Can restrictions on redemption timing boost profitability of loyalty programs in competitive environments?

Abstract

This research investigates whether it is beneficial for competing firms offering loyalty programs (LPs) to restrict the reward redemption time. We develop a game-theoretic model where competing firms decide an LP’s redemption policy and pricing and identify firms’ restriction levels. The results show that, at equilibrium, firms implement a restrictive policy when customers value rewards more than time, while an unrestricted policy is implemented when customers value time. Each firm should increase prices in response to its competitor’s restrictive policy.

Appendix

See Tables 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24 and 25.

Table 13 Firm $i$’s optimal profits when both firms apply the unrestricted policy $({I}_{i}^{UR,UR}$)

Table 14 Firm $i$’s optimal profits when both firms apply the moderately restricted policy $({I}_{i}^{M,M}$)

Table 15 Firm $i$’s optimal profits when both firms apply the highly restricted policy $({I}_{i}^{H, H}$)

Table 16 Optimal profits of the firm that applies the moderately restricted policy in the M–UR subgame $({I}_{a}^{M, UR}$)

Table 17 Optimal profits of the firm that applies the unrestricted policy in the M–UR subgame $({I}_{b}^{M, UR}$)

Table 18 Optimal profits of the firm that applies the moderately restricted policy in the M–H subgame $({I}_{a}^{M, H}$)

Table 19 Optimal profits of the firm that applies the highly restricted policy in the M–H subgame $({I}_{b}^{M, H}$)

Table 20 Scaled payoff matrices for the game unrestricted vs. highly restricted policies

Table 21 Scaled payoff matrices of the main game*

Table 22 Firm $i$’s optimal prices in symmetric scenarios of UR–UR, M–M, and H–H

Table 23 The optimal prices of the firm that applies the M policy in scenarios UR–M and H–M

Table 24 The optimal prices of the firm that applies the H policy in scenario H–M

Table 25 The optimal prices of the firm that applies the UR policy in scenario UR–M