Reciprocity, social exchange and cheater detection
Part 1. Basic game theory
Game theory is a branch of mathematics that analyzes games, and the strategies that would lead to the best payoffs in those games. It was developed in World War II in the U.S. as an attempt to formalize strategic thinking, and became very important during the Cold War for developing military and diplomatic policies concerning nuclear weapons. For game theorists, a game is any well-defined interaction among two or more players in which the final payoff to each player depends on the choices of the other players. It assumes that each player adopts a strategy (a description of what choices he/she would make at every choice point in the game) that is picked to maximize the player’s payoff. Running alone for your pleasure may be just an exercise, but running in a race is a game, because winning the race not only depends on how fast you run, but also depends on how fast others run. This interdependence reflects important aspects of social interaction in many social organisms, including humans. Similarly, driving on the left side or the right side of the road is a game, because surviving or dying depends not only on what you do, but also on what others do. This is why behavioral scientists who are interested in the social behavior of animals (whether human or nonhuman) are also interested in game theory. Evolutionary game theory was developed out of game theory, but looks at what strategies evolve over time when (1) there are multiple generations of players playing the same game, (2) they inherit their strategies from the preceding generation, and (3) the proportion of each strategy in the next generation is determined by the previous frequency of each strategy, times the payoffs to those strategies in the preceding generation. Evolutionary biologists and evolutionary psychologists are interested in game theory because our ancestors, over evolutionary time, faced different kinds of situations that recurred across generations (i.e., have sex with multiple partners vs. be monogamous; run or freeze in the presence of a lion; share food help when a band member is in need vs. keep your food for yourself and your family). The process of mutation among ancestral humans would have created alternative cognitive and motivational designs, and these designs would play these games differently. The designs that consistently, generation after generation, got the highest payoffs (led to the highest net reproduction and kin reproduction) would have spread throughout the species. That is, our minds are designed, cognitively and motivationally, to play these games (i.e., behave in these interactions) in some ways and not others because those ways led to the highest fitness payoffs among our ancestors.
1. Is rock, paper, and scissors a game?
2. If your opponent chooses the rock strategy, what is your best response?
3. If you choose the paper strategy, what is your opponent’s best response?
Evolutionary game theory is a useful tool for studying the evolution of alternative designs of organisms because the process of evolution by natural selection is a process by which relatively better designs (better = achieve higher fitness payoffs) are selected to spread in the population. So, the evolutionary process sets different designs (different alleles) against each other in games (situations) that recur across generations. An understanding of game theory gives us insights into the process and results of evolution. Depending on the “game”, designs can be said to have strategies at the molecular level (e.g., the rate of cell growth, types of immune system), the morphological level (e.g., differences in body size), and the behavioral strategy (e.g., help close kin, defer when overmatched) etc.
4. Suppose there is a population of organisms all of whom are wired to play the rock strategy. (a) What happens when they play each other? Does the population evolve? Suppose further that these organisms survive and reproduce based on their rates of winning. Now consider the fate of a mutation that appears with the paper strategy appears and starts to interact with the other rock strategy organisms. (b) What would happen in this population in terms of the relative frequency of the two strategies? (When an allele spreads and becomes 100% of the population, it is said to go to fixation.)
5. An evolutionarily stable strategy (or ESS) is a strategy which, if adopted by a population of players, cannot be outcompeted by any alternative strategy that is initially low frequency. Now suppose the rock strategy organisms in the population in the previous question are fully supplanted by the paper strategy organisms. Is this paper strategy in this population an evolutionarily stable strategy? What would happen if one mutant with the scissors strategy appears and start to interact with other paper strategies?
6. Can you predict possible long term group dynamics in this population in terms of the rock, paper, and scissors strategy frequencies? Would any strategy go to a fixation? Or would the population shows some cyclical pattern?
Part 2. The prisoner’s dilemma
Different types of games in game theory model different aspects of social interactions. The game of rock, paper, scissors was interesting but does not capture games in which one strategy consistently yields the best payoffs. Moreover, no single game will be able to address the diversity of human sociality: interactions between friends, enemies, family members, co-workers, relatives, sexes, even different species (like predators and prey). However, there are a number of formal games that parallel different families of real situations that humans consistently face. Understanding them helps to understand why our minds evolved to respond to certain social situations in certain specific ways:
For example, the Prisoner’s Dilemma game (PD game) is one widely used model of social interaction. In the PD, two organisms (players) can as individuals choose either to cooperate or defect with their partner—as a single, unrepeated interaction. The payoffs of a PD are set so that (1) mutual cooperation would yield the best payoffs to the players, (2) mutual defection is worse than mutual cooperation for both players, but (3) each player is better off defecting than cooperating if his/her partner cooperates, and (4) each partner is better off defecting if his/her partner defects. For example, imagine that you are a ruthless drug dealer, out only for money. Imagine that there is a proposed exchange: You have offered your Colombian connection Igor $20,000 for a kilo of cocaine, and he has agreed. You have both agreed not to bring guns to the exchange. But what should you actually plan to do at the meeting? What will Igor do? If you both do as agreed, you both benefit: You get the cocaine, which you can then sell for far more than $20,000. Igor gets the $20,000, which is far more than he paid the refiners for the kilo. On the other hand, if you pull a gun on Igor, you get to keep the money, and take the cocaine, so you are better off cheating than honestly carrying out the bargain. If Igor brings a gun and you do not, then he gets both the money and the cocaine, which he can then sell to someone else (who hasn’t heard about his proclivity for cheating). You lose $20,000, so you are worse off than if you had never attempted an exchange with Igor. If however, you both simultaneously cheat and bring guns, you each keep what you have, and neither of you gets what you wanted more. So, you reason: Either Igor cheats or he doesn’t. If he cheats, then you are better off cheating too, and bringing a gun. If he doesn’t cheat, and comes without a gun, then you are still better off bringing a gun: You get the cocaine without paying for it. (Game theorists call cheating or not cooperating defecting.) Igor will look at the situation in the same way: He is better off bringing a gun if you cheat and bring one. He is better off bringing a gun if you foolishly trust him, and come without a gun. So, the winning strategy for both parties is defecting (bringing a gun). This is a sad and ironic result, because both of you would have been better off if you both cooperated, yet individually the best strategy is to defect. In the one-shot Prisoner’s Dilemma, the best option—mutual cooperation—will not be reached by rational players looking for the best payoffs. In the PD, game theorists describe defection as the dominant strategy, because it is the best paying strategy no matter what your partner chooses to do—that is, the defection is the dominant strategy over cooperation. The payoff matrix in game theory is a good way of describing this kind of strategic situation. We have two players (You, Igor) with two strategies for each (cooperate, defect). Based on the outcome of two individual choices, each player will get payoff which is specified in each cell (your payoff first, Igor’s payoff second).
Igor
don’t bring gun
(cooperate) bring gun
(defect)
You don’t bring gun
(cooperate) get cocaine, get $20,000 lost $20,000, gets cocaine & $20,000
bring gun get cocaine & keep $20,000 / loses cocaine get nothing, get nothing
Or this is a general version of prisoner’s dilemma payoff matrix
Player B
Cooperate Defect
Player A Cooperate A’s payoff R, B’s payoff R
(informally: win-win) A’s payoff S, B’s payoff T
(informally: big loss, big win)
Defect A’s payoff T, B’s payoff S
(informally: big win, big loss) A’s payoff P, B’s payoff P
(informally: lose, lose)
Where T stands for Temptation to defect, R for Reward for mutual cooperation, P for Punishment for mutual defection and S for Sucker’s payoff. To be defined as prisoner’s dilemma, the following inequalities must hold: T > R > P > S.
7. What is your best response to Igor’s choice, if Igor was not bringing a gun?
8. What is your best response to Igor’s choice, if Igor was bringing a gun?
9. Given your answers to question 7 and 8, what would you choose to do, if your only goal were attaining the best payoff for yourself?
10. What about Igor? What should Igor do if his only goal is obtaining the best payoff?
11. What is the payoff that each of you end up with? Compare it with the payoff that each of you would have received, had both of you chosen the other strategy.
The game theoretic analysis of prisoner’s dilemma situation is interesting for the study of animal social behavior and evolution for at least two reasons. First, it captures important aspects of a common situation that many social organisms face in real life. This is the situation in which two animals could cooperate with each other but cooperation does not take place because defection or cheating on the other is systematically higher paying. Second, the analysis of the prisoner’s dilemma game gives some insight into why it is difficult to achieve mutually cooperative outcomes in many cases and why cooperation is rare among nonhumans in the absence of genetic relatedness.
Part 3. Repeated interaction and cheater detection
12. Now, consider modern life in post-industrial societies. Even in cities, where one-time interaction with strangers is not uncommon, much of our social life is based on repeated interactions with people of known identity. What do you think would be the best strategy if the prisoner’s dilemma game is played repeatedly with same partner?
Although cooperation is not the winning strategy when PDs involve a single round of play, it turns out that cooperation can be a winning strategy when the interaction is repeated between two players. Because ancestral hunter-gatherers interacted with the same small set of people over and over, our ancestors’ lives were characterized by a large number of repeated PDs, perhaps along with some one-shot PDs. However, cooperation can only be a winning strategy in repeated PDs if your partner is also cooperating. If your partner consistently defects on you, then your best strategy is defecting. So the highest paying strategy is some kind of conditional cooperation: Cooperate on the first interaction. If you partner cooperates, then continue to cooperate as long as your partner cooperates. If your partner cheats on you (defects), then defect. If there are enough conditional cooperators around, this strategy beats always defect, because the gains from cooperation are larger than the costs of being defected on by an always defect once. This game theoretic structure acted as a selection pressure shaping human psychology throughout the human evolutionary history. You can benefit yourself by being cooperative with another cooperator AND by not cooperating with defectors. To avoid cheaters, one must be able to detect them. So evolutionary psychologists hypothesized that humans might be particularly good at detecting violations of conditional rules when those conditional rules corresponded to social exchanges (PDs) and violation corresponded to cheating. A social interaction in which one party delivers a benefit to another, conditional on the other party meeting a requirement (usually, delivering a benefit in return) is called a social contract. So, how to test whether humans are better at detecting cheaters than other violations, such as broken promises, or broken social rules?
Part 4. The Wason selection task: Tests of conditional reasoning about conditional cooperation
The Wason selection task was originally developed for testing how well people could perform conditional reasoning. The philosopher of science Karl Popper had proposed that science progressed by falsification—detecting when proposed hypotheses were violated. Inspired by Popper, some psychologists had proposed that humans learn by attempting to falsify their own hypotheses. Peter Wason developed the selection task to see if this was true. He discovered that, in general, people were bad at conditional reasoning. Evolutionary psychologists then used the Wason task to test whether people were good at detecting cheaters—indeed, whether they have a cheater detection mechanism. The following two Wason selection tasks are typical of the experimental stimuli used in this research and provided here as examples. Try to solve the tasks yourself as if you are taking part of a psychology experiment.
Wason selection task 1: David planted a garden with flowers of every color. He has not been able to enjoy it, though, because deer from the forest nearby have been eating his plants, killing some of them. He would like to keep the deer out of his garden. His grandmother told him that in the old days, she kept deer away by spraying an herbal tea—hawthorn tea—in her garden. She said: “If you spray hawthorn tea on your flowers, deer will stay out of your yard.” This sounded dubious. Still, David convinced some of his neighbors to spray their flowers with Hawthorn tea, to see what would happen. You are interested in seeing whether any of the results of this experiment violate his grandmother’s rule.
The cards below represent four yards near David’s house. Each card represents one yard. One side of the card tells whether or not Hawthorn tea was sprayed on the flowers in a yard, and the other side tells whether or not deer stayed out of that yard. Indicate which of the following cards would you definitely need to turn over to see if events in these yards violated David’s grandmother’s rule:
“If you spray hawthorn tea on your flowers, deer will stay out of your yard.”
Don’t turn over any more cards than are absolutely necessary.
sprayed with hawthorn tea not sprayed with hawthorn tea deer stayed away deer did not stay away
Wason selection task 2: Teenagers who don’t have their own cars usually end up borrowing their parents’ cars. In return for the privilege of borrowing the car, the Goldsteins have given their kids the following rule:
“If you borrow my car, then you have to fill up the tank with gas.”
Of course, teenagers are sometimes careless and irresponsible. You are interested in seeing whether any of the Goldstein teenagers broke this rule. These cards represent four of the Goldstein teenagers. Each card represents one teenager. One side of the card tells whether or not a teenager has borrowed the parents’ car on a particular day, and the other side tells whether or not that teenager filled up the tank with gas on that day. Which of the following cards would you definitely need to turn over to see if any of these teenagers are breaking their parents’ rule:
“If you borrow my car, then you have to fill up the tank with gas.”
Don’t turn over any more cards than are absolutely necessary.
borrowed car
did not borrow car
filled up tank with gas
did not fill up tank with gas
Which problem did you find easier to solve? Problem 1 elicited the logically correct response from only 20% of UCSB undergraduates. The problem 2 elicited the correct response from 76% of UCSB undergraduates. If people had conditional reasoning as one general learning mechanism, then subjects should have been able to do well on both problems, and equally well. Formally, the two problems are identical in terms of their logical structure.
General structure of Wason selection task: Here is a rule: “ If P then Q”.
The cards below have information about four situations. Each card represents one situation. One side of a card tells whether P happened, and the other side of the card tells whether Q happened. Indicate only those card(s) you definitely need to turn over to see if any of these situations violate the rule.
P
not-P
Q
not-Q
The logically correct answer is to choose the P card (to see if there is a not-Q on the back) and the not-Q card (to see if there is a P on the back). This is because the rule is violated (according to the propositional calculus) by any situation in which P happens and Q does not.
Now, consider the rule and cards from Wason selection task 1 again.
“If [you spray hawthorn tea on your flowers], then [deer will stay out of your yard.]”
“If P happens, then Q happens”
sprayed with hawthorn tea
P
not sprayed with hawthorn tea
not-P
deer stayed away
Q
deer did not stay away
not-Q
Thus, the logically correct answer is: P = sprayed with hawthorn tea and not-Q = deer did not stay away
The problem 2 shares the same logical structure as problem 1. But there is one important difference. The rule in problem 2 is a social contract. There is no such social contract in problem 1, because it just describes a causal relationship. Dozens of different social contracts have been tested around the world, along with other kinds of conditional rules. People are consistently very good at detecting violations of rules if the rules correspond to social exchanges, and detecting violations corresponds to detecting cheaters. In contrast, humans are generally poor at most other kinds of rules, no matter how familiar or sensible. The interpretation is that the mind contains a specialization that nonconsciously tags information in terms of whether acts correspond to taking the benefit, and paying the cost. It looks for situations in which someone has taken the benefit without paying the cost,
specific rule: “If you borrow my car, then you have to fill up the tank with gas.”
mental template: “If you take the benefit, then you are obligated to satisfy the requirement.”
borrowed car
took the benefit
did not borrow car
did not take the benefit filled up tank with gas
satisfied the requirement did not fill up tank with gas
did not satisfy the requirement
Took the benefit = borrowed the car (= P)
and
Did not satisfy the requirement = did not fill up the tank with gas (= not-Q)
Notice that for this particular social contract, the correct cheater detection answer happens to be the logically correct answer, P & not-Q. If our minds are trying to detect a violation of social contract, P and not-Q will be the cards that the cheater detection system causes to pop out as obvious. In the absence of a social contract, such as in the first selection task we encountered above, our minds struggle to solve a logical problem, a task which our evolved minds are not very good at.
Finally, imagine a rule like: If you fill up my tank, you may borrow my car. This is a social contract, but in this particular task, the logically correct answer (P and not-Q cards) does not correspond to “Took the benefit” card and “Did not satisfy the requirement” card. Here the correct cheater detection response: did not fill up my tank, and borrowed my car correspond to not-P and Q, which are incorrect responses according to formal logic. However, subjects pick the cards that are correct according to cheater detection, even though these are illogical. This supports the view that humans are equipped with an evolved logic of social exchange, rather than a general conditional reasoning system.
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