偏好在經濟分析中是相當基本而重要的，傳統上一般都假設偏好是一種先天給定的特質。而演化賽局理論從自然選擇的觀點，能夠對動物先天特質提出強而有力的解釋。基於這個想法，本文根據「鷹鴿賽局」此一基本模型做延伸，建立一個兩期生命模型，在個體存活兩期且爭鬥可能致死的情境下，探討競爭態度、耐性這兩項特質於群體中的演化動態及演化穩定均衡。分析顯示競爭態度的強弱程度受環境因子影響，而在給定共同耐性的情況下，均衡會是混合策略，但如果戰勝者能藉由戰績來降低未來受挑戰的機率，且此種宣示效果大到一定程度的話，則可能讓群體朝向全為鷹的均衡演化。然後，在考慮耐性非外生給定的情況，模型可決定均衡的耐性水準，根據數值模擬顯示，達成演化穩定下，鴿策略會搭配較高的耐性。

Preference is an important element in economic analysis, but usually regarded an inborn and exogenous characteristic. By the concept of natural selection, evolutionary game theory can explain lots of animal characteristics, including humans. With this idea, this paper extends the classical Hawk-Dove game to a two-period-life model, in which fights can cause deaths. We derive the population dynamics and the evolutiona-rily stable strategy. The competitive attitude and patience are determined by resource value and cost. And under a given common patience level, the evolutionarily stable strategy is a mixed strategy. But if the “announcement effect,” an extra benefit from showing the winning record, is large enough, all-hawk may be the equilibrium. In ad-dition, under variable patient levels, the model can determine the equilibrium patience, and numerical simulation shows that dove-strategy accompanies a higher patient level than hawk.

1 Introduction........................................................................1
2 Literature Review .............................................................2
2.1 Preferences and Patience..............................................2
2.2 Evolutionary Game Theory .............................................4
2.3 The Standard Hawk-Dove Game and ESS.................5
3 Model..................................................................................7
3.1 An Extended Two-Period-Life Model............................7
3.2 Population Dynamics....................................................10
3.3 ESS Analysis...................................................................12
3.3.1 Best Response.......................................................12
3.3.2 Stability Criterion.....................................................13
3.4 Numerical Results.........................................................17
4 Patience and ESS...........................................................20
4.1 Model Modification..........................................................20
4.2 ESS Analysis...................................................................21
4.2.1 Best Response.......................................................21
4.2.2 Stability Criterion.....................................................24
4.3 Numerical Results.........................................................26
5 Conclusion......................................................................29
Appendix..................................................................................30
References..............................................................................31

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