Under what conditions will cooperation emerge in a world of egoists without central authority? …cooperation does occur…. answer has fundamental affect….
Hobbes answer was pessimistic…Ever since … arguments about scope of government are can cooperation emerge without policing authority
Relevant especially to international relations, everyday reciprocity, legislation
Approach here: make simple assumptions about individual motives and deduce consequences for entire system
Hayek argued that agents that follow pro-social rules can create social order without central authority. Schelling showed how even without anti-social rules, interaction can yield unfavored outcomes (coordination yes, cooperation no). Adam Smith argued that you have to start from the premise that people have different skills and such and that their complementarity means that working together they can increase the size of the pie they will split. But this still assumes cooperation. Axelrod takes up the challenge of why we can expect that these bargains can be struck. The short answer, the secret of society, is "repeated play."
Robert Axelrod (born 1943) is a professor of political science and public policy (his actual title is "Professor of Human Understanding") at the University of Michigan. His work on human cooperation, complexity, and emergence makes use of game theory, mathematics, and agent-based modeling.
1. Axelerod's fundamental question here has four parts:
It's in the first line (175.4):
- under what conditions
- does cooperation emerge
- in a world of egoists
- without central authority
2. How does Axelrod motivate the question?
We know people are "not angels" bu that cooperation does happen. (175.4)
3. What are some of the examples of cooperation without central authority that Axelrod mentions?
4. How does Axelrod sum up the methodological approach he will use here?
- make some assumptions about individual motives (or the rules individuals will follow)
- deduce consequences for the behavior of the entire system. (175.9)
Note that this is very much the same approach introduced by Schelling.
5. What is the practical/policy motivation for this approach?
We want to discover the conditions in which cooperation can emerge — we assume that individuals are never acting in a pure social vacuum and that things in the environment (including arrangements of the agents, numbers, distributions of information, etc.) can have an effect on whether they cooperate. A successful predictive theory would then allow us to intervene to foster cooperation in particular settings (177.1).
6. Explain the basic idea of the prisoner's dilemma.
The name prisoner's dilemma comes from a scenario that fits a generic arrangement of two actors' intertwined fates: two people are arrested and charged with a crime; the police separate them and offer each a deal — betray your partner in crime and receive a lighter sentence, or risk being betrayed by your partner and receiving a harsher sentence. The best outcome occurs if you both keep your mouth shut, the worst overall if you both talk, but the worst for you as an individual is if you get ratted out and the best for you as an individual is if you rat out your partner.
If you keep your mouth shut we say you are cooperating with your partner; if you talk you are defecting from the partnership. (177.7)
7. Sketch and explain the table for prisoner's dilemma
A "game" can be represented by a grid in which the rows represent the moves that can be made by one player and the columns the moves that can be made by the other. The cells represent what happens for each combination of a move by the first player and a move by the second player. (178.1)
Each cell has two numbers in it. The first is the "payoff" for the row player and the second for the column player.
8. Consider the observation (178.5) that "it is better to defect if you think the other player will cooperate, and it is better to defect if you think the other player will defect." What does this imply about the "best" strategy for playing this game?
A bit of terminology: we call the action a player chooses her "strategy" — here, the defect strategy is better regardless of what we anticipate the other player will do. When a strategy has this property we call it a "dominant" strategy.
9. What are some basic findings (deductions) about prisoner's dilemma (179)
- Egoists playing the game once will defect.
- Egoists playing finite number of times have no incentive to cooperate.
- When the number of plays is indefinite, cooperation can emerge — the question is, under what conditions?
10. The PD is bare bones (even "unrealistic"!) but this is what makes it useful as a starting point. What four assumptions does Axelrod make to be sure he is looking at the simple, bare-bones case?
- No threats or commitments;
- No information about what other player will do except what she has done so far;
- You can't quit the game
- No changing the payoffs (179.8-181.2)
11. "So, unlike chess, in the Prisoner's Dilemma it is not safe to assume that the other player is out to get you." What is it about the structure of this game that makes it seem to contradict Hobbes' image of the world?
12. What do you make of the discussion on 180-181 about "discounting" and "the future" and the parameter w?
In what sense does the future come into play in my current decision? If I consider my current move, I may say, there's a chance my opponent will cooperate, so I think I'll defect…but, we might have to play again and if I defect this time that will increase the likelihood that she will defect next time. (180.1ff)
13. On 182-183 Axelrod lays out six "restrictive assumptions" that we can avoid. What is the point of this? (and what are they?)
In general, a theory is more powerful the fewer assumptions it depends on. In this sense we can think of assumptions as special or limiting circumstances: "this theory is correct but it only applies to cases where …."
Axelrod relaxes constraints on the payoffs, on how we interpret "cooperate," on our model of the agent (doesn't have to be "rational"), and even whether the game has to be played consciously. Together these allow the theory to "apply" to a much wider range of phenomena (182.7-183.3).
14. Axelrod acknowledges (183.8) that PD leaves out many if not most of the real world things that complicate cooperation between individuals but says this is a valuable approach precisely because it does. Explain and agree or disagree and say why you think so.
As Weber did with ideal types, the analyst using these tools can look at a pure example of a generic behavior
15. How did they do the research on what the best strategy was?
16. Wait a minute: how can we say TIT FOR TAT is best strategy when we just "proved" that there was no best strategy? (on page 181/2)
That proposition was that there is no best strategy that is INDEPENDENT of the other player's strategy. In other words, what we proved is that a best strategy has to take the choices of the other player into account.
16. What won?
TIT FOR TAT — a strategy in which you cooperate and then simply do whatever your opponent did last time (184.3)
17. What does Axelrod think is the reason this strategy is best?
- avoid unnecessary conflict by starting out cooperating
- your strategy responds quickly to defection by other
- immediate forgiveness
- clarity (184.5)
17. What does Axelrod say is the big conclusion?
we learn about how context can affect cooperation and, especially, how including knowledge about cooperation theory as a part of that context can promote cooperation. (184.6)
iterated prisoner's dilemma
TIT FOR TAT
zero-sum game (176.5)
Last problem was 0480 (HELP)
Q196. Explain this table:
Q197. Explain and give an example of a dominant strategy in a prisoner's dilemma game.
Q198. What is "tit-for-tat" and why, according to Robert Axelrod, is it so effective?
Q199. In the November 2012 general elections some sitting members of congress and the senate failed in their re-election effort and some opted not to run for re-election. After the election we describe those who are still in office but won't be in January as "lame ducks." Drawing on theoretical ideas and empirical ideas in the work of Robert Axelrod, make some predictions of how the dynamics of voting and deal making might be different during a lame duck session.
Q200. One of the most important concepts coming out of market, rational choice, and game theory models is "equilibrium." What do we mean by an equilibrium in game theory? Give an example and explain what we would mean if we said "get caught in a bad equilibrium."
Q217. Sociologists and anthropologists gripe endlessly about rational actor models, failing, over and over again, to understand that they are MODELS, not descriptions. Explicate and comment on this passage to show that you understand what the value of a model like prisoner's dilemma is for social theory.
The Cooperation Theory that is presented…is based upon an investigation of individuals who pursue their own self-interest without the aid of a central authority to force them to cooperate with each other. The reason for assuming self-interest is that it allows an examination of the difficult case in which cooperation is not completely based upon a concern for others or upon the welfare of the group as a whole. It must, however, be stressed that this assumption is actually much less restrictive than it appears. … So the assumption of self interest is really just an assumption that concern for others does not completely solve the problem of when to cooperate with them and when not to (Axelrod 1984: 177.2).
Q218. Explicate and comment:
The result was another victory for TIT FOR TAT! The analysis of the data from these tournaments reveals four properties which tend to make a decision rule successful: avoidance of unnecessary conflict by cooperating as long as the other player does, provocability in the face of an uncalled for defection by the other, forgiveness after responding to a provocation, and clarity of behavior so that the other player can adapt to your pattern of action.
These results from the tournaments demonstrate that under suitable conditions, cooperation can indeed emerge in a world of egoists without central authority (Axelrod 1984: 184.5).
Q236. In a prisoner’s dilemma game, the rational thing for both players is to defect. This makes mutual defection an equilibrium, though it is not a preferred one (the collective would be better off with another outcome). In other words, in a single game of prisoner’s dilemma, cooperation is “impossible.” But cooperation does happen in the world.
Demonstrate your understanding of Axelrod's ideas by describing the mechanism and conditions under which this can happen without assuming anything “social” about the agents.
Explain how this works and how it adds to or modifies Smith’s and Hayek’s story about how markets can be a source of social order.
Q411. What is Axelerod's fundamental question in "The Evolution of Cooperation"? It has four parts.
Q412. Explain the basic idea of the prisoner's dilemma.
Q412. Explain the basic idea of the prisoner's dilemma.
Q414. Explain why the study of the "emergence of cooperation" might be especially relevant in international relations. How does this observation suggest a fundamental limit to the Hobbesian model?
Q415. Explain what we mean by "norm of reciprocity" and how it is relevant to the course.
Q416. Explain what we mean by distinguishing a one-shot PD from an iterated PD and why this is important.
Q417. In the context of game theory/prisoner's dilemma, what does "words are cheap" mean?
Q418. Context and explication, please: "if the future is important, there is no one best strategy."
If the discount parameter, w, is sufficiently high, there is no best strategy independent of the strategy used by the other player.
Q422. What do we mean saying that Axelrod is trying to discover the conditions in which cooperation can emerge?
- 0196 Prisoner's Dilemma
- 0197 Prisoner's Dilemma
- 0198 The "tit-for-tat" strategy
- 0199 Game Theory: Lame Ducks
- 0200 Game Theory: Equilibrium
- 0210 Hayek: "Cosmos and Taxis"
- 0213 Hayek: "Cosmos and Taxis"
- 0217 Axlerod: Cooperation
- 0218 Axelrod: "tit-for-tat"
- 0236 Axelrod: "The Evolution of Cooperation"
- 0238 Fehr and Gintis
- Exam Markets 2012
- Life Of A Pencil
- Hayek "Cosmos & Taxis" (R014)
- Schelling: "Micromotives, Macrobehaviors" (R015)
- Adam Smith : The Division of Labor (R016)
- Axelrod "Live and Let Live" (R018)