruism in Bats and Other Mammals," Ethology and Social Biology 9(2-4): 85-100
Human Social Cooperation
David Hume
1711—1776
“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.”
A Treatise on Human Nature} (1740): Book III, Part II, (\S) V
Human Social Cooperation
Adam Smith
1723-1790
"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 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. 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. 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).
Cooperation, Even in Extreme Circumstances
Despite mass killing in WWI, peace would occasionally “flare” up across entrenched lines
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
“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)
(In)complete Contracts
In economics & contract theory, a complete contract specifies all actions or transfers that parties must take under every possible contingency
In the real world of uncertainty, complete contracts are impossible
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 enforcement costs
- argument about interpretation
- slow litigation process, legal fees
Gives rise to post-contractual opportunism (shirking, fraud, renegotiation, hold-up, etc)
Asides: I/O & Theory of Firm
Research in industrial organization about how 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 firms are a solution to high transaction cost situations; the law is another
Using Market Forces to Enforce Contracts: Reputation
- Essentially playing an infinitely repeated Prisoners' Dilemma
- Cooperate = fulfill contract
- Defect = don't buy, cheat, renege, hold up, opportunism
The Revival of International Trade (c.1100)
The Revival of International Trade (c.1100)
Commercial Revolution in the 12th Century, developments in economy and technology
Resumption of long distance international trade (not since Roman era) took place in fairs, like the Champagne Fair
The Revival of International Trade (c.1100)
No established commercial law or State enforcement of contracts
International merchants can’t depend on weak & biased local governments to enforce international contracts!
Transactions at fairs: transfer of goods in exchange for promissory note to be paid at next fair
- Ample room for dishonest merchants to trade
Lex Mercatoria
Merchants adopted their own “laws” and best practices to facilitate commerce & minimize transaction costs
- Lex Mercatoria
For-profit merchant courts emerge to settle disputes and enforce international contracts
- More efficient, cheaper, and less partisan than Royal courts
- Legal and jurisdictional competition
Developed contract law and advanced legal instruments — debt, credit, loans, equity contracts
Lex Mercatoria
Not part of government, had no official power to enforce judgments!
Was successful (and foundation of most international and commercial law today), so must have worked
Reputation Again
What prevents a merchant from cheating?
- Reputation and sanction by other merchants
- If two specific merchants repeatedly interact, honesty can be sustained by trigger strategies (sufficiently high δ or θ, etc)
Then why need a legal system?
- Merchants require information about other merchants and their histories
- Role of third party
Reputation Again
Milgrom, North, and Weingast (1990) model these interactions as a multi-stage repeated game (p.11):
- Traders may (at a cost Q>0) ask LM (publicly reports whether any trader has any unpaid judgments) about their current partner
- Two traders play a prisoners' dilemma (Honest or Cheat)
- If LM was asked before (in stage 1), either player may Appeal outcome to LM at a cost C>0
- If Appealed, LM awards damages (J) to Plaintiff if he was Honest and his partner Cheated; otherwise nothing
- Defendant chooses to Pay J or Not
- Unpaid judgments recorded by LM
Milgrom, Paul R, Douglass C North, and Barry R Weingast, 1990, “The Role of Institutions in the Revival of Trade: The Law Merchant, Private Judges, and the Champagne Fairs,” Economics and Politics 2(1): 1-23
Reputation Again
If costs of asking judge are not too high, and if players are sufficiently patient (high enough δ or θ), can sustain honest trade
Merchant courts have strong incentive to be quick and efficient (promotes commerce)
- State/local courts biased against foreigners, inefficient
Milgrom, Paul R, Douglass C North, and Barry R Weingast, 1990, “The Role of Institutions in the Revival of Trade: The Law Merchant, Private Judges, and the Champagne Fairs,” Economics and Politics 2(1): 1-23