Just Don’t Do It Minority Games and the Stock Market

To start the ball rolling…we go back to where it all began Comparisons with P Beauty Contest If we assume rationality (game theorists playing), perfect information, we can derive a dominant strategy “0” No matter what our assumptions, any dominant strategy would always fail in a minority game

Some features of MG Negative feedback Market entry games Phase transitions As z increases… Other properties Frustration…spin glasses Individual heterogeneity Collective coordination…collusion?

Efficient market hypothesis No arbitrage hypothesis Random walk prices Stock markets basics

Who puts information in prices? If markets are unpredictable, why are people wasting their time? Prices over the short term do not follow random walks Stock markets basics??

When there are fewer sellers than buyers, prices go up, sellers profit. When there are fewer buyers than sellers…. G i (t)=-a i (t)*A(t) Minority always wins…??? Stock markets and MG

Assume at t-1/2, agent thinks that p(t) > p(t+1) What should the agent do? Place sell order Again if p(t) < p(t+1) Place buy order Agent gain/loss is G i $ (t+1/2)=a i (t-1/2)*A(t+1/2) The $ Game

The $ game with a Market Maker R(t) = A(t)-S M (t)/ Market Maker provides clearing mechanism The $ Game

Low values of m, lesser strategies Coordination to only buy or only sell Arbitrage the market maker Positive feedback Non ideal/boom scenarios…finally limited. The $ Game

High values of m, too many strategies Curse of intelligence Market maker arbitrages agents as a group. Some agents with non equilibrium strategies still manage to profit. The $ Game

MGs have a small contribution to self organization of markets Driving force among agents is to make money and not be in the minority Best strategy is to shift opportunistically The $ Game Conclusions

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