Controlled predatory pricing in a multiperiod Stackelberg game: an MPEC approach |
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Authors: | Joe Naoum-Sawaya Samir Elhedhli |
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Institution: | (1) Department of Finance and Banking, Kun Shan University, Tainan Hsien, 71003, Taiwan, Republic of China;(2) Department of Applied Economics, National University of Kaohsiung, No.700, Kaohsiung University Road, Nan-Tzu District 811, Kaohsiung, Taiwan, Republic of China;; |
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Abstract: | We analyze a multiperiod oligopolistic market where each period is a Stackelberg game between a leader firm and multiple follower
firms. The leader chooses his production level first, taking into account the reaction of the followers. Then, the follower
firms decide their production levels after observing the leader’s decision. The difference between the proposed model and
other models discussed in literature is that the leader firm has the power to force the follower firms out of business by
preventing them from achieving a target sales level in a given time period. The leader firm has an incentive to lower the
market prices possibly lower than the Stackelberg equilibrium in order to push the followers to sell less and eventually go
out of business. Intentionally lowering the market prices to force competitors to fail is known as predatory pricing, and
is illegal under antitrust laws since it negatively affects consumer welfare. In this work, we show that there exists a predatory
pricing strategy where the market price is above the average cost and consumer welfare is preserved. We develop a mixed integer
nonlinear problem (MINLP) that models the multiperiod Stackelberg game. The MINLP problem is transformed to a mixed integer
linear problem (MILP) by using binary variables and piecewise linearization. A cutting plane algorithm is used to solve the
resulting MILP. The results show that firms can engage in predatory pricing even if the average market price is forced to
remain higher than the average cost. Furthermore, we show that in order to protect the consumers, antitrust laws can control
predatory pricing by setting rules on consumer welfare. |
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