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支付等价性和直接互惠的完整战略空间
Philip LaPorte1,2, Christian Hilbe3,4, Nikoleta E Glynatsi3,5
1Department of Mathematics, University of California, Berkeley, CA 94720.
概括
完整的战略空间确保了精确的进化游戏理论模拟. 确保空间是最好的回应和完整的回报,可以防止策略的不稳定性,并有助于确定在重复和随机游戏中最好的回应.
科学领域:
- 游戏理论 游戏理论
- 进化的动力学.
- 计算经济学计算经济学
背景情况:
- 重复和随机游戏是直接互惠的模型,玩家对过去的行为做出反应.
- 当前的战略空间限制在进化动态限制了结果的解释.
- 当允许更复杂的策略时,受限制的战略空间可能会导致不稳定的策略.
研究的目的:
- 在战略空间中引入和分析最佳答案完整性和回报完整性的概念.
- 为了证明最佳答案完整性的条件也足以在有限记忆策略中获得回报的完整性.
- 为简单游戏构建完整的战略空间提供一种方法.
主要方法:
- 定义最佳答案完整性:每个策略在空间内都有最佳答案.
- 定义回报完整性:在空间内,策略可以被同等的策略取代,而不会改变回报.
- 在有界的内存策略空间中证明现有条件对于回报完整性的充分性.
主要成果:
- 对于最好的答案完整性的条件也足以满足有限内存策略的回报完整性.
- 介绍了一种用于构建许多简单游戏的完整策略空间的方法.
- 完整的战略空间解决了进化模拟中的战略不稳定性和解释问题.
结论:
- 完整的战略空间对于可靠的进化模拟和准确的最佳反应确定至关重要.
- 这些发现将完整性概念的适用性扩展到有界记忆策略.
- 这项工作为游戏理论研究中设计强大的战略空间提供了理论基础.
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