This chapter provides a general survey of three strands of literature in oligoply theory. The first deals with the existence of Cournot equilibrium in the general asymmetric case, via the property of strategic substitutes. The second is concerned with the effects of exogenous entry by identical firms on market performance for a Cournot industry. The third strand deals with Bertrand competition with differentiated products as a game of strategic complements. These strands of literature share one important unifying common feature: they were achieved via the application of lattice-theoretic methods. The presentation style of this survey is precise but at the same time somewhat informal in that concepts and ideas are given precedence over formal proofs. In addition, illustrative examples are included whenever possible.
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