Ticket resale, bots, and the fair price ticketing curse

Abstract

The fair price ticketing curse occurs when an event organizer sells tickets at prices that do not correspond to underlying demand conditions and does not want resellers to profit from resale opportunities. The curse has been exacerbated with the advent of online ticketing. The challenge is to facilitate genuine ticket exchange while eliminating resale for profit. None of the attempted public or private solutions solve the problem. We propose a simple mechanism, identify a key set of necessary conditions for it to work, and discuss recent technological innovations that facilitate its implementation.

Appendix

Proof of Proposition 1

We have $\frac{d}{d \beta } W_{{\mathrm{RM}}}=\overline{V}K \left( \delta _{{\mathrm{v}}} - \tau (\beta ) - (1-\alpha ) (\delta _{{\mathrm{v}}}- \tilde{\tau }) + \beta \tau '(\beta ) \right)$. $\frac{d}{d \beta } W_{{\mathrm{RM}}}<0$ is equivalent to $\tau (\beta )- \delta _{{\mathrm{v}}} > -\beta \tau '(\beta ) + (1-\alpha ) (\tilde{\tau }-\delta _{{\mathrm{v}}})$. To demonstrate that this inequality holds, observe that: (1) $\tau (\beta )- \delta _{{\mathrm{v}}} > 0$ under free entry and Assumption 1; (2) the first term on the right hand side, $-\beta \tau '(\beta )$, is negative; and (3) to deal with the second term consider two possibilities. If $\delta _{{\mathrm{v}}} \ge \tilde{\tau }$, this term is negative and the inequality holds. If $\tilde{\tau } \ge \delta _{{\mathrm{v}}}$, the inequality is a consequence of $\tau (\beta ) \ge \tilde{\tau }$. □

Proof of Proposition 2

RM dominates CE if and only if

$$\begin{aligned} \overline{V}K \left( 1+(1-\alpha (1-\beta )) \delta _{{\mathrm{v}}}-\tau (\beta ) \beta -\tilde{\tau }(1-\alpha )(1-\beta ) \right) >\overline{V} K \left( 1-\tilde{\tau }(1-\alpha ) \right) \end{aligned}$$

which simplifies to

$$\begin{aligned} \beta \left( (1-\alpha ) (\tau (\beta ) - \tilde{\tau } )-\alpha (\delta _{{\mathrm{v}}}-\tau (\beta ) \right) < (1-\alpha ) \delta _{{\mathrm{v}}} \end{aligned}$$

This inequality always hold when $\delta _{{\mathrm{v}}}-\tau (\beta ) \ge \frac{1-\alpha }{\alpha } (\tau (\beta )-\tilde{\tau })$. When this is not the case, that is $\delta _{{\mathrm{v}}}-\tau (\beta )< \frac{1-\alpha }{\alpha } (\tau (\beta )-\tilde{\tau })$, RM dominates CE for any value of $\beta$ if $\beta _{{\mathrm{CE,RM}}}>1$ which is equivalent to $\delta _{{\mathrm{v}}}-\tau (\beta )>-(1-\alpha ) \tilde{\tau }$. Since $\frac{1-\alpha }{\alpha } (\tau (\beta )-\tilde{\tau })>-(1-\alpha )\tilde{\tau }$, we conclude that RM dominates CE for any value of $\beta$ when $\delta _{{\mathrm{v}}} - \tau (\beta ) >-(1-\alpha )\tilde{\tau }$. This establishes claim (1a) in Proposition 2.

When $\delta _{{\mathrm{v}}} - \tau (\beta ) <-(1-\alpha )\tilde{\tau }$, RM dominates CE when $\beta <\beta _{{\mathrm{CE,RM}}}$ and CE dominates RM otherwise. This, together with the definition of $\beta _{{\mathrm{RM,RB}}}$ establishes claims (1b), (2) and (3) in Proposition 2. □

1.1 Analysis of CE

The CE mechanism has four features (see Table 2, Column 1): (RfR) refund for return, (RA) random reallocation of returned tickets, (L) ledger of current legitimate owner, and (ID) check at admission that identification of ticket holder matches the name on ledger. We compare the CE with a situation where all these features are not implemented jointly. When a feature is not implemented, we assume that the default feature presented in Column 2 applies. For example, fans are not refunded anything instead of RfR (line 1), returned tickets are unused instead of RA (line 2), and so on...Clearly, other default options than those presented in Column 2 could be considered. Since the point is to demonstrate the importance of the four design features of a CE, we select defaults used in practice.

Some of these measures have been implemented separately but never together with one exception. As mentioned in Sect. 4, some artists have used multiple technologies to match identity at admission (feature 4), Twickets reallocates returned tickets (feature 2), and some startups (Blocktix, BitTicket) offer block chain technologies for ticket exchange that allow to track-and-trace the ownership chain (feature 3). However, we argue that these measures alone do not solve the problems of no-shows and resale for profit.

Table 2 Design features of centralized exchange (CE) and default features

The timing of events goes as follows: (1) the event organizer announces which of the four design features are implemented. A default feature applies when a design feature is not selected. (2) Fraction $\beta$ of tickets are bought by brokers. (3) Fraction $1-\beta$ of remaining tickets are randomly distributed to fans. (4) Fans find out whether they can attend the event: Fraction $\alpha (1-\beta ) \frac{K}{N}$ of fans own a ticket and can attend, $(1-\alpha )(1-\beta )\frac{K}{N}$ own a ticket and cannot attend, $\alpha \left( 1- (1-\beta ) \frac{K}{N} \right)$ do not have a ticket and can attend. (5) Brokers post price $p_{{\mathrm{r}}}>p_0$. (6) Fans may buy tickets from brokers, sell tickets in RM, or return tickets if this option is available. The cost of reallocating a ticket within CE is $\tilde{\tau }$. (7) Tickets are redeemed. A ticket bought in RM does not entitle admission when L and ID apply.

Proposition 3

$W_{{\mathrm{RM}}}=\overline{V} K \left( 1-\tilde{\tau }(1-\alpha ) \right)$if and only if$({\mathrm{RfR}}, {\mathrm{RA}}, L, {\mathrm{ID}})$are implemented.

When $({\mathrm{RfR}}, {\mathrm{RA}}, L, {\mathrm{ID}})$ are implemented no broker enter: (1) $\beta =0$, (2) fraction $1-\alpha$ of tickets are resold, (3) all tickets are used, and (4) the average valuation among users is $\overline{V}$. We have $W_{{\mathrm{RM}}}=K \overline{V} \left( 1-\tilde{\tau }(1-\alpha ) \right)$.

Next, we show that welfare changes if all four components of a CE are not present together. We consider here eliminating a single feature at a time, keeping in mind that the argument generalizes when multiple features are eliminated jointly: (a) when RfR is not implemented, fans do not return tickets and welfare is $\alpha K \overline{V}$; (b) when RA is not implemented, returned tickets are unused and we have again that welfare is equal to $\alpha K \overline{V}$; (c) when L is not implemented but ID is, reallocated tickets cannot be redeemed. Welfare is $\alpha K \overline{V}$; (d) when ID is not implemented, we are back to the RM outcome. This concludes the proof.

Ed Sheeran has come closest to a CE for his 2018 tour.²³ A shortcoming of his scheme is that each buyer can purchase up to four tickets and only the identity of the buyer is checked at admission.²⁴ Scalpers have arranged to enter the venue with those who purchase their extra tickets. But the take away is that the basic building block necessary to implement a CE is available and has been used. Achieving the desired outcome is just a matter of implementing the different building blocks together.

To conclude, we consider a fan-to-fan face exchange (FtF) because it has been used in practice. Doing so also clarifies the role of random reallocation in CE. FtF has the RfR feature but the difference is that the other features do not apply. Implemented alone, FtF does not deter brokers from reselling tickets in RM. To make the argument more interesting, assume that FtF is implemented along with L and ID. This does not achieve the first best outcome because brokers are not deterred. Brokers can benefit by selling at face value on FtF in order to make sure that the buyer is the new legitimate owner on the ledger (recall that L and ID apply) conditional on receiving a side payment from the buyer. Such side payments would be difficult to detect and punish. It is now clear why random reallocation of returned tickets (RA) is necessary to deter broker entry.