Non-collusive oligopoly: game theor

Non-collusive oligopoly: game theory
The simplest case is where there are just two firms with identical costs, products and demand. They are both considering which of two alternative prices to charge. Table 7.1 shows typical profits they could each make.
Let us assume that at present both firms (X and Y) are charging a price of $2 and that they are each making a profit of $10 million, giving a total industry profit of $20 million. This is shown in the top left-hand box (A).
Now assume they are both (independently) considering reducing their price to $1.80. In making this decision they will need to take into account what their rival might do, and how this will affect them. Let us consider X’s position. In out simple example there are just two things that its rival, firm Y, might do. Either Y could cut its price to $1.80 or it could leave its price at $2. What should X do?
One alternative is to go for the cautious approach and think of the worst thing that is rival could do. If X kept its price at $2, the worst thing for X would be if its rival Y cut its price. This is shown by box C: X’s profit falls to $5 million. If, however, X cut its price to $1.80, the worst outcome would again be for Y to cut its price, but this time X’s profit only falls to $8 million. In this case, then, if X is cautious, it will cut its price to $1.80. Note that Y will argue along similar lines, and if it is cautious, it too will cut its price to $1.80. This policy of adopting the safer strategy is known as maximin. Following a maximin strategy, the firm will opt for the alternative that will maximise its minimum possible profit.
An alternative strategy is to go for the optimistic approach and assume that your rivals react in the way most favourable to you. Here the firm goes for the strategy that yields the highest possible profit. In X’s case this again means cutting price, only this time on the optimistic assumption that frim Y will leave its price unchanged. If firm X is correct in its assumption, it will move to box B and achieve the maximum possible profit of $12 million. This strategy of going for the maximum possible profit is known as maximax. Note that, again, the same argument applies to Y. Its maximax strategy will be to cut price and hopefully end up in box C.
Given that in this ‘game’ both approaches, maximin and maximax, lead to the same strategy (namely, cutting price), this is known as a dominant strategy game. The result is that the firms will end up, in Box D, earning a lower profit ($8 million each) than if they had charged the higher price ($10 million each in Box A).
The equilibrium outcome of a game where there is no collusion between the players is known as a Nash equilibrium, after John Nash, a US mathematician who introduced the concept in 1951. Thus collusion, rather than a price war, would have benefited both. Yet, even if they did collude, both would be tempted to cheat and cut prices. This is known as the prisoners’ dilemma.

Hasil (Bahasa Indonesia) 1:

Bebas-kolusi Oligopoli: teori permainanHal termudah adalah di mana ada hanya dua perusahaan dengan biaya yang identik, produk dan permintaan. Mereka berdua mempertimbangkan mana dari dua alternatif harga untuk mengisi. 7.1 tabel menunjukkan keuntungan khas mereka bisa masing-masing. Mari kita asumsikan bahwa saat ini kedua perusahaan (X dan Y) pengisian harga $2 dan bahwa mereka adalah masing-masing menghasilkan keuntungan sebesar $10 juta, memberikan total industri keuntungan sebesar $20 juta. Ini ditampilkan dalam kotak kiri atas (A). Sekarang berasumsi mereka keduanya (mandiri) mempertimbangkan untuk mengurangi harga mereka untuk $1.80. Dalam membuat keputusan ini mereka akan perlu memperhitungkan saingan apa yang mereka bisa lakukan, dan bagaimana ini akan mempengaruhi mereka. Mari kita mempertimbangkan posisi x. Di luar contoh sederhana ada hanya dua hal yang saingan, perusahaan Y, mungkin dilakukan. Baik Y bisa memotong harga untuk $1.80 atau bisa meninggalkan harga di $2. Apa yang harus lakukan X? Salah satu alternatif adalah untuk pergi untuk pendekatan berhati-hati dan berpikir yang terburuk yang saingan bisa lakukan. Jika X terus harga di $2, yang terburuk untuk X akan jika saingan Y memotong harga. Hal ini ditunjukkan oleh kotak x C: keuntungan jatuh untuk $5 juta. Jika, namun, X memotong harga $1.80, hasil terburuk lagi akan untuk Y untuk memotong harga, tapi kali ini x laba falls hanya menjadi $8 juta. Dalam kasus ini, kemudian, jika X berhati-hati, itu akan memotong harga untuk $1.80. Perhatikan bahwa Y akan berdebat sepanjang baris yang sama, dan jika itu berhati-hati, juga akan memotong harga untuk $1.80. Kebijakan ini mengadopsi strategi aman dikenal sebagai maximin. Mengikuti strategi maximin, perusahaan akan memilih alternatif yang akan memaksimalkan laba mungkin minimum. Strategi alternatif adalah untuk pergi untuk pendekatan optimis dan menganggap bahwa pesaing Anda bereaksi dengan cara yang paling menguntungkan bagi Anda. Di sini perusahaan berlaku untuk strategi yang menghasilkan keuntungan tertinggi mungkin. Di x kasus ini lagi berarti memotong harga, hanya kali ini asumsi optimis bahwa frim Y akan meninggalkan harganya tidak berubah. Jika perusahaan X benar dalam asumsi yang, itu akan pindah ke kotak B dan mencapai keuntungan mungkin maksimum sebesar $12 juta. Strategi ini akan untuk keuntungan maksimum mungkin dikenal sebagai maximax. Perhatikan bahwa, sekali lagi, argumen yang sama berlaku untuk Y. Strategi maximax akan memotong harga dan mudah-mudahan berakhir di box C. Given that in this ‘game’ both approaches, maximin and maximax, lead to the same strategy (namely, cutting price), this is known as a dominant strategy game. The result is that the firms will end up, in Box D, earning a lower profit ($8 million each) than if they had charged the higher price ($10 million each in Box A). The equilibrium outcome of a game where there is no collusion between the players is known as a Nash equilibrium, after John Nash, a US mathematician who introduced the concept in 1951. Thus collusion, rather than a price war, would have benefited both. Yet, even if they did collude, both would be tempted to cheat and cut prices. This is known as the prisoners’ dilemma.