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Minority Games. A Complex Systems Project. Going to a concert…. But which night to pick? Friday or Saturday? You want to go on the night with the least people. So you try and guess which night. You can base your guess on previous attendence. But so does everyone else.
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Minority Games A Complex Systems Project
Going to a concert… • But which night to pick? Friday or Saturday? • You want to go on the night with the least people. So you try and guess which night. • You can base your guess on previous attendence. But so does everyone else. • This is a minority game. • What happens if the concert is on every night?
Properties of Minority Games • Participants try to pick the least common choice. • Communication between participants is only through results of previous attempts. • Each participant thus makes decisions based upon their private strategies and the public history. • Example: The Stock Market
Why are Minority Games Complex Systems? • Large numbers of agents, each with their own strategy sets. • The system adapts to new information each round. • The history is important. • The system is frustrated: the more successful a strategy is, the worse it gets.
Choose a Number! • Pick an integer number between 1 and 10, and try to get the least common number. • We used the first year physics class as our system. • The experiment was repeated, but each time the results of the last round were left up. • 6 rounds were run in total.
The jaggedness Parameter (a) 3 2 1 4 a=57.4
Our Models • 100 agents • Each agent chooses a number according to a strategy • Calculate histogram of results • Rank each number from 1-10 based on popularity. Example • Strategies got 1 point if they led to the least popular number and 0 otherwise.
Model 1 Distribution of Variance Variance
Model 1 Distribution of Variance Variance Variance with Time Variance
Previous round 25 20 15 10 5 0 1 2 3 4 5 6 7 8 9 10 What is happening here? a=5.6
Model 2 • During the Trial: • Agents choose a number and stick with it. • Every p rounds, consider changing. • When changing, change to best number of previous round. Before the Trial: Agents given patience parameter, p.
And then this happened… Insert alpha distribution.
Model 3 • During the Trial: • Agents choose a number and stick with it. • Every round, agents have a probability .02 that they will consider changing. • When changing, change to best number of previous round.
Good for wealth distribution too. Average wealth = 4542 Average wealth =2733
Formalism 2 choice minority game • extension of the El Farol Bar problem N players, two choices: 0 or 1 Rules: At each turn, every agent chooses a side (0 or 1), those that end up in the minority side, win.
Formalism • Memory: the bit-string of past winning outcomes. eg. minority side trial one – 1, trial two -1, trial three – 0, trail four - 1, trial five - 0. M = {1,1,0,1,0} with length: m = 5.
Strategy Space Strategies defined in an abstract way - no psychology. Strategy s – a ‘card’ with a prediction for each possible past history. eg. Strategy1 Strategy2 Strategy 3 etc…
Minority Game Structure • Odd number (N) of agents, each given two or more strategies selected at random from the strategy space. • At each turn, the strategies are evaluated; a point is awarded to each strategy that predicts the correct minority result. The strategy with the highest number of points is chosen for the next turn. • Evaluated for large number of time steps, for different memory lengths m.
Complex behaviour Savit et al, 1999. Region 1: Small number of strategies, crowded behaviour – similar to model 1 of the MCMG. Region 3: Very large strategy space. Less probability of cooperation. Region 2: More available strategies. Able to cooperate to achieve low variance.
Conclusions • Interesting behaviour • Possible to do better-than-random but with abstract/slightly contrived strategies • Further study to see the stability of better-than-random systems with plausible strategy sets.
