To the peaceful memory of Professor Anatol Rapoport
“One cannot play chess if one becomes aware of the pieces as living souls and of the fact that the Whites and the Blacks have more in common with each other than with the players. Suddenly one loses all interest in who will be champion.” – Strategy and Conscience
In everyday life we are making decisions whose outcomes affect others. A friend may ask us for a favour, we might have business relations with some people et c. Every one of us has sometime felt betrayed by a friend that stopped creating that, up to that point, successful “chain” of mutual cooperation between us. There are people that we define as cheaters and others that we are sure that can be trusted. There are others that we trust and we are proved to be mistaken. Or people often try to gain the trust of others in order to delude them. Although society is supposed to be teaching the ethics of cooperation for centuries now, experience shows that deceit is very common in humanity either we like it or not. The reason is that deceit looks sweet.
We the homo sapiens have the natural tendency to be magnetized by the minimum energy costs of money, time, energy et c. And deceit is gain without loss in the short term while cooperation is gain AND loss. Of course this comes from the basic idea of evolution and the “egoism” of the genes to increase by any means their chances of replication.
However, nature seemed to be quite more complex because there were very often situations of successful long term cooperation observed. The individuals that share genes between them (relatives) were providing affection and security to each other because this was deep down a help from the genes to their own replicas to continue existing. At the same time even if the individuals did not share the same genes they were sometimes exchanging resources or services. Common examples on this is when monkeys are scratching each other’s backs because they are not able to scratch their own or the tribalism among wolves, humans, dolphins and a whole lot of other animals. Cooperation was even found among bacteria in the microbial level. Dr. Robert Trivers explained it with the term Reciprocal Altruism and found that even the losses of this cooperation (compared to just being scratched and go away), in the long term it served for the good of survival of each individual.
But it was several years later when Robert Axelrod and William D. Hamilton in their famous study “The Evolution of Cooperation” evolved Trivers’ term by supporting it with a mathematical grounding. This study explained WHY the individuals were coming to cooperation, the idea of this genetically predisposed strategy for achieving the desired goal. They used Game Theory to create an evolutionary model and study the effects (gains and losses) of the interactions among individuals in nature. Game Theory was firstly used by Economists to describe the strategies the individuals were using in a competitive market. Axelrod’s model was another version of the Prisoner’s Dilemma, a game that mixed trusting cooperation and individual selfishness presenting a real dilemma in many social interactions.
The idea is that there is a ballot that has set specific expected payoffs according to the two players’ behaviour. Each player has to make the decision whether to cooperate or to defect without knowing the other player’s move. The most important thing is the rank of the outcomes. The temptation to defect must be better than the outcome of mutual cooperation, which must be better than the outcome of mutual defect which must be better than the outcome of the individual who cooperated when the other defected. The below figure summarizes the above
You can also calculate the following: If player 1 cooperates and player 2 defects, player 1 gets 0 and player 2 gets 5. If in the next move player 1 defects and player 2 cooperates, player 1 takes 5 and player 2 gets 0. In the case it keeps going, on the average gain from each move would be 2, 5 for each of the players whereas if they were always cooperating would be 3. So cooperation is more effective than an equal exchange of cooperation and defect.
What Axelrod did was to create a computer tournament where strategies were submitted by game theory experts in economics, sociology, political science and mathematics. Every player had to submit a strategy for 200 moves and they played all against each other. Most of the strategies were quite complex. “An example is one which on each move models the behaviour of the other player as a Markov process, and then uses Bayesian inference to select what seems the best for the long run” mentions Axelrod. However, the most interesting and surprising fact was that the winner was the simplest tactic of all and it was named tit for tat coming from Professor Anatol Rapoport of the Institute for Advanced Study (Vienna). Tit for tat’s strategy is simply acting with an altruistic predisposition always cooperating in the first move and afterwards copying the previous move of the other player.
After the repeating of the game with more moves (in order to be more realistic) and updated strategies, tit for tat won the tournament once again. It was also discovered that most of the nasty strategies (the ones that were defecting first) finished in the lowest rankings one reason being that they engaged in mutual defections against each other. Remember this is the worst outcome after the sucker’s payoff (when the player cooperates and the other defects).
While reading about Anatol Rapoport, it seems to me that he managed to create a simple strategy that contained all his attitude and dreams about the world. Apart from the magnificent beauty of its simplicity, Tit for tat was first of all optimistic and altruistic. It was nice. It always trusts the other player. It voluntarily gives value first regardless the receiver. And this was a surprise to many of the game theorists who believed that usual attacks of defect could offer better outcomes. But tit for tat is not a sucker. When defected always retaliates and may unfortunately end up in situations of mutual defection. But it is forgiving, too. Even after a long-run mutual defection, if the other player cooperates, tit for tat cooperates again. The most amazing of all its characteristics though is that in a specific game it never wins! Tit for tat is non-envious. The best case scenario is being equal with another nice strategy where they have engaged in mutual cooperation taking both 3 points in each move. So, tit for tat is not measuring its success by how well is doing with the immediate opponent but is delayed gratified after several interactions in an environment and this is what counts, the finishing line.
In everyday life tit for tat is simply a way of being more effective as humanity. The irrationality and win-lose games that conquer our world can be substituted by efficiently created win-win situations where both parts participating have both gains. For example all these beautiful cities of the world are built through mutual cooperation among the members. Many partnerships have resulted in wealth and there exist examples of successfull athletic teams with that kind of mentality. From each one of us’ side, the more people engage in situations of mutual cooperation and start playing tit for tat the more the cheats disappear from the environment. Axelrod proved this mathematically, as well. From my own side I started feeling much more chilled when I read about these. It is clearer now how things are working and most of the times this is the mentality I follow. It is very simple and has all the positive predispositions not be accused by anyone. At the same time I am not sceptical when providing first value to a person I do not know and most of the times I do not regret it if I’ve been deceived, as far as I am sure that I knew what I was doing.
“Human intelligence has yet to design a society where free competition among members works for the good of the whole.” ~Egbert Leigh (biologist at the Smithsonian Tropical Research Institute)