Downside Risk-Aware Equilibria for Strategic Decision-Making
Oliver Slumbers, Benjamin Patrick Evans, Sumitra Ganesh, Leo Ardon
传统上,博弈论对风险的看法相对有限,基于玩家的预期奖励如何受到其他玩家行为的不确定性的影响。 最近,一种新的游戏理论方法提供了更全面的风险观,也考虑了奖励变量。 然而,这些基于方差的方法衡量了上行和下行的奖励方差。 在许多领域,如金融,下行风险只至关重要,因为这意味着与决策相关的潜在损失。 相比之下,大上行“风险”(例如利润)不是问题。 为了解决这种限制性的风险观,我们提出了一种新的解决方案概念,基于较低的部分时刻的下行风险意识均衡(DRAE)。 DRAE限制了下行风险,同时对上行风险没有限制,此外,还模拟了高阶风险偏好。 我们展示了DRAE在几款游戏中的适用性,成功地找到了平衡,平衡了下行风险与预期回报,并证明了这种平衡的存在和最佳性。
Game theory has traditionally had a relatively limited view of risk based on how a player's expected reward is impacted by the uncertainty of the actions of other players. Recently, a new game-theoretic approach provides a more holistic view of risk also considering the reward-variance. However, these variance-based approaches measure variance of the reward on both the upside and downside. In many domains, such as finance, downside risk only is of key importance, as this represents the potential...