Mobile Telephony in Emerging Markets: The Importance of Dual-SIM Phones

Implications of Assumption 1

The purpose of this appendix is to discuss the implications of our assumption that the H-types do not multisim. This assumption can be justified by the H-types having a significant hassle cost h of using two sims and/or high transportation costs t. If h is high and both types of customers have the same hassle cost, also the L-types do not multisim and we are back in the world in which all users have just one subscription from one network. If h = 0, and t takes an intermediate value, some but not all of the H-types multisim. The intrinsic utility of being connected, v₀, is high enough that every H-types wants to be connected to at least one network. However, it is more preferable for an H-type in the center of the Hotelling line to sign up to a second network, compared to an H-type close to the extremes. For instance, an H-type located at x = 0 would incur additional travel costs of t and an H-type located at x = 0.5 would just incur 0.5t. Consequently, depending on t, more or less H-types close to the center would multi-sim, whereas the remaining would use only one network. This is an intriguing case to be analyzed in future research. When handt are low, one may intuitively think all customers multisim. However this is not correct. Given that all other customers multisim, an H-type can reach all others on-net (and off-net) and hence has an incentive to use only one network to save transportation cost.^[13] As a consequence, some H-types would always single-sim, presumably those close to the extremes of the Hotelling line.

Would it still make sense for the networks to use the off-net prices in the linear tariffs as a segmentation device when some of the H-types use two tariffs? This depends on how many H-types multisim, given p̄ij is high. If few, we are back in the world of our model. If many, then these customers could arbitrage away off-net/on-net price differentials. Moreover, there would be an upper bound on the equilibrium subscription fee in the two-part tariff as otherwise more H-types would start multi-simming on the linear tariffs. Presumably, the networks would abandon our pricing strategy in that case. Hence, a prediction of our model would then be that price discriminating contracts in emerging markets would become less prevalent as both the hassle of having and using more than one tariff decreases. What happens to networks’ profits as first a few and then more and more H-types start multi-simming? As long as the networks use our pricing strategy, we conjecture that networks’ profits would decrease in the beginning. In our model, the networks have a monopoly on the calls from the L-types to their own H-types, increasing the on-net prices in the linear tariffs. When the L-types can reach more and more H-types on-net, this effect diminishes.

Shubik–Levitan call utility

The point of this subsection is to demonstrate a quadratic Shubik–Levitan type utility function that satisfies (1) and (2). Recall that a multi-simmer makes two types of calls: calls to single-simmers and calls to other multi-simmers. Suppose that a multi-simmer’s utility of a call to a singlesimmer at network i is given by bq − q²/2, where b is a positive constant so that the indirect utility amounts to v(p̄1)=(b−p̄1)2/2 and the call demand is q(p̄1)=b−p̄1. Moreover, suppose that for calls to other multi-simmers the L-types have a Shubik–Levitan type utility function, or more precisely u(q1,q2)=b(q1+q2)−(z(q1+q2)2+2(1−z)(q12+q22))/2. Here, q₁ and q₂ are the calls made with SIM 1 and SIM 2, respectively, and z is a constant satisfying 0 ≤ z < 1. The parameter z reflects to which degree an L-type considers the two SIMs as substitutes: calling with SIM 1 and SIM 2 are independent when z = 0, and perfect substitutes when z → 1. Indirect utility is given by Maxq1,q2{u(q1,q2)−p̄1q1−p̄2q2}, which after some manipulation can be written as

Hence, the demand for calls with the two SIMs is

Inserting symmetric prices in the above functions, we see directly that (1) and (2) are satisfied for all z ∈ [0, 1).

Proof of Proposition 2

So far we have considered extremes, but that does not mean our equilibrium does not exist otherwise. If we insert the Shubik–Levitan demand functions specified above in (21) we can give some indications on the parameter space where a pure strategy equilibrium (pse) exists.^[17] For simplicity, we have done all simulations for a = c and f = 0. Note that a > c will increase the parameter space where a pse exists since a network’s termination rate is maximized for equal market shares. The extremes are easily verified: if α = 1, a pse exists for all values of z ∈ [0, 1⟩, and when α < 1, a pse does not exist when z → 1. When we look at intermediate case other parameters come in to play. It can be shown that when (b − 2c)²/2 < t < 9, a pse exists for all λ > 0, α ∈ [1/2, 1⟩, and all z ∈ [0, 0.94⟩. Thus, in general, substitution (z) must be quite high for the pse to break down. Moreover, (b − 2c)²/2 < t < 9 is only a sufficient condition for a pse to exist in this {λ, α, z} space: in general it is not necessary when we evaluate (21) for specific values of λ, α,and z. Whether a pse exists for even higher values of z, i.e for z ∈ [0.94, z^UP⟩ where 0.94 < z^UP < 1 depends on α and λ. In general we can assert the following: given the previous sufficient condition, a pse will exist for z^UP arbitrarely close to 1, (i) for all λ > 0 and all α ∈ [α^LOW, 1⟩, where 1/2 < α^LOW < 1, if α^LOW is sufficiently close 1, or (ii) for all λ > λ^MIN and all α ∈ [1/2, 1⟩ if λ^MIN is sufficently large. For example: if z^UP = 0.98 and α^LOW = 0.8 then a pse exists if λ > 1.25, i.e. λ^MIN = 1.25. The intuition for the minimum λ requirement is that it secures that the network looses revenues from L-types calling each other when it deviates to p̄onM.

Proof of Proposition 3

Proof of ∂p̄on*∂z<0, (17)