CS136 Final Project: Simulating a Profitable LMSR

Running the simulation

python simulation.py [options] PeerClass1[,cnt] PeerClass2[,cnt] ...

--loglevel Set the logging level: 'debug' or 'info'; default is set to info
--num_rounds Decide how many times agents get to bid i.e. --num_rounds=100; default is set to 10
--budget Set agents' budget i.e. --budget=5.
--seed Seed for random numbers i.e. --seed=2; default is None
--sigma Sigma = alpha + beta for agent priors; type is int; default is None
--noise At noise = 0, agents always correctly interpret their signal
--alpha_lmsr For Profitable LMSR; see page 14:10, section 3.5 in Othman et al. 2013; The higher the alpha, the more we charge. For alpha >1. no trades will go through
---beta_lmsr The beta for normal LMSR; The higher the beta the more liquidity; With a higher beta the market becomes less sensitive to each trade and prices converge to 1/m where m is the number of outcomes
--mkt_type Choose either LMSR or LMSRProfit; LMSRProfit is the modified version
--num_trials Decide how many times to run the market i.e. --num_trials=100; default is set to 10
--initial_state How many shares already sold? Default is 0.01,0.01; At 0.,0. the LMSRProfit will break so run with value >0.
-v Store the output value
-q Don't store output value; default is -q

PA means prediction accuracy

PA/profit vs market composition play around with the populations of agents (Truthful, BuyOne, ZeroI)
PA/profit vs beta (LMSR only) vary populations
PA vs alpha for LMSRProfit only; alpha in (0.,1.] (will fail at 1 probably, meaning no trades will occur)
profit vs alpha for LMSRProfit only; alpha in (0.,1.]
PA vs noise both for LMSR and LMSRProfit; noise in [0.,1.]
profit vs noise both for LMSR and LMSRProfit; noise in [0.,1.]
PA/profit vs various alpha and noise for different agent populations see the above.
PA with most profitable alpha vs noise in [0, 1] for LMSRProfit
PA with most accurate alpha vs noise in [0, 1] for LMSRProfit
profit with most profitable alpha vs noise in [0, 1] for LMSRProfit
profit with most accurate alpha vs noise in [0, 1] for LMSRProfit
PA with most profitable noise vs alpha in [0, 1] for LMSRProfit
profit with most profitable noise vs alpha in [0, 1] for LMSRProfit
PA/profit vs initial conditions both LMSR and LMSRProfit; initial conditions in (0.,100.],(0.,100.]; vary each condition individually and then both of them at the same time.
market probability over time (use upper/lower bound); Do we converge to the true probability? Line graph with two lines.
PA/profit vs budget (keep population homogeneous)
PA vs revenue (write down the revenue/prediction accuracy as it happens)