The Effects of Exogenous and Endogenous Uncertainty in Static Games 外因與內因的不確定對靜態賽局的影響 Sea-Shon Chen 陳世雄
賽局理論基本上在處理均衡的問題 價格戰、數量戰 外因與內因的不確定使得均衡的達成變化多端
For all i, ui(si*, s–1*) ≥ ui(si’, s–1*) for all si 原理 1 Game G = {strategies S1, …, Sn; utilities u1, …, un} 效用 Strategy profile s* 輪廓 For all i, ui(si*, s–1*) ≥ ui(si’, s–1*) for all si
原理 2 Player 1’s or 2’s expected payoff 收益
設局 Table I. The payoff matrix of the mineral water drilling game Nature: Gushing (probability p) 設局 CLA Don’t drill Narrow Wide TAI pT1 pC1 pC2 pC3 pT2 pT3 Nature: Dry well (probability q) CLA Don’t drill Narrow Wide TAI qT1 qC1 qC2 qC3 qT2 qT3 Table II. The Expected payoff matrix of the mineral water drilling game CLA Don’t drill Narrow Wide TAI Tu1 Cu1 Cu2 Cu3 Tu2 Tu3 Note: Tui = pTi× p - qTi × q and Cuj = pCj × p - qCj × q
結果1 Symmetric Figure 1 If gushing probability p > 0.5, the strategy {Narrow, Narrow} hold pure equilibrium and the payoffs increase by the gushing probability. 價格戰、數量戰
結果2 Figure 2 If gushing probabilities are in the range 0.273 ≤ p ≤ 0.50, mixed equilibriums are hold. Nash equilibrium is {(Don’t drill: 0.3, Narrow: 0.7), (Don’t drill: 0.3, Narrow: 0.7)} if gushing probability p = 0.40 Nash equilibrium is {(Don’t drill: 0.5, Narrow: 0.5), (Don’t drill: 0.5, Narrow: 0.5)} if gushing probability p = 0.354
結果2-1 Profits in mixed strategy
結果3 Figure 3 Probability of outcome when mixed strategy equilibrium is adopted
結果4 Asymmetric Figure 4 Gushing probability and payoffs for two firms.
Conclusion 成功是X % 的管理和 (1－X %) 的機運 Nature has two faces: exogenous and endogenous uncertainty. Both of them will influence the process of game and its results. 成功是X % 的管理和 (1－X %) 的機運