The haggling coordination game

The TVHE blog had an interesting post about haggling earlier this week:

[Gulnara]

On a recent trip to my beautician – link to her website below – I started negotiating the price of my visit. However, I quickly caught myself doing so and stopped. She understood where I was coming from, as she is also from the former Soviet Union, where such haggling is a normal part of daily life. But that isn’t the case in a country like New Zealand – which is why we both put a stop to it.

So why is haggling culture so different in different countries, and what are the economic consequences of this?

[Matt]

That is really interesting Gulnara. Such bargaining does depend on the expectations of consumers and producers – so bargaining cultures will tend to support individuals bargaining while societies that do not do that will make it costly.

This strategic complementarity implies that both societies with bargaining and those without are “equilibrium” outcomes – where people’s incentive is to do what everyone else is doing. We call these bargaining and non-bargaining equilibrium “states of the world”...

Strategic complementarity implies that there is a coordination game here. We can show how it works, and how there are two equilibrium outcomes, using some simple game theory. Consider two players, the buyer and seller, decided whether to haggle over prices. The game is outlined in the payoff table below. If the seller expects to haggle, they set a relatively high price, which might put off buyers who do not haggle. Hence, the seller gets a lower profit and the buyer is worse off as well. If the seller expects to haggle and the buyer haggles, then both benefit from the sale. On the other hand, if the seller doesn't expect to haggle, they set a lower price. If the buyer haggles, the sale may go through, or the seller may get pissed off and choose not to proceed. Hence, the seller gets a lower average profit and the buyer is worse off as well (not just by the chance that the sale doesn't go through, but because of the possibility of social sanctions on them). As Matt notes in the TVHE post linked above:

The willingness to haggle on both the customer’s and the firm’s behalf depends on whether it is something they expect other people to do – it feels pretty stink to go and haggle just for the other person, and other customers, to look down their nose at you. However, this is more than just some concern about underlying social judgment – the act of haggling is something the firm would like to be prepared for, and the act of undertaking haggling puts pressure on these other customers to take on the cost of haggling themselves.

Finally, if the seller expects not to haggle, and the player doesn't haggle, then both benefit from the sale.

We can establish the locations of Nash equilibriums using the 'best response method'. To do this, we track: for each player, for each strategy, what is the best response of the other player. Where both players are selecting a best response, they are doing the best they can, given the choice of the other player (this is the textbook definition of Nash equilibrium). In this game, the best responses are:

1. If the buyer chooses to haggle, the seller's best response is to expect to haggle (since 10 is a better payoff than 8) [we track the best responses with ticks, and not-best-responses with crosses; Note: I'm also tracking which payoffs I am comparing with numbers corresponding to the numbers in this list];
2. If the buyer chooses not to haggle, the seller's best response is not to expect to haggle (since 10 is a better payoff than 8);
3. If the seller chooses to expect to haggle, the buyer's best response is to haggle (since 10 is a better payoff than 5); and
4. If the seller chooses to not expect to haggle, the buyer's best response is not to haggle (since 10 is a better payoff than 4).

Notice that there are two Nash equilibriums in this game: (1) where the seller expects to haggle and the buyer haggles; and (2) where the seller expects not to haggle and the buyer doesn't haggle. The problem now, as with all of these sorts of coordination games, is: in which equilibrium will we end up? Sometimes this can be solved through government enacting laws. Think about which side of the road we drive on. It is a coordination game, where you want everyone to drive on the same side of the road, but it doesn't really matter too much which side that is.

In the case of haggling though, the TVHE blog provides some discussion about the consequences of being in one equilibrium or the other (and is worth reading for that reason). They conclude that:

...with price discrimination and tacit collusion, we’ve outlined two of the possible mechanisms that may differentiate market outcomes in countries with active market bargaining and those without.  Both of these arguments appeared to show bargaining in a favourable light – however, they also did point to trade-offs that may reverse this, namely the cost of bargaining, the proliferation of excess product variety, and broader related distributional consequences.

Unfortunately, that doesn't really answer the question of how we end up in one equilibrium or the other. So, let me venture a hypothesis: trust. In countries with relatively high levels of trust between buyers and sellers, the buyers can trust that sellers are not setting high prices that require haggling. The sellers realise this, and recognise that it is in their best interest not to set such high prices. On the other hand, in a lower trust society, a seller setting a lower price would make themselves worse off as they have set a lower starting point for the haggling process.

The problem with this hypothesis is that, if true, it simply shifts the question of 'why' on step further back. Instead of wondering why we are in a haggling or non-haggling equilibrium, we are left wondering why we are in a low-trust or high-trust environment. Unfortunately, that's about as far as the theory can get us. To understand more, we would need to look at some data.