Sneak Review by Udara Weerakoon

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A Memetic Framework for Describing and Simulating Spatial Prisoner’s Dilemma with Coalition Formation. Sneak Review by Udara Weerakoon. Duality form of the problem. Agents get a percentage of compromise when cooperating with other agents

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### A Memetic Framework for Describing and Simulating Spatial Prisoner’s Dilemma with Coalition Formation

Sneak Review by UdaraWeerakoon

Duality form of the problem
• Agents get a percentage of compromise when cooperating with other agents
• Leaders impose taxes to the other agents belonging to its coalition
Prisoner's Dilemma
• Two men are collectively charged with a crime and held in separate cells. They have no way of communicating with each other or making any kind of agreement. The two men are told that:
• if one of them confesses to the crime and the other does not, the confessor will be freed, and the other will be jailed for three years; and
• if both confess to the crime, then each will be jailed for two years.
PD cont…
• Both prisoners know that if neither confesses, then they will each be jailed for one year
PD Strategies
• ALL-D. This is the 'hawk' strategy, which encodes what a game-theoretic analysis tells us is the 'rational' strategy in the finitely iterated prisoner's dilemma: always defect, no matter what your opponent has done.
• RANDOM. This strategy is a control: it ignores what its opponent has done on previous rounds, and selects either C or D at random, with equal probability of either outcome.
• TIT-FOR-TAT. This strategy is as follows:
• (1) on the first round, cooperate;
• (2) on round t > 1, do what your opponent did on round t - 1.
PD Strategies cont…
• TESTER. This strategy was intended to exploit computer programs that did not punish defection: as its name suggests, on the first round it tested its opponent by defecting. If the opponent ever retaliated with defection, then it subsequently played TIT-FOR-TAT. If the opponent did not defect, then it played a repeated sequence of cooperating for two rounds, then defecting.
• JOSS. Like TESTER, the JOSS strategy was intended to exploit 'weak' opponents. It is essentially TIT-FOR-TAT, but 10% of the time, instead of cooperating, it will defect.
Evolutionary Game Theory
• Evolutionary game theory (EGT) is the application of game theory to interaction dependent strategy evolution in populations. EGT differs from classical game theory by focusing on the dynamics of strategy change more than the properties of strategy equilibria. Despite its name, evolutionary game theory has become of increasing interest to economists, sociologists, anthropologists, and philosophers (source: common in Wikipedia and the paper).
• Replicator Dynamics
• Replicator dynamics refers to picking the percent of each agent type to match the percent of total utility earned by agents of that type. So if 50% of the agents use strategy A and earn 60% of the utility, in the next round, 60% of the agents should be strategy A. It doesn’t matter which agent has which type, but only the percentages of each.
• Imitator Dynamics
Evolutionarily Stable Strategy

Nash Equilibrium is defect

Unfailing Bayesian Rationality
• Baysian: To evaluate the probability of a hypothesis, the Bayesian probabilist specifies some prior probability, which is then updated in the light of new relevant data.

prior probability

conditional probability

marginal probability

posterior probability

Memetics
• “Memes” are a non-organic replicator form e.g. tunes, catch-phrases, taboos
• “In the memetics model, less successful individuals and groups within a population imitate the behavior of the more successful peers in order to improve their competence for resources. Accordingly, the more above average an individual is, the more others copy his behavior”
Spatial Distribution
• Two dimensional square lattice of N nodes
• Each cell is rules by an agent
• It can follow two strategies
• Defections
• Cooperation
• Cell could be
• Independent cell
• Coalition cell