肯尼將軍嘅任務係要盡可能噉破壞日軍嘅支援計劃,等盟軍可以喺巴布亞新畿內亞打緊嘅戰鬥當中佔上風。透過軍事情報,肯尼將軍知道敵軍嘅運輸船隊有呢兩條路線可以行,而根據佢啲參謀人員嘅預測,北面路線將會有惡劣天氣,令到佢指揮嘅空軍喺嗰度得兩日時間可以進行轟炸,而南面路線嘅好天氣令佢嘅空軍喺嗰度可以一連三日都進行轟炸;對於日軍嚟講,無論揀邊條路,佢哋嘅運輸船隊都需要三日時間先去到目的地。喺呢場戰事裏面,雙方指揮官都有兩個選項,所以呢場戰事可以睇做一場 2 x 2 嘅(零和)博弈,有四個可能結果(報償係美軍總共有幾多日可以進行轟炸):
博弈論要到 1930 年代先正式成為一個應用數學子領域。1928 年,匈牙利裔美國數學家馮紐曼[歐 39]出版咗一份論文《On the Theory of Games of Strategy》(粵文:論策略博弈嘅理論)[91]。喺呢篇論文入面,馮紐曼佢對博弈嘅概念做咗一啲基本嘅分析,證明咗多條相關嘅定理[92]。及後佢喺 1944 年出咗本書叫《Theory of Games and Economic Behavior》(粵文:博弈同經濟行為嘅理論),呢本書詳細噉討論咗好似係兩人零和博弈等嘅概念。而喺跟住落嚟嘅時間,好似係合作博弈等嘅概念都出咗嚟,令到博弈論基本成形[93]。
喺 1938 年,法國數學家伊苖波里出咗本書叫《Applications aux Jeux de Hasard》(粵文:隨機遊戲嘅應用),喺呢本書入面,波里佢分析咗兩個人玩嘅零和對稱博弈嘅矩陣,並且證明咗一啲相關嘅定理,而且佢嘅分析仲有實用價值。波里仲進一步猜想,喺某啲情況下,有限嘅兩人零和博弈可能有陣時會冇混合策略均衡點(不過馮紐曼後來證明咗佢係錯嘅)[94]。
喺 1950 年,學界開始咗對監犯困境嘅數學討論,而且仲有數學家用實驗方法展視監犯困境嘅博弈現象,同埋有人嘗試將呢個分析應用落去核戰略上-即係開始有人將博弈論用落去政治學嗰度[95]。大概喺同一時間,美國數學家莊·拿殊提出咗拿殊均衡點嘅諗頭,並且將呢個概念應用嚟去分析多個當時已知嘅博弈。拿殊佢跟手仲證明咗,喺混合策略嘅情況下,是但俾一個有 n 個博弈者、非零和、非合作嘅有限博弈,場博弈實會有個拿殊均衡點。由嗰陣時開始,博弈論就俾經濟學家同生物學家等多個領域嘅學者採用嚟解釋佢哋所研究嘅現象,成為咗一個舉足輕重嘅數學理論[7]。
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