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ABSTRACT
The objective of this study was to compare two strategies - the Bertrand game and the Stackelberg game - which can be applied to prices, set by four terminals in two ports of Pakistan. Numerical results were obtained by solving the multinomial logit model. The results show that in a Bertrand game, one container terminal (KICT), despite charging higher prices, captured a higher market share compared to its competitors. The results reflect the real data on the situation in the two ports in question. Because there are differences in market shares and costs among the container terminals, this study also analyzed a hypothetical leader-follower strategy using four sub cases. These results reveal that the leader can charge a monopolist price. However, it can capture a very high market share only when it has some natural advantages over its competitors. Moreover, there is a possibility that the leader will be wrong in assuming that the others will adopt its price. On this basis, it may be concluded that the Bertrand game in prices is probably the only one that consistently assumes rational and fully informed players.
Keywords: Bertrand game, Stackelberg game, container terminals, game theory, competition
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1. INTRODUCTION
In an oligopoly market with homogeneous products, the Cournot model is most often chosen to describe market interaction. The Cournot model derived Nash equilibrium when firms compete in output. In a competitive situation with few players and an inhomogeneous product, however, the outcome in terms of market shares and prices can often be treated as the result of a game in which each player maximizes profit, but with due consideration of the expected reactions of its competitors. When the competitor's actions are confined to setting the prices of their own product (service), the outcome can be modeled as Bertrand equilibrium (Pindyck and Rubinfeld, 2001). Each of these static, simultaneous-decision models of oligopoly has a sequential-decision counterpart. These sequential-decision models are the result of von Stackelberg's strategic analysis of quantity setting. Stackelberg models rely on leadership by one of the rivals. Von Stackelberg originally extended the Cournot model to include leadership behavior (von Stackelberg, 1952). This means that the Stackelberg leader's output choice influences the output choices of its rivals, and the...