Do Hangover Effects Exist?

Kahneman and Tversky seemingly started a revolution in the 1970s culminating in 1979 with "Prospect Theory: An Analysis of Decision Under Risk" which would later be rightly rewarded with the Nobel Prize in Economics.  In the popular narrative, they challenged the old orthodoxy of rational agents optimizing expected utility when facing risky decisions.  Now that their ideas are marching towards the half century mark, it is probably appropriate to understand their critique.

It is important to realize that their theory applies more to the decision makers operating the casino than to the customers gambling.  We talk about hangover effects, because it is easier for managers to describe hangover effects than it is to talk about and measure the intertemporal substitution decisions players make when they buy more during a sale.

Every player has a budget and would prefer to spend a certain amount of money on gambling over a week.  When the casino offers a sale, the player can choose to spend more money on that day.  What we notice is that there is less money spent on average on the next day.  Is this an irrational hangover effect from players being over stimulated or is it the rational moving of money to today that would have been spent in the future?  The answer is of course some of both, so it needs to be measured.

I'll write out a model to measure the effects from the economy accounting identity, but first here are a few more empirical points.  Players expect sales, so these factor into their spending behaviors.  This means it is important to look at events not just one day to the next but also at weekly and other frequencies.  The following model is more appropriate when the variables are weekly totals rather than daily totals.  Finally to motivate the exploration, I have seen slot economies for unique reasons stop special sales and events.  Within a week the daily average spent smoothed out and rose compared to non-sale days when sales were used regularly.

In this model we again apply the equilibrium conditions of wallets staying on average constant, (Wt-Wt-1)/Bt = 0, and of an economy up to this point being stable, ft-1 + et-1 + pt-1 = rake. So looking at the equation for the day of the new sale,

ft + et + pt = rake (1),

we expand purchases pt = (D+d)*(X+x) = D*X + D*x + d*X +d*x.  D is yesterday's demand to buy coins in $; d is the additional demand today from the sale; X is yesterday's exchange rate of coins per $; x is the additional coins given in today's sale compared to yesterday's exchange rate.

Remember that all of these variables in (1) have been divided by total bets  Bt = Bt-1*(1+c), and we are going to find a simple relationship with the growth in bets, c.

ft-1/(1+c) + et-1/(1+c) + (DX+Dx+dX+dx)/Bt-1/(1+c) = rake (2),

is derived from (1) with the above substitutions and equilibrium conditions and reorganizing we get

ft-1/(1+c) + et-1/(1+c) + DX/Bt-1/(1+c) + (Dx+dX+dx)/Bt-1/(1+c) = rake (3),

which by definition is,

ft-1/(1+c) + et-1/(1+c) + pt-1/(1+c) + (Dx+dX+dx)/Bt-1/(1+c) = rake (4).

Imposing our equilibrium condition again,

rake/(1+c) + (Dx+dX+dx)/Bt-1/(1+c) = rake (5),

and simplifying we get

(Dx+dX+dx)/Bt-1 = c*rake (6).

We are basically done here as conceptually by renaming Dx + dX + dx as new demand in coins,

New Demand = c*rake*Bt-1 (7),

or solving for d,

d = ( c*rake*Bt-1 - x*D ) / Exchange Rate (8),

gives the equilibrium condition relating new $ demand, d, to the growth in coins bet, c.  The details of these equations will be slightly altered depending on how your sales are structured, but you are looking for equations very similar to these.

If you want to apply Kahneman's Thinking, Fast and Slow, it needs to be by looking at this equilibrium condition and inducing the players to change this equation to the casino’s advantage.

Amazon.com: Thinking, Fast and Slow eBook: Kahneman, Daniel: Kindle Store