Potential based prediction markets: a machine learning perspective
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A prediction market is a special type of market which offers trades for securities associated with future states that are observable at a certain time in the future. Recently, prediction markets have shown the promise of being an abstract framework for designing distributed, scalable and self-incentivized machine learning systems which could then apply to large scale problems. However, existing designs of prediction markets are far from achieving such machine learning goal, due to (1) the limited belief modelling power and also (2) an inadequate understanding of the market dynamics. This work is thus motivated by improving and extending current prediction market design in both aspects. This research is focused on potential based prediction markets, that is, prediction markets that are administered by potential (or cost function) based market makers (PMM). To improve the market’s modelling power, we first propose the partially-observable potential based market maker (PoPMM), which generalizes the standard PMM such that it allows securities to be defined and evaluated on future states that are only partially-observable, while also maintaining the key properties of the standard PMM. Next, we complete and extend the theory of generalized exponential families (GEFs), and use GEFs to free the belief models encoded in the PMM/PoPMM from always being in exponential families. To have a better understanding of the market dynamics and its link to model learning, we discuss the market equilibrium and convergence in two main settings: convergence driven by traders, and convergence driven by the market maker. In the former case, we show that a market-wise objective will emerge from the traders’ personal objectives and will be optimized through traders’ selfish behaviours in trading. We then draw intimate links between the convergence result to popular algorithms in convex optimization and machine learning. In the latter case, we augment the PMM with an extra belief model and a bid-ask spread, and model the market dynamics as an optimal control problem. This convergence result requires no specific models on traders, and is suitable for understanding the markets involving less controllable traders.