Okada Isamu, Yamamoto Hitoshi, Toriumi Fujio, Sasaki Tatsuya
Department of Business Administration, Soka University, Tokyo, Japan; Department of Information Systems and Operations, Vienna University of Economics and Business, Vienna, Austria.
Department of Business Administration, Rissho University, Tokyo, Japan.
PLoS Comput Biol. 2015 May 14;11(5):e1004232. doi: 10.1371/journal.pcbi.1004232. eCollection 2015 May.
Although positive incentives for cooperators and/or negative incentives for free-riders in social dilemmas play an important role in maintaining cooperation, there is still the outstanding issue of who should pay the cost of incentives. The second-order free-rider problem, in which players who do not provide the incentives dominate in a game, is a well-known academic challenge. In order to meet this challenge, we devise and analyze a meta-incentive game that integrates positive incentives (rewards) and negative incentives (punishments) with second-order incentives, which are incentives for other players' incentives. The critical assumption of our model is that players who tend to provide incentives to other players for their cooperative or non-cooperative behavior also tend to provide incentives to their incentive behaviors. In this paper, we solve the replicator dynamics for a simple version of the game and analytically categorize the game types into four groups. We find that the second-order free-rider problem is completely resolved without any third-order or higher (meta) incentive under the assumption. To do so, a second-order costly incentive, which is given individually (peer-to-peer) after playing donation games, is needed. The paper concludes that (1) second-order incentives for first-order reward are necessary for cooperative regimes, (2) a system without first-order rewards cannot maintain a cooperative regime, (3) a system with first-order rewards and no incentives for rewards is the worst because it never reaches cooperation, and (4) a system with rewards for incentives is more likely to be a cooperative regime than a system with punishments for incentives when the cost-effect ratio of incentives is sufficiently large. This solution is general and strong in the sense that the game does not need any centralized institution or proactive system for incentives.
尽管在社会困境中对合作者的积极激励和/或对搭便车者的消极激励在维持合作方面发挥着重要作用，但谁应该承担激励成本这一突出问题仍然存在。二阶搭便车问题，即在游戏中不提供激励的参与者占主导地位，是一个著名的学术挑战。为了应对这一挑战，我们设计并分析了一种元激励博弈，该博弈将积极激励（奖励）和消极激励（惩罚）与二阶激励相结合，二阶激励是对其他参与者激励行为的激励。我们模型的关键假设是，那些倾向于因其他参与者的合作或非合作行为而向其提供激励的参与者，也倾向于对自己的激励行为提供激励。在本文中，我们求解了该博弈简单版本的复制动态，并通过分析将博弈类型分为四类。我们发现，在该假设下，无需任何三阶或更高阶（元）激励就能完全解决二阶搭便车问题。为此，需要在进行捐赠博弈后单独（点对点）给予二阶成本激励。本文得出以下结论：（1）对于合作机制而言，对一阶奖励的二阶激励是必要的；（2）没有一阶奖励的系统无法维持合作机制；（3）有一阶奖励但没有奖励激励的系统是最差的，因为它永远无法达成合作；（4）当激励的成本效益比足够大时，有奖励激励的系统比有惩罚激励的系统更有可能成为合作机制。这种解决方案具有普遍性和强大性，因为该博弈不需要任何集中机构或主动的激励系统。
