Anatol Rapoport is dead

Anatol Rapoport has died at the age of 95. Among many contributions, perhaps his most widely-known was the Tit-for-Tat rule for repeated games of the Prisoner’s Dilemma, embodied in a four-line program Rapaport successfully entered in a contest run by Robert Axelrod. Rapoport’s program co-operates inititially, and thereafter matches the other player’s last action, defecting in response to a defection, and returning to co-operation if the other player does so. There’s more here from Tom Slee.

8 thoughts on “Anatol Rapoport is dead

  1. Thankyou for bringing to our attention Prof Rapoport’s work. Game theory and Rapoport’s tit-for-tat rule is very relevant to the question of whether government’s and other entities cooperate or engage in ‘free-riding’ on the issue of climate change mitigation. There is some interesting discussion of these issues in the Stern Review on pages 451-453.

    These issues are particularly relevant for Australia where the federal government seems to be supporting a policy of free-riding on climate change mitigation and only focusing on adaptation. This was illustrated by Environment Minister Malcolm Turnbull’s recent announcement. Not sure what to make of Howard’s very recent announcement on carbon trading, it is good news though. Whether Australia cooperates or engages in free-riding will depend on the coverage and emissions cap of an emissions trading scheme.

  2. While Anatol Rapoports work towards peace was important, tit-for-that is of little use in understanding actual cooperation and non-cooperation. Ken Binmore has a review of a book by Axelrod in which he analyzes the whole tit-for-that craze.

  3. Thanks for that excellent link, Michael Greinecker. Many years ago I did an uni essay on the Prisoner’s Dilemma and Tit-for-Tat, and while it is interesting work, it was not clear how well it described the real world. Binmore’s essay clarifies the situation considerably for me.

  4. I worked for months back in the early nineties trying to incorporate “tit-for-tat” in a simulation of oligopolistic competition. Never could get it to work properly, but that probably says more about me than him. 🙂

  5. Good link Michael Greinecker. Binmore’s conclusion”.. such conjectures can only be evaluated in a scientific manner by running properly controlled robustness tests that have been designed using a knowledge of the underlying theory.” is IMHO , inescapable. Simulation can’t be used to explore spaces of possible results. The size and nature of a solution space has to be determined by theory. Simulation then is a form of statistics.

  6. Some funny things about that Binmore article. He says Tat for Tit was Simpleton (or Pavlov). But Simpleton does not begin with Defect. It begins with Cooperate according to the table of strategies on page 44 of Johansson’s 1999 thesis at

    Click to access joha99_1.pdf

    (It is a 121 page pdf. Fairly plainly written; a lot of interesting stuff.)

    Johansson indicates, contra Binmore, that Simpleton is toward the cooperative end of the scale of strategies; it cooperates when previous moves are the same but defects when they differed. I don’t know enough to resolve these contradictions but his colourful language and aggressive tone make me wary.

    He says “popularisers are so seduced by the idea that evolution will necessarily make us nice�. I should have thought the opposite was the case.

    He complains of a “prejudicial name� but then himself speaks of a “mean machine�. I note he quotes Nowak and Sigmund but not: Nowak, M A and K Sigmund. 1998. “Evolution of indirect reciprocity by image scoring.� Nature 393:573-577. Perhaps he predates this article, the guts of which is:

    “Here we present a new theoretical framework, which is based on indirect reciprocity and does not require the same two individuals ever to meet again. Individual selection can nevertheless favour cooperative strategies directed towards recipients that have helped others in the past. Cooperation pays because it confers the image of a valuable community member to the cooperating individual. We present computer simulations and analytic models that specify the conditions required for evolutionary stability of indirect reciprocity.� (573)

    Binmore obviously knows a lot about it but he is on some kind of mission.

  7. I don’t think Binmore describes TIT-FOR-TAT, he assumes it’s familiar, but it does start with cooperation (that’s the “nice” attribute Axelrod identifies).

    Rapoport’s main interest in Prisoners’ Dilemma was that in his view it compels a shift from individual rationality (a basic assumption in game theory) to collective rationality: as long as a player tries to maximize her own payoff, she is stuck with the Nash equilibrium, double defection. If she and her co-player (no “opponents” in a non-zero-sum game!) both consider both their outcomes, they can both do better with double cooperation.

    Axelrod’s work is intriguing because his simulations don’t depend on a player’s thought, self-knowledge, empathy, or any psychological factors, but rather take place in a quasi-biological, deterministic environment.

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