Capacity sharing within a shipping alliance: firm optimization and welfare analysis

ABSTRACT

The global shipping industry still frequently faces the problems of low profitability and excessive capacity despite the claimed benefits of capacity sharing between alliance members. This paper investigates capacity sharing within shipping alliance members and its impacts on social welfare under stochastic demand. The dynamic game models constructed in this study examine four scenarios based on whether the alliance members share their surplus capacities and whether their pricing is flexible (their prices are determined before or after the demand realization). The results suggest that flexible pricing always harms the social welfare while capacity sharing improves the social welfare. Without capacity sharing, the government’s subsidy or tax is needed when the carriers’ service substitute degree is low or high, respectively. If the carriers agree with capacity sharing, the tax is needed under flexible pricing while neither subsidy nor tax is needed under the inflexible pricing. This paper provides explanations on the low profits of the shipping lines with their pricing and alliance strategies. Moreover, the policy implications identified in this study can provide support for governments to make their regulation on carriers.

KEYWORDS:

• Capacity sharing
• shipping alliances
• stochastic demand
• pricing decision
• regulation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. It is worthy pointing out that the carriers within a transportation alliance still compete with each other. E.g., Chun, Kleywegt, and Shapiro (2017) state that the shipping alliance members separately manage their operations and thereby compete against each other even after their capacity exchange.

2. The shadow cost of subsidy or tax is the cost to collect the subsidy or tax (public funds) by the government. Public fund collection adds costs to the whole society (see Laffont and Tirole 1993 for further discussions on this issue).

3. Due to the difficult to find or estimate the parameters, e.g., the capacity exchange prices between the alliance members, and lack of enough samples to estimate a demand function properly, we cannot use the real data to estimate the parameter values. However, after lots of simulations, we find that $\mathit{\beta }$ has crucial impacts on the modeling results. Therefore, we traverse it in our numerical experiments to illustrate the possible results.

4. In our frame, two carriers engage in the price competition. Meanwhile, they have the capacity constraints, i.e., their outputs cannot exceed their capacity, $Q_i\le K_i$. According to the classic industrial organization theory (Tirole 1988), the price competition with the capacity constraints has the same outcomes as the Cournot competition. An alternative explanation is that the following two games are equivalent: (a) a two stage game in which firms decide their own capacities in the first stage, and then in the second stage compete in price to clear the market; and (b) a simultaneous capacity competition game (i.e. Cournot output/capacity competition). For mathematical proof and discussions, see Tirole (1988).

5. We do not obtain their decisions on the use of flexible/inflexible pricing and sharing/not sharing their surplus capacities. To further examine whether they should use these strategies, we need to analyze the asymmetry between the two carriers. For example, if we wish to analyze whether the carriers should choose capacity sharing or not sharing, we need to further calculate the carriers’ profits with one carrier undertaking the sharing strategy while the other undertaking not-sharing strategy. Due to the model complexity, it is very difficult to obtain the two carriers’ individual pricing and capacity decisions under such asymmetry. In solving of our model, we make full use of the symmetry of the two carriers and their optimal pricing and capacities are the same in the equilibrium. Mathematical tractability cannot be kept without such a simplification.

6. In the original setting of prisoners’ dilemma, both prisoners choose to confess although they could be better off if both remain silent.

7. In the APWS scenario, the capacity sharing can always be achieved if necessary because the carrier’s capacity investment is a sunk cost and any positive exogenous $\mathit{\varphi }$ can rescue the carrier’s surplus capacity. However, in the PPWS scenario, whether the capacity sharing can be achieved depends on the comparison of $\mathit{\varphi }$ and the ex post prices $p_i$ and $p_j$, because the carriers have another option to deal with their surplus capacities by lowering their prices (after the demand realization and before the capacity sharing) in this scenario. From Figure A-2 we know that the non-sharing areas shrink as $\mathit{\varphi }$ increases, because the capacity transaction costs increase.

Additional information

Funding

The authors would like to thank the anonymous referees for their very helpful comments and suggestions. This work was supported in part by the National Key Research and Development Program of China (Grants#: 2020YFE0201200) and the National Natural Science Foundation of China (Grants#: 72031005, 72072113). Hong Kong Polytechnic University DGRF P0035755 (UAKR).