Game of Trust: a Game about Game Theory

The game of trust is a game created by Nicky Case inspired by Robert Axelrod's 1984 book, "The Evolution of Cooperation" and his 1997 sequel, "The Complexity of Cooperation", and Robert D. Putnam's 2000 book on America's declining "social capital", Bowling Alone.

The game let's you play an iterated prisoner's dilemma. Do you know the prisoners' dilemma? Not sure about the payoffs? Have a look at Nicky Case's model for an easy to remember ruleset:

You have one choice. In front of you is a machine: if you put a coin in the machine, the other player gets three coins – and vice versa. You both can either choose to COOPERATE (put in coin), or CHEAT (don't put in coin).

Experience game theory with entertaining graphics by Nicky Case

Now visit the game page of the game of trust and have fun!

Evolution as a tool for understanding and designing collaborative systems

Saudações de São Paulo (Greetings from Sao Paulo)!

I was invited to the IFIP Working Conference on Virtual Enterprises (PRO-VE 2011) to give the keynote talk on evolution as a tool for understanding and designing collaborative systems.

Here is a short summary of the talk:

Research on collaboration addresses the common tension between

• what is good for the individual actor in the short run, and
  
• what is good for the group in the long run
  

This research is based on game theory and, therefore, employs such models as the Prisoner’s Dilemma or public goods games as the basis for analysis. Using game theory, you can approach the question What is the most rational strategy? for a given model. However, in real systems often converge towards equilibria with behavior different from the calculated rational one. In order to explain these results, evolutionary approaches are a useful tool. To solve the contradiction, it is necessary to realize that typically interaction properties have not been designed by a central ruler but evolved over time. However, finding the appropriate interaction rules that induce a particular overall behavior is difficult due to the unpredictable or counterintuitive nature of such emergent and complex systems. Therefore, we propose evolutionary models to examine and extrapolate the effect and development of particular collaboration rules. An example of such an approach is our work on evolving cooperative behavior with neural controllers. Evolution, in this context, does not replace the work of analyzing complex social systems, but complements existing techniques of simulation, modeling, and game theory in order to lead for a new understanding of interrelations in collaborative systems. If you want to learn more, quickly come to the conference in Sao Paulo and/or check the slides below :-)

Evolution as a Tool for Understanding and Designing Collaborative Systems

Evolving cooperative behavior with neural controllers

In a computer experiment, we have investigated the evolution of cooperative behavior in multi-player games. Players were randomly mixed into groups and had the chance to increase their investment by paying money into a pot where it was multiplied. However, the payout money was evenly distributed to all of the players regardless of their contribution. So a freerider could get money without paying into the pot as long as some others did.
The players were controlled by a neural network that controlled the setting strategy. Using our evolutionary design tool FREVO, we evolved the behavior in order to maximize the profit for each player. There was a pool of players controlled by neural networks. After several rounds, the more successful (thus richer) individuals were allowed to stay in the pool and produce more offspring than the less successful ones.
In the first scenario the payout was the pot times three. So if, everybody would cooperate, you can earn your money gets tripled. If the maximum bet was 20$ this means a 60$ return, in other words a 40$ revenue. But if everybody in a group pays in, it's even better to defect - let's say five out of six cooperate, you get a 50$ revenue.
The game was played iteratively 10 rounds. Originally, we expected a strategy like Tit-for-Tat to evolve and prevail. However, defection turned out to be the only stable strategy. For each system state, individuals with the defecting gene could make more revenue. In other words, ruthless behavior paid off.
The situation changed, when we introduced a "synergy factor" into the payoffs. This meant that the money of cooperating players was not multiplied linearly, but over proportionally. Assume you are working with some colleagues on a common project, let's say writing a book. If you alone invest enough time into you chapter, the book still sucks because of the other chapters which are lame or missing. If half of the authors cooperate, the book might be accepted by a mediocre publisher, but still would not be that promising. But if everybody cooperates, the result is not double the revenue of the 50% case but much more!
In the experiment we reflected this issue by a quadratic factor in the pot function. Evolving the stable strategies again showed that after some generations of defecting players, cooperation evolved as a stable strategy!

This still gives hope for our civilization - although reading the daily newspaper does not always feed this hope.

• I. Fehérvári and W. Elmenreich. Towards evolving cooperative behavior with neural controllers.In IFIP Fourth International Workshop on Self-Organizing Systems, 2009.
• Public Goods Game@Wikipedia
• Prisoner's Dilemma@Wikipedia
• FREVO - a tool for engineering self-organizing systems
• Our project DEMESOS

Prisoner's Dilemma at the swimming pool

At my vacation I was witness of "beach chair reserving behavior". As soon as the pool opens, some guests reserve their beach chairs by putting towels on a couple of beach chairs. Then they go for breakfast or whatever. So, some time later, there are several empty but reserved beach chairs around the pool. Wanting no trouble, people have to sit on the ground. Doing some quick count during the day, I noticed that there were 20 beach chairs and - surprise! - in average only 20 people at the pool. So the system would work pretty well if nobody reserved the chairs and thus getting a good chance to find an empty chair when needed. For all the participants this would be a relief: the beach chair blockers don't have to get up so early in the morning and the others suffer less of beach chair shortage.

This can be modelled as a game theoretic problem, namely the multiplayer Prisoner's Dilemma. The Prisoners Dilemma is named after a fictional story where two suspects are interrogated regarding a major crime. The police have insufficient evidence for a conviction, so they offer the prisoners separately a deal: if one confesses (defects), he goes free (temptation payoff) and the other one gets a high conviction (sucker payoff). However, if both confess, both get punished (punishment payoff). If no one confesses, both get a less severe verdict, in overall the best for everyone (reward payoff).

The following table shows the possible strategies and payoffs (exemplified with the payoffs 0,1,2,3, the higher the better):

	Prisoner B stays silent (cooperate)	Prisoner B tells (defect)
Prisoner A stays silent (cooperate)	(2,2) both get off with small sentence	(0,3) Player A gets punished for everything, Player B goes free
Prisoner A tells (defect)	(3,0) Player A goes free, Player B gets punished for everything	(1,1) both get punished

At the pool, we have the case of a multiplayer Prisoner's Dilemma with the options to reserve a beach chair in the morning or to refrain from this behavior.

	Most others do not reserve chairs (cooperate)	Most others do reserve chairs (defect)
Player does not reserve chair (cooperate)	(2,2) all get a fair chance for a beach chair when needed	(0,3) player must sit on the ground, some others enjoy their reserved chairs
Player does reserve chair (defect)	(3,0) player has guaranteed beach chair, others are suffering slightly	(1,1) only chance to get a chair is reserving in the morning, worse situation than in upper left case

Unfortunately, with a sufficient number of defecting players (people who reserve a beach chair early in the morning) there is no merit in not reserving - you will go without a pool chair then (sucker payoff). So the only feasible strategy is to struggle for any free one in the morning and probably get one chair reserved for your family of 4 people. Another problem is that the people are constantly changing. So even if a cooperative behavior could be agreed on, there might be the arrival of a new bunch of defectors the next day, who would then feel themselves lucky to get all the chairs they desire so easily. There is certainly a tempation to reserve if nobody reserves, because then you have your beach chair guaranteed (otherwise there is still the chance that you get none, if already more than 20 people are at the pool). So, defecting is a stable strategy, although it is in overall worse for the whole group - this a tragedy of the commons.