Dynamic Pricing Platform (5/5)
So far, we have covered following chapters:
Chapter 2: Littlewood’s rule and EMSR
Chapter 3: Technical Architecture
Chapter 4: Details & Reasoning
In this final chapter let’s introduce some more theory to layout the future scopes, and also the complexities involved that dynamic pricing platforms need to address. Any of the platform built to optimize, will surely need way to act like humans do i.e. think and apply strategies. One of the intriguing thought that has been there is about the “Game Theory”. Yes, you have read it right “Game Theory”. In short as per Wikipedia “Game theory is the study of mathematical models of strategic interactions among rational agents.”. Since there are many players in market, and their offerings are available to end user, so, now the question that can be put forward is that, do dynamic pricing algorithms need to consider the whole scenario of demand and supply as
- Cooperative / non-cooperative,
- Symmetric / asymmetric,
- Zero-sum / non-zero-sum, or,
- Simultaneous / sequential ?
The answer to the question would really depend on how much of the information is available at the time of modeling the problem. Let’s see the situation here for Cooperative/non-cooperative model. As the definition goes as per Wikipedia “A game is cooperative if the players are able to form binding commitments externally enforced (e.g. through contract law). A game is non-cooperative if players cannot form alliances or if all agreements need to be self-enforcing (e.g. through credible threats).” If airlines or travel agencies form alliances then this situation can occur. But, the governing rules and other factors make this as “non-cooperative model”. That, then translates into inefficient use of the resources.
Next model under discussion is “Symmetric / asymmetric”. Let’s look at short definition “A symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them.”. What one can imagine is that if the pricing strategy is such a way that it doesn’t matter who the pricing is done for, then it is a symmetric model. But, this can apply to a sector where demand is much higher than the supply. The asymmetric case would be there if there were options for bus operators to give offers to customers with “fair” or “unfair” prices.
This is the most interesting one to debate about, the “Zero-sum (constant-sum) / non-zero-sum” model. Let’s look at short definition “Zero-sum game is a mathematical representation in game theory and economic theory of a situation which involves two sides, where the result is an advantage for one side and an equivalent loss for the other.”. Translating to the demand supply problem, if two service providers have similar prices for certain inventory or seats then that goes to zero-sum model, and if the service providers can see each other's pricing they may end up changing the fares. This situation may not always be effective as, it will end up being non-cooperative strategy, ending in inefficient pricing. But this is also the easiest one to implement. Recommendation is to avoid this strategy, or else this is likely to result in under pricing scenarios more often.
If the dynamic pricing strategies can be built in “Simultaneous” model, Then those could be the best of the kind. Lets look at the Wikipedia definition, “Simultaneous games are games where both players move simultaneously, or instead the later players are unaware of the earlier players’ actions (making them effectively simultaneous). Sequential games (or dynamic games) are games where later players have some knowledge about earlier actions.”. In reality the systems would end up being “Sequential” model.
Leaving those strategies for future articles and brainstorming sessions, lets look at what we have achieved so far. The ideal case scenario is as per the image below:
With real-life situations, revMax from redBus is fulfilling the theory in practice:
Future and beyond
As compared to the airlines industry, dynamic pricing in bus travel domain has just started, on relative time scale. Nevertheless, learning from what airlines have done and have been doing, time has been saved in building the dynamic pricing platform. Now on top of the platform, the various ways to optimize the yield will continue to take shape and then reshaped and so on. Judging by the “Game Theory” as Nash Equilibrium is understood (taken from Wikipedia) “If each player has chosen a strategy — an action plan based on what has happened so far in the game — and no one can increase one’s own expected payoff by changing one’s strategy while the other players keep theirs unchanged, then the current set of strategy choices constitutes a Nash equilibrium.” and “…. is the most common way to define the solution of a non-cooperative game involving two or more players.”, it is unlikely that Nash equilibrium will be constituted for pricing. So, this is going to be a continuous process of coming up with newer strategies and counter-strategies. This really has opened up space for exciting new solutions can use the advances in next gen AI and ML algorithms. With this let’s conclude the series of the five chapters.
Chapter 2: Littlewood’s rule and EMSR
Chapter 3: Technical Architecture
