## Friday, 21 September 2018

### The prisoners' dilemma and construction tenders

After my post on the construction industry yesterday, where I suggested that clients should adopt a second-price auction to reduce risk of construction firm failures, a student noted on Facebook:
Stop undercutting the competition so that companies can actually DO the jobs they claim they can do.
In yesterday's post, I neglected to elaborate on why the construction industry can't solve the problem of firms under-pricing bids by themselves. So, in this follow-up post, let's see why, using a little bit of game theory.

Consider an industry with just two construction firms (Firm A and Firm B). [*] Both firms are bidding for a construction contract, which they know will go to the lowest bidder. The firms can choose to bid high, or bid low. Both firms are choosing their bid strategy at the same time - this is what economists refer to as a simultaneous game. The game itself is laid out in the payoff table below. If both firms price low, they each have a 50% chance of winning the contract and earning a low profit (and a 50% chance of not getting the contract and facing the loss of the resources they spent preparing their bid). If both firms price high, they each have a 50% chance of winning the contract and earning a high profit (and a 50% chance of not getting the contract and facing the loss of the resources they spent preparing their bid). If one firm prices high and the other prices low, the low-price firm wins the contract for sure and makes a low profit, and the high-price firm misses out on the contract for sure and loses the resources they spent preparing their bid. Let's further assume that winning the contract for sure at a low price is preferred over a half chance of winning the contract at a high price. [**]

To find the Nash equilibrium in this game, we use 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 definition of Nash equilibrium). In this game, the best responses are:
1. If Firm A bids high, Firm B's best response is to bid low (since winning the contract for sure at a low price is better than a 50% chance of winning the contract at a high price) [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 Firm A bids low, Firm B's best response is to bid low (since a 50% of winning the contract at a low price is better than certainly losing the resources spent preparing the bid);
3. If Firm B bids high, Firm A's best response is to bid low (since winning the contract for sure at a low price is better than a 50% chance of winning the contract at a high price); and
4. If Firm B bids low, Firm A's best response is to bid low (since a 50% of winning the contract at a low price is better than certainly losing the resources spent preparing the bid).
Note that Firm A's best response is always to bid low. This is their dominant strategy. Likewise, Firm B's best response is always to bid low, which makes it their dominant strategy as well. The single Nash equilibrium occurs where both players are playing a best response (where there are two ticks), which is where both construction firms choose to bid low.

Notice that both firms would be unambiguously better if they bid high. However, both will choose to bid low, which makes them both worse off. This is a prisoners' dilemma game (it's a dilemma because, when both players act in their own best interests, both are made worse off). Both firms will choose to bid low, and whichever firm wins the contract will be at risk of having bid too low and suffering the winner's curse, as I noted yesterday. This is why the construction industry cannot solve this problem on its own.

Of course, the simple example above assumes this is a non-repeated game. A non-repeated game is played once only, after which the two players go their separate ways, never to interact again. Most games in the real world are not like that - they are repeated games. In a repeated game, the outcome may different from the equilibrium of the non-repeated game, because the players can learn to work together to obtain the best outcome.

However, cooperative strategies will not work in the construction firms' dilemma game, because such cooperation is illegal collusion. The firms would be subject to prosecution by the Commerce Commission for cartel behaviour.

So, to reiterate yesterday's conclusion, it is up to the clients of construction firms to solve this issue:
We need to ensure that sustainable contract prices are being paid, and the current system is clearly failing.
*****

[*] Limiting ourselves to two firms makes this example easy to follow, but it would work much the same if we had 20 or 200 firms (albeit being much harder to create a payoff table for!).
[**] This seems unlikely in the case of two firms, where there is a 50% chance of winning the contract, and a 50% chance of wasting time preparing the bid. However, if there are ten firms bidding, then there is a 10% chance of winning the contract, and a 90% chance of wasting time, which makes this preference seem more likely.