The Effects of Exogenous and Endogenous Uncertainty in Static Games

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1 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

2 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

3 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

4 原理 2 Player 1’s or 2’s expected payoff 收益

5 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

6 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

7 結果2 Figure 2 If gushing probabilities are in the range ≤ 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

8 結果2-1 Profits in mixed strategy

9 結果3 Figure 3 Probability of outcome when mixed strategy equilibrium is adopted

10 結果4 Asymmetric Figure 4 Gushing probability and payoffs for two firms.

11 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