My Way Or The Highway -- LogoMoth -- A NetLogo Moth Simulation
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view/download model file: Moth.nlogo
WHAT IS IT?
LogoMoth demonstrates that insofar as Iterated PD games have served as models to explain animal and human social behavior, they have limited our imaginations concerning the strategies used by social agents in choosing associates. Iterated PD games operate on the assumption that two players are "stuck" with one another throughout each match of a simulation; under that constraint, the strategy that has done famously well is Tit For Tat, a strategy that cooperates on the first game of the match and then imitates its opponent's previous move in every subsequent game of the match. The success of of Tit for Tat in PD games has made it the model for hundreds of explanations of "reciprocity" in animal and human social relations.
This focus on Tit for Tat reciprocity as a key to animal sociality may be inappropriatte. The structure of the Axelrod game constrains the players to remain paired, even in non-productive partnership. This constraint is highly un-natural in animal (and human) social systems where individuals typically break off relationships if a partnership is not productive. In mapping Tit for Tat reciprocity on to natural social systems, theorists have implicitly recognised this artificiality in the tournament structure when they have interpreted Tit for Tat as requiring a considerable level of cognitive complexity: instead of being bound to one another as the tournament structure demands, partners must recognise one another and remember what they did on the previous occasion. (ref) A simpler ... and therefore more universal... basis for social clustering would be one in which social agents are programmed to attach themselves to agents who have benefitted them in some way. In the language of the PD literature, such an agent would respond to defection by breaking up a partnership and looking for another partner amongst other unattached agents. Far from requiring recognition, such a strategy would require only very simple operant conditioning at most. We call this strategy, "Myway Or The Highway", or simply MOTH. (Not a great name, but I am afraid it has stuck.)
HOW IT WORKS
A LogoMoth simulation starts by assigning N agents, each playing one of eight strategies, to partnerships to play a series of PD games called a "Match". According to their strategies, LogoMoth agents make two sorts of decisions: whether to cooperate with a partner and whether to continue to play with a particular partner in the next game of the match. Either member of a partnership can desolve it and both players then return to the pool of unpartnered players. Strategies can be conditional or non-conditional in that an agent may or may not use the behavior of its partner on the previous round to decide what to do on the next. The eight strategies are as follows:
Nice Always cooperates; doesn't leave. This is Axelrod, ALLC
Nasty Always defects; doesn't leave. This is Axelrod, ALLD
Tit4Tat Cooperates first; plays as partner did previously; doesn't leave. Cf Axelrod
Moth Cooperates until partner defects, then leaves.
Hit&Run Defects in every game, then leaves.
Santa Cooperates in every game, then leaves.
NasMoth Always defects; but leaves only when partner defects.
NNHnRun Defects twice; leaves immediately if partner defects on the first game; leaves unconditionally after the second game.
The first three strategy will be familiar to any reader of Axelrod and Hamilton's Evolution of Cooperation. The second five are all strategies that make use of leaving in some way. MOTH is the one that most closely resembles what we think animals are likely to do in most failed cooperation situations. The rest are chosen to exploit various perceived weaknesses of the other strategies, but are exhaustive only in the sense that these are the ones we could quickly think of. One of our goals in getting LogoMoth into circulation, is to encourage others to think of better challanges to MOTH.
LogoMoth is an evolutionary program, i.e., it is designed to simulate the Darwinian competition between organisms seeking to out-reproduce one another in a population whose numbers are arbitrarily limited to some number, P, for each simulation. Consequently, at the end of each match of N games, the number of points scored by the players of each strategy is summed, divided by the number of players of that strategy, and players are allocated to the strategies in the next match in proportion to the average winnings of individual players playing that strategy in the previous one. Between matches, the population number (i.e., the total number of players in the match) is always returned to the starting number. To provide representation proportional to success, the proportion of the average winnings of a player of each strategy to the total average winnings of all players of all strategies is multiplied by the fixed total number of players to find out how many players will be assigned to each strategy in the subsequent match.
For each round of games, the formula for the average score (S) of players playing strategy i would be SumSi/Pi.where Sum Si is the total score accued by the Pi players of the i-th strategy.
The formula for the number of players playing the i-th strategy in the next round would be SumSi/Pi x P, where P = sum Pi for all values of i. Since these multiplications rarely produced integer results, and since the population was always capped at P for each match, remainders were inevitable and had to be distributed as addional players to some of the strategies and not to others.
This was one of the details in which the devil was found. By the time we had gotten done thinking about this distribution process, we had come up with five different methods for making it. Only two were kept. One method privileged the most sucessful strategies. We simply assigned the extra players so that those strategies with the best records in the previous match were most likely to receive the extra players. The other method privileged the strategies with the largest remainders: we assigned the extra players so that those strategies with the largest remainders in the previous match were most likely to recieve the extra players. Readers interested in the other methods we considered are encouraged to contact Owen Densmore as Owen@backspaces.net for details.
HOW TO USE IT
LogoMoth is a research program to designed to accomodate many sorts of curiosity about the relation between the idea of conditional altruism and the idea of conditional leaving. You can manipulate many features of the game, the players, the matches, and the simulation AND you can save your experiments using NetLogo's behavior space.
As in the standard prisonner's dilemma game, LogoMoth is based on the idea that two players play against one another for payoffs which depend on what the two players do. Their two choices are to cooperate (C) or defect (D)-- in some worlds, to be an altruist or selfish. This conceptualization produces four cells, which for simplicity sake, we will always identify here in their "reading" order: i.e., Top Left (Cc), Top Right (Cd) , Bottow Left (Dc), and Bottom right (Dd). The payoffs in each cell always represent the payoff to the left marginal player, playing one of two strategies, against the top marginal player, playing the same two strategies. Thus, the standard Prisonners' Dilemma game, in which a cooperator receives 3 playing against another cooperator, 0 playing against a defector, while a defector receives 5 playing against a defector and 1 playing agaisnt another defector, will be represented here as a 3,0,5,1 game.
Each combination of cell payoffs yields a different game-type, and the possibilities are, of course, infinite. Although you can choose any combination of payoffs you like, LogoMoth features three particular examples. One is the standard PD game, 3,0,5,1. PD games, by definition are those whose payoffs follow the rules, Dc>Cc>Dd>Cd and 2Cc > Cd + Dc Another game of interest to us, we call the altruist game in which the payoffs must be consistent with b-c, -c, b, 0, where b>c>0. Some altruists games meet the criteria for PD games, 3, -2, 0, 5, for instance, and LogoMoth features this choice as well. But a PD game need not be an altruist game. For modeling purposes, minus numbers supply additional conceptual devils, and so we offer what we call a AG+ game, in which a constant has been added to each cell to dispense with negative numbers: 5, 0, 7, 2. The AG+ game is a PD game, but it is not strictly speaking an altruist game. However, the differences between the payoffs of the 4 cells is preserved, and we have found no computation that we are in the habit of performing with AG games that is affected by the difference.
You may choose any combination of strategies by "zeroing out" strategies that DONT interest you. Using the same sliders, you can also test whether a strategy is robust against invasion by giving it many players and introducing the other stategies, one by one, with small numbers of players. Or you an see which strategy is a good invader by holding the the numbers of players of other strategies at maximum and introducing small numbers of different invaders, one by one.
Finally, you can evaluate the impact of the number of games in a match and the number of matches in a simulation by moving the sliders provided.
THINGS TO NOTICE
Notice first whether the model replicates the tradional Axelrod results. Reassurance on this point can be sought by zeroing out those strategies that were not in the original AXelrod Tournament. As as been reported repeatedly in the PD literature, Tit for Tat in LogoMoth is a robust competitor, although it sometimes fails against Nice and Nasty.
Then check out MOTH's ability as a competitor. Look first at how well moth does againsts TfT's original competitors. The short answer is "better", It wins more often than TFT, and it usually wins quicker. Now take a look at Moth's competition against all three Axselrod strategies, Nice, Nasty, and TfT. You will find that as long as matches are reasonably long, MOTH always predominates in simulations containing all of the other Axelrod strategies. If matches are short ... less than 10 games per match ..... the result begins to be much more unpredictable. Finally examine how MOTH does against all 7 other strategies. Once again, if matches are reasonably long it almost always predominates. However it rarely excludes all other competitors. A typical result is that MOTH and either Nice or TfT are left standing at the end of the simulation.
Another fascinating project is locating tipping points, A match size of 7 seems to be an important tipping point. We also think that important tipping points will be found in changes in the payoff matrix
CREDITS AND REFERENCES
LogoMoth is a "docking" of an earler java program (The Battle Applet), one of a series of applications of the MOTH idea that were created by David Joyce of Clark University's Math and Computer Science. Readers who found LogoMoth interesting are strongly encouraged to have a look at the whole series of applets, which may be found at:
We also owe a tremendous debt of thanks to the members of the Santa Fe Applied Complexity Group (“FRIAM”), in particular to Carl Tollander and Frank Wimberly.
• David Joyce and John Kennison
– Department of Mathematics and Computer Sciences
– Clark University,
– Worcester MA 01610
– Djoyce or jkennison, @clarku.edu
• Owen Densmore* and Stephen Guerin*
– Redfish Group and Friam Applied Complexity Group
– 843 Agua Fria Road.
– Santa Fe, NM, 87501
– Owen or Stephen, @ redfish.com
• Nick Thompson*
– Program in Social, Evolutionary, and Cultural Psychology,
– Departments of Biology and Psychology
– Clark University,
– Worcester MA, 01610.
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